Rf And Microwave Circuit Design Pdf: Fill & Download for Free

I have a pretty good idea on the 6th gen requirements and that is by watching the progress of other countries. Answer might or might not be favorable by the end of this post.6th Gen Requirements: Photonic Radars?Information that I have read from Mig-41 and BAE Tempest says they track missiles and aircrafts from all directions. antennas for NGAD will be like smartskin so from this point I am assuming that a 360 degree radar view is a requirement. But the kind of radar it will be is on my list. 4th gen: GaAS AESA, 5th gen: GaN AESA, 6th gen: photonic radar, 7th gen quantum radar.U.S. Company Raytheon 2019 PDF"With all the advances occurring inemerging PIC technologies, Raytheonresearchers and engineers are activelypursuing both internal research andcustomer-funded development programsto investigate applications of PICtechnology in next generation products,as well as to develop lower cost, higheryield PIC packaging and manufacturingprocesses"DARPAIndustry asked to develop microwave photonics components for RF and microwave applications like radarDARPA wants lithium-niobate field-configurable modulator arrays (FCMAs) for RF links, RF signal processing, radar, and RF spectrum management.Although microwave photonics represents an important technology for military applications, the military microwave photonic systems deployed to date repurpose commercial components for military functions.The most recent developments in industrial telecommunications have been in specialized application-specific photonic integrated circuits (PICs). Today's military applications cannot use these devices, however, because application-specific PICs cannot be repurposed.The FCMA must be able to operate from 1 MHz to 18 GHz, and use the nonlinear response of a Mach-Zehnder modulator to suppress a continuous-wave interference signal by 60 decibels to suppress an interference signal with 10 MHz instantaneous bandwidth by 40 decibels -- both while reducing the largest intermodulation distortion by 30 decibels.The signals-intelligence configuration will improve the intrinsic third-order-limited spurious-free dynamic range of a Mach-Zehnder modulator by 10 decibels.The radar-beamforming application will provide 360 degrees of RF phase shift that can be modulated at 100 kHz. The communications configuration, meanwhile, must support 10 gigabits per second of modulation on each of the in-phase and quadrature components of a lightwave.Russian Company RTIAs for semiconductormodulators in microchipperformance, then in 2019 the researchwork on this topic in whichOKB-Planeta OJSC is an industrial partner.Within three to five years is possibleorganization of the development, design and production of photonicintegrated circuits (FIS) both in packageless execution, and in the case.The implementation of these plans will allowJSC "RTI" take a leading positionin development and productionadvanced domestic radio systems based on componentradiophotonic bases.VEGA, RTI and KRET all state having photonic radar prototypes and VEGA seems to have demonstrated the the photonic radar antennas which the source states is as thin as paint but a little thicker. In other words this is the ideal smart skin layout 6th gens are dreamed of having for sensing targets in all directions.6th Gen Requirements: Communication/Computers/Data speeds?I do not know the internet traffic of the city Edinburgh in a second in determining the information the BAE Tempest radar can gather, but I do know that it is in the UK and the UK in 2020 reports that on a busy day traffic can go high as up to 132 terabits per second, while the speed transmission of information for a photonic radar is hundreds of terabits per second according to Alexey Leonkov. DARPA wants communication to receive 10 gigabits per second, RTI in a 2017 article pdf states in 100ghz speeds of 400 gigabits per second can be received. I know that MADL uses high frequency in 20–30ghz for gigabit speeds. DoD’s broader Network Services 2020 plan calls for aircrafts to exchange 100 gigabits per second.I take it that current 4 or 5th gens will use just electronic computers. 6th gen will use optical(photonic) computers and 7th gen will use functional quantum computers. Scientists of the Mendeleev Russian state technical University have grown nonlinear optical crystals in their lab from glass to turn invisible infrared radiation into visible light which is a requirement needed for a functioning optical computer.6th Gen Requirements: Engine/ Variable Cycle/ high supersonic to hypersonic?The F-22 has a high bypass ratio meaning the range is limited but supersonic cruise is possible. Some calculations were made in removing its two external fuel tanks with a range of 2,049 kms but I wouldn't say that is entire accurate. While current engines of Su-35 and Su-57 are low bypass ratio along with F-35 where they maximize range more than speed to not bleed as much fuel. So it is argued that variable cycle engines is a requirement for 6th gen aircrafts which combines the best of both worlds. New ADVENT engine as a variable cycle engine for F-35 proposes 35% increase in range, 25% reduction in fuel consumption 10% thrust increase. Designers for Team Tempest say this variable cycle engine is a requirement for a 6th gen aircraft but also say they are developing reaction engines. The FCAS proposes a SABER engine for their 6th gen which is to reach hypersonic speeds and of course same kind of information was said about the Mig-41. But I have no idea if NGAD proposes variable cycle or a near to right at hypersonic speeds engines. U.S. and Russia are the only countries that have demonstrated airbreathing aircraft engines.It is even argued that the Izdelie 30 or 2nd stage Su-57 engine could be a variable cycle. But that does make sense because 18,000 kg of thrust is offered and the previous AL-41F1 engine is 15,000 kg of thrust. Stated to be 30% lighter than previous engine with better fuel efficiency. So there is a 20% increase in thrust while reports have said range will stay the same or be increased. However if ranges do stay the same as an example that means the quality of a low bypass ratio engine are still there and with speed capabilities for super sonic cruise show the quality of a high bypass ratio like the F-22 means that it has the qualities of an adaptive cycle engine.6th Gen Requirements: Controlling drones?Su-57 gets the Su-70, BAE Tempest gets BAE Taranis, FCAS gets Neuron and F-35 is to get the MQ-25 Stingray since they are considering bringing it back besides refuel purposes. Currently the Su-70 is the only drone with set production date for 2024 and the only drone that has an interceptor role because it extends the radar of the Su-57 and the 2nd half of this year to fire air to air missiles. two more prototypes will be introduced with the 3rd prototype looking like the Maks 2019 airshow design. The Su-70 is able to control 10 lightning drones that have the capabilities to fly and detonate few hundred kilometers away from targets. 6th gen programs strongly emphasize on having networks controlling drones.6th Gen Requirements: Central Nervous system?The ATD-X program was to be lead to the Mitsubishi F-3 6th gen program which has a feature known as the self-healing flight control function and the Su-57 is being given a central nervous system. Russians have used fiber optics to be spread around the body which I assume is the same as Japan control function feature. But this is a good feature to have if there is wear and tear in some of the composites to pin point where issues have occurred in the aircraft to reduce maintenance costs.6th Gen Requirements: Electric Actuators?Japans F-3, U.S. NGAD and Russia 2nd Su-57 variant undergoing testing in 2022–2024 are dumping hydraulics for electric actuators. Such benefits are radar visibility of the machine is reduced, increase its maneuverability and simplify maintenance.6th Gen Requirements: Energy Weapons?Of course this has been said many times but the talk of using lasers and microwave weapons. F-X, Mig-41, FCAS, i3 fighter, Tempest, NGAD talk about using microwave weapons and lasers that physically destroy things. F-35 has presented a 100 kilowatt laser and although the current Su-57 is the only 5th gen with a functional DIRCM that blinds missile, the avionics upgrade for 2nd variant might or might not have a laser that can physically destroy a missile.6th Gen Requirement: Metamaterials for Stealth?I currently know the Japanese like to emphasize that the i3 fighter and F-x will use metamaterials for their stealth. Russia and China say it is a great application for stealth technology from their following quotes.“This new, lab-made “metamaterial,” in essence a very fine mesh with microscopic etchings, could shrink the radar signature of a fighter jet, warship, or missile by a thousand times, claimed the scientists at the Chengdu-based Institute of Optics and Electronics, part of the Chinese Academy of Sciences.”“The new metamaterial is completely transparent to electromagnetic waves due to the excitation of "anapoles" in them. Russian and Italian scientists have developed technology to camouflage military equipment. When detecting an object using a radar, a wave signal is sent to it, and its location is determined by the reflection of the wave.Modern stealth camouflage techniques aim to ensure that the wave reflected from an object is absorbed by the cloaking coating, minimizing the response to the radar. However, the coating alone is not capable of reducing this response to zero due to a combination of factors: surface geometry, high speed of movement, progressive highly sensitive methods of location, ineffectiveness of absorption of stealth coating.”ConclusionI heard not having vertical stabilizers as a design concept for 6th gen. But not enough info if that is the final design or why other 6th gen design concepts have not presented it. Also options of going unmanned and A.I. pilot functions have already been beaten to death on current operational 5th gens(F-35/Su-57) to 6th gen aircraft projects. It is argued that some 6th gens have 5th gen features and that some 5th gens have many 6th gen features.I do not want to be a comedian but the 2nd variant Su-57(not the in production 1st variant Su-57) undergoing testing in 2022–2024 pretty much already has its foot in the door to qualify as a 6th gen aircraft before even introducing the Mig-41 or Rostec starting their own 5th gen programs which might be the LMFS which design wise looks like the X-32 could incorporate 6th gen features.70% certainty 2nd Su-57 variant will have photonic radar. RTI stated in September 2019 that in a few years their prototype photonic radar will be mounted on a multifunctional fighter. mass scale production of PICs might take place between 2022–2024 which is the timeframe that the new Su-57 will tests its new avionics. Could be a possibility that RTI could be talking about Rostecs 5th gen development or the mig-41.80–90% certainty that the 2nd stage engine is variable cycle. But if all 6th gen go with close to hypersonic or hypersonic speeds than variable cycle wont be a 6th gen. But I still have high doubts Europe can create a hypersonic engine for an aircraft before the U.S. or Russia.70% certainty with communication and data speeds, but 0–3% certainty it will have a photonic computer because the discovery by Mendeleev University was not to long ago and that they have yet to present a functional photonic computer.Russia’s lightning drones, Lockheed Martin’s Speed racer drones and FCAS concept image of drones look exactly alike. Since Su-70 has a production date their is 100 % certainty the Su-57 will just be using drones the majority of its time in which even those drones control other drones. This is the most talked about feature with Tempest, NGAD and FCAS.Central nervous system type feature was recommended by Japan and not too long ago implemented by the Su-57 so 100% certainty. Also I am sure news reports might be shown later of other 6th gen programs recommending a type of feature that would show wears and tears in material as a smart feature to quickly resolve issue.NGAD and F-X what a more electric use aircraft. And it is already guaranteed the 2nd variant Su-57 will have it so 100% certainty.50% certainty on lasers to destroy things(they already can blind things), they have demonstrated a 1 megawatt KPVC laser and the Peresvet laser which uses a nuclear fuel pump and being bigger than the KPVC in size determines 1–10 megawatts, while other countries at best are still stuck on presenting new kilowatt range land lasers. the DIRCM is part of the avionics package which 2nd variant Su-57 is being upgraded with new avionics. But this rests on a 50/50 choice happening.0% certainty on 2nd Su-57 using metamaterials because they want to use the metamaterials as elements of qubits of quantum computers and would require re-doing the physical layout of the Su-57 which they emphasize they would not do for the 2nd Su-57. So it is questionable if current 6th gen programs plan on using it while having an operational 6th gen. Что такое анаполь? Новый метаматериал для стелс-покрытийI think the Su-57 2nd variant will be leaning on almost all the 6th gen requirements, if it isnt than its pushed to a 5th gen++. For example Japan’s 6th gen radar feature is using GaN MMIC while the U.S. and Russia are dead set on acquiring PICs which offer better performance. Even though the Su-57 might not have metamaterial present will other 6th gens have them present in the end? How many in the end are going with the variable cycle than the hypersonic approach? How many will actually have functional high power lasers or microwave weapons in the end?Hard to decide what 6th gen technologies are, depending if some take easier or harder routes setting those standards.SourcesTempest drives forward as Leonardo unveils new radar sensing technologyWork is proceeding at pace to meet the ambitious timescale for Tempest, which is expected to go into-service in 2035 New radar receiver/warner technology is four times as accurate as existing sensors in a package 1/10th the size The lab demo was part of conceptual and development activities for the Tempest sensor suite and mission system, which Leonardo is leading Leonardo UK has demonstrated the performance of a new radar receiver/warner technology as part of its on-going development work for Tempest, the next generation combat air project which will see the UK, Italy and Sweden working closely together. In a laboratory demonstration for the UK Ministry of Defence and other Team Tempest partners, the new sensor demonstrated a direction finding performance of four times what is possible with a typical radar warning receiver while being just 1/10th the size of a standard system. Leonardo UK is one of the four founding members of Team Tempest , which was brought together by the UK MOD to develop a next generation combat air system for the UK and partner nations: since the team was contracted to begin development work in 2018, Italy and Sweden have announced their intent to work with the UK on this project. Leonardo’s UK role in the team is to develop Tempest’s sensor package and integrate these sensors into the platform’s mission system. The ambitious timescale for the Tempest project, which is working towards seeing a new aircraft in-service with the RAF in 2035, means that Leonardo in the UK is already hard at work developing some of the advanced technologies which will be needed to face the threats of the future. One such area of development, and the focus of the recent lab demonstration, is in radar warning . This technology is used to sense the radio frequency (RF) signals emitted by potentially hostile radars and then use this information for a variety of uses, including warning an operator that an enemy is trying to ‘lock on’ to their aircraft. Such sensors can also support tasks such as intelligence gathering and combat identification. In future, threat radars are likely to use a range of technologies and software techniques to make it harder to identify their signals, meaning that Tempest’s sensors will need to be sophisticated enough to be able to counter such techniques and flexible enough to be updated in response to new technologies as they emerge on the battlefield. The reduced size and weight of Leonardo’s new receiver technology , as well as reduced power requirements, means that it will be possible to integrate the sensor into a multi-function array. This concept, one of a number of innovative ideas being considered for Tempest, could see a number of multi-purpose sensors spread around the aircraft, simultaneously sensing and tracking enemy aircraft, incoming missiles and other threats from all directions, while being fully integrated with a forward-facing radar.https://www.leonardocompany.com/en/press-release-detail/-/detail/18-12-2019-tempest-drives-forward-as-leonardo-unveils-new-radar-sensing-technology6G stealth fighter planes: The quarterback of the kill web - Military Embedded SystemsWARFARE EVOLUTION BLOG: There are 14 countries working on 6th Generation (6G) fighter planes these days: the U.S. (PCA, F/A-XX, NGAD); the United Kingdom, Sweden, Italy, and maybe India (Tempest); France, Germany, and Spain (FCAS); Japan (F-3); Taiwan (ADF); South Korea and Indonesia (KF-X); Russia (MiG-41); and China (J-XX). Before we get into the details, we need to define what a 6G fighter jet is. The F-35 and F-22 are 5G fighter planes. There are six aircraft generation classification charts out there: Hallion, Aerospaceweb, Air Force Magazine, Winchester, Air Power Development Center, and China’s Air Force. All these templates have been overcome by advances in technology and evolving mission requirements. So, we’ll be breaking new ground in this essay, by adding to the common 6G characteristics from the old charts and building an updated definition. Then, we’ll integrate those new aircraft into the kill web.https://militaryembedded.com/avionics/computers/6g-stealth-fighter-planes-the-quarterback-of-the-kill-webStackPathPlease Enable Cookies www.militaryaerospace.com is using a security service for protection against online attacks. The service requires full cookie support in order to view this website. Please enable cookies on your browser and try again. Please Enable JavaScript www.militaryaerospace.com is using a security service for protection against online attacks. The service requires full JavaScript support in order to view this website. Please enable JavaScript on your browser and try again. www.militaryaerospace.com is using a security service for protection against online attacks. This process is automatic. You will be redirected once the validation is complete.https://www.militaryaerospace.com/rf-analog/article/14178607/rf-and-microwave-photonics-radarhttps://www.raytheon.com/sites/defa...9/05/Raytheon_TechnologyToday_Issue2_2019.pdfhttps://itech.aorti.ru/ No. 1 (20) of 2018Разработанная в рамках проекта ФПИ антенна вошла в Топ-10 изобретений 2020 годаРазработанная в рамках проекта Фонда перспективных исследований антенна малой высоты профиля, способная работать с широкой полосой частот, вошла в Топ-10 лучших изобретений 2020 года по версии Роспатента. На основе изобретения созданы макеты антенн, построена антенная решетка первого в мировой практике действующего демонстрационного макета радиооптической фазированной активной антенной решетки. Технология позволяет создавать антенны и антенные решетки, которые могут быть выполнены в виде активной обшивки различных носителей с толщиной немногим более толщины лакокрасочного покрытия.https://fpi.gov.ru/press/news/razrabotannaya-v-ramkakh-proekta-fpi-antenna-voshla-v-top-10-izobreteniy-2020-goda/Fighter Tempest's New Radar - Collects a City's Worth of Data per Second | IE (interestingengineering.com)В России создан фотонный радар, способный обнаружить любую цель – Новости РуАН (ru-an.info)United_Kingdom_2020_Forecast_Highlights.pdf (cisco.com)https://itech.aorti.ru/upload/iblock/467/rti_ii_4_19_2017.pdf page 24Patterson_AY17-18_ISR_RTF.pdf (af.edu)Online site translation into English and other languages – Yandex.TranslateGE Adaptive Cycle Engine | GE AviationFuture of British air power: the next-gen Tempest (sae.org)U.S. Navy May Expand MQ-25 Mission Set | Aviation Week NetworkУдарный беспилотник "Гром" сможет управлять роем из десяти дронов "Молния" - Армия и ОПК - ТАСС (tass.ru)The project of the unmanned complex of group use "Lightning" (topwar.ru)高運動飛行制御システムの研究,三菱重工技報 Vol.45 No.4(2008) (mhi.co.jp)404 Not Found (mod.go.jp)Небесная электромеханика: Су-57 получит новейшие системы управления | Статьи | Известия (iz.ru)F-X Fighter Aircraft (globalsecurity.org)Metamaterials: Has China Just Made a Major Stealth Breakthrough? (thedailybeast.com)Что такое анаполь? Новый метаматериал для стелс-покрытий (naukatehnika.com)

There are 3 different generation of radars with better detection performance in tracking stealth and a new method that will be tested later.GaN AESA Radar MMICs SourcesНовейший российский истребитель получил один из ключевых элементовИстребитель пятого поколения Т-50 будет оснащен новейшей станцией радиоэлектронной борьбы "Гималаи", первые образцы которой уже изготавливаются.https://web.archive.org/web/20140428131143/http://ria.ru/defense_safety/20140424/1005305871.html"We are involved in the manufacture of the Himalayas station. We are already making the first samples," Alexander Logvinov, the plant's general director, told reporters on Thursday."KRET spotlights new Khibiny-M EW system at MAKS 2017This website uses cookies to manage authentication, navigation, and other functions. By using our website, you agree that we can place these types of cookies on your device.https://www.airrecognition.com/index.php/news/airshow/air-show-2017/maks-2017-news-coverage-report/3641-kret-spotlights-new-khibiny-m-ew-system-at-maks-2017.html"We are showing the Khibiny-M system onboard a Sukhoi Su-35 [NATO reporting name: Flanker-E+] plane for the first time here. Just one year ago, the system completed its state trials. We are delivering it to the Russian Armed Forces and foreign countries where it is in great demand," adviser to the KRET first deputy CEO Vladimir Mikheyev said at a press conference during the MAKS 2017 airshow.The L-265M10-02 Khibiny-M station is used by frontline aircraft for self- and mutual defense. The station jams radioelectronic fire control systems making part of air defense missile, antiaircraft artillery and air-launched missile systems."https://structure.mil.ru%2Fstructure%2Fokruga%2Fwest%2Fnews%2Fmore.htm%3Fid%[email protected]/structure/okruga/west/news/more.htm?id=12173927%40egNews"Su-34 SVO bombers have expanded their combat potential by upgrading the Hibini REB complex"/ Авиаполк ЦВО в Челябинской области пополнился модернизированным истребителем-бомбардировщиком Су-34Авиаполк ЦВО в Челябинской области пополнился модернизированным истребителем-бомбардировщиком Су-34 ЦАМТО, 12 марта. На вооружение смешанного авиационного полка Центрального военного округа (ЦВО) в Челябинской области поступил модернизированный истребитель-бомбардировщик Су-34 поколения 4++. Летный и инженерно-технический состав полка принял обновленный самолет на заводе-изготовителе и совершил перелет на аэродром постоянного базирования в Челябинской области. Усовершенствованный истребитель-бомбардировщик Су-34 оснащен специальным оборудованием, увеличивающим возможности самолета по обнаружению воздушных, наземных целей и расширяющим арсенал применяемых средств авиационного поражения. Поступивший самолет стал первым в Центральном военном округе истребителем-бомбардировщиком Су-34, прошедшим модернизацию и поступившим на вооружение армии военно-воздушных сил и противовоздушной обороны ЦВО в 2021 году, сообщает пресс-служба Центрального военного округа. Добавить в избранное | Распечатать | Отправить по e-mail 7 апреля 2021 года 16:00 Минобороны США объявило о подписании командованием по заключению контрактов СВ США с компанией Sikorsky Aircraft соглашения на поставку очередной партии многоцелевых вертолетов UH-60M «Блэк Хок» для Национальной гвардии Саудовской Аравии. 14:35 Военно-воздушные силы Бельгии приступили к передаче избыточных штурмовиков / учебно-боевых самолетов «Альфа Джет» канадской компании Top Aces Inc. 14:05 Как ожидается, в ближайшее время группа представителей Военно-воздушных сил Малайзии прибудет в Индию для оценки легкого боевого самолета LCA «Теджас» в версии Mk.1A. 13:30 Тайвань планирует приобрести в США неназванное количество ракет-перехватчиков PAC-3 MSE (Patriot Advanced Capability-3 Missile Segment Enhancement) производства корпорации Lockheed Martin для усиления возможностей системы ПВО/ПРО на фоне эскалации напряженности в отношениях с Китаем. 13:10 Агентство программ оборонных закупок МНО Республики Корея (DAPA – Defense Acquisition Program Administration) опубликовало подробности планируемой закупки дополнительных 36 ударных вертолетов иностранного производства для СВ страны. 12:40 Командование ВВС США 5 апреля объявило, что разработанный компанией Kratos БЛА XQ-58A «Валькирия» (Valkyrie) успешно выполнил пуск малоразмерного беспилотного летательного аппарата из внутреннего отсека вооружения. 12:15 Холдинг «Росэлектроника» Госкорпорации Ростех разработал не имеющие отечественных аналогов комбинированные оптико-электронные приборы наблюдения и разведки. 11:40 Korea Aerospace Industries Co. (KAI) 4 апреля объявила о намерении разработать транспортный и многоцелевой самолеты для Вооруженных сил страны. 11:05 На своей странице в Twitter технический директор компании Baykar Makina Сельчук Байрактар сообщил о начале летных испытаний третьего опытного образца вооруженного средневысотного БЛА большой продолжительности полета «Акинчи». 10:35 Сторожевой корабль (СКР) «Ладный» Черноморского флота (ЧФ) вышел в морской полигон бhttps://armstrade.org/includes/periodics/news/2021/0312/095561974/detail.shtml"CAMTO, March 12. The mixed aviation regiment of the Central Military District (CVO) in the Chelyabinsk region has received an upgraded Su-34 generation fighter-bomber.The regiment's flight and engineering staff accepted the updated aircraft at the manufacturer and flew to a permanent airfield in the Chelyabinsk region.The advanced Su-34 fighter-bomber is equipped with special equipment that enhances the aircraft's ability to detect air, ground targets and expands the arsenal of used aircraft strike capabilities.The aircraft was the first Su-34 fighter-bomber in the Central Military District to be upgraded and commissioned by the Air Force and Air Defense Forces in 2021, according to the press service of the Central Military District."Russian aerospace industry developing new Su-34 ISR/EW variantsThe Russian aerospace industry is developing two new variants of the Sukhoi Su-34 (NATO reporting name: Fullback) frontline bomber, namely, an electronic warfare (EW) plane and an intelligence, surveillance and reconnaissance (ISR) aircraft, according to Aviation Week & Space Technology (AW&ST) magazine. One of the three Su-34 fighter jets recently inducted by the Russian Central Military District (Credit: Russian Federation Ministry of Defence) " The ministry this month announced it plans to sign, next month, a USD3.9 million contract to enable the Su-34s to use unified reconnaissance pods, including installing pylons, a contract that will be implemented this year and into 2019 ," AW&ST said. Under the aforementioned contract, the Su-34 aircraft will receive the BKR-3 (Baseline Reconnaissance Complex 3 or Bazovy Kompleks Razvedki-3) electronic intelligence (ELINT) station. The subsystem will comprise the M400A ISR device developed by the scientific-and-research institute NII Kulon (a subsidiary of Rostec State Corporation) in externally mounted UKR-family (Universal Container Pod) pods. " The adaptation of the Su-34 for carrying UKR series pods and performing reconnaissance tasks is fairly straightforward, costs about USD1 million and is a modification that can be applied to many different aircraft, " AW&ST said. The UKR family of EW/ISR pods comprises three models, the UKR-RL (the radiolocation variant), the UKR-RT (the radio-technical, or ISR, variant), and the UKR-OE (the optical-electronic variant). The UKR-RL houses the M402 Pika-M (Spike M) side-looking radar developed by NII Kulon. The export-oriented variant of the subsystem has a target detection range of up to 300 km and a resolving power of some 1-1.5 m, the developer claims. The UKR-RT stores the M410 ELINT system developed by the scientific-and-research institute TsNIIRTI , while the UKR-OE features the Antrakt camera and the M433 Raduga-VM infrared scanner. " Each pod [also] houses a data storage and wideband data link for real-time transmission to a ground station, " AW&ST said. According to the magazine, NII Kulon has already started serial production of the pods " on a piece-production basis ". Along with the ISR variant of the Su-34, the aerospace industry is developing an EW modification of the Fullback. To this end, Russia upgrades the Su-34`s baseline electronic jammer, the Khibiny-10 (L175V) station and integrates a new under-fuselage jamming pod with the subsystem. The L175V C-/X-/Ku-band station can be augmented by three additional EW pods, namely, the L-175VU-1, L175VU-2 (both stations are power transmitters only) and L175VSh-1 (a C-/L-band station). The L175VSh-1 is designed to counter both airborne early warning and control (AEW&C) air platforms and ground-based radars of various air defense systems. " Deliveries of these [the three] pods to operational units started in late 2015 ," AW&ST said. In October, the Novosibirsk Aviation Plant (NAZ, a subsidiary of the Sukhoihttps://www.airrecognition.com/index.php/archive-world-worldwide-news-air-force-aviation-aerospace-air-military-defence-industry/global-defense-security-news/global-news-2018/november/4603-russian-air-force-developing-new-su-34-isr-ew-variants.html"The Su-34M was developed under the Sych R&D [research-and-development] program and was recently cleared for series production," the magazine said. According to AW&ST, the updated aircraft has received the K-102M targeting subsystem on the base of the Elbrus microprocessor, Sh141M radar subsystem, and other modernized devices. Most foreign-made nods of the aircraft have been replaced by those of the Russian origins"https://vpk-news.ru/news/32554In particular, the station implements the function of processing radar information in real time, as well as provided a mode of telescopic observation with a resolution of up to 30 cm. In particular, the locator is able to "see" the elements of the aircraft in detail - engine, keel, armament and determine by characteristic characteristics of its type.The serial production of the Pika-M radar as part of the United Instrumentation Corporation is conducted by the Kulon Research Institute. Initially, the product was developed for multifunctional fighter-bomber Su-34, but can be used on other types of aircraft, including drones."Pica-M" is part of the brKR-3 on-board complex, which provides radar reconnaissance in all weather conditions and at any time of the day. The station has a mapping capacity of up to 1-1.5 m and an object detection range of up to 300 km.The radar successfully completed the state test program in 2016. At the same time, the "Research Kulon" on the order of the Ministry of Industry and Trade is developing the technology to create a fifth-generation side-view radar with an active phased antenna grille (AFAR).Acquiring GaN MMIC to be one generation aheadRussia currently is behind the U.S. 10–15 years in MMICs, But current U.S. AFAIK have not received any news reports on block upgrades regarding newer MMIC replacements in EW or radar systems. Because of that there is a possibility that Russians are currently using GaN MMICs with the U.S. still using GaAS MMICs. 2014 Rostec had displayed 3 GaN MMICs for 3 air borne EW systems. And those new EW systems came for the Su-57 in late 2014, 2016 Su-35 tested their new ones in Syria and 2018 Su-34 received their new EW systems. So technically speaking that sounds like they GaN MMICs in their jammers. But that's not all it appears that the Su-57 Sh-121 is now Sh-121M and Su-34 Sh-141 is now Sh-141M, AFAIK there is no new reports of the Su-35’s radar system but still this means that not only new GaN MMICs have been replaced on their EW systems but that possibility is raised towards their radars as well. If they did indeed get everything to go with GaN MMICs than they are one generation ahead.Photonic Radar PIC SourcesU.S. Company Raytheon 2019 PDFhttps://www.raytheon.com/sites/default/files/technology-today/2019/issue2/wp-content/uploads/2019/05/Raytheon_TechnologyToday_Issue2_2019.pdf"With all the advances occurring inemerging PIC technologies, Raytheonresearchers and engineers are activelypursuing both internal research andcustomer-funded development programsto investigate applications of PICtechnology in next generation products,as well as to develop lower cost, higheryield PIC packaging and manufacturingprocesses"DARPAStackPathPlease Enable Cookies www.militaryaerospace.com is using a security service for protection against online attacks. The service requires full cookie support in order to view this website. Please enable cookies on your browser and try again. Please Enable JavaScript www.militaryaerospace.com is using a security service for protection against online attacks. The service requires full JavaScript support in order to view this website. Please enable JavaScript on your browser and try again. www.militaryaerospace.com is using a security service for protection against online attacks. This process is automatic. You will be redirected once the validation is complete.https://www.militaryaerospace.com/rf-analog/article/14178607/rf-and-microwave-photonics-radarIndustry asked to develop microwave photonics components for RF and microwave applications like radarDARPA wants lithium-niobate field-configurable modulator arrays (FCMAs) for RF links, RF signal processing, radar, and RF spectrum management.Although microwave photonics represents an important technology for military applications, the military microwave photonic systems deployed to date repurpose commercial components for military functions.The most recent developments in industrial telecommunications have been in specialized application-specific photonic integrated circuits (PICs). Today's military applications cannot use these devices, however, because application-specific PICs cannot be repurposed.The FCMA must be able to operate from 1 MHz to 18 GHz, and use the nonlinear response of a Mach-Zehnder modulator to suppress a continuous-wave interference signal by 60 decibels to suppress an interference signal with 10 MHz instantaneous bandwidth by 40 decibels -- both while reducing the largest intermodulation distortion by 30 decibels.The signals-intelligence configuration will improve the intrinsic third-order-limited spurious-free dynamic range of a Mach-Zehnder modulator by 10 decibels.The radar-beamforming application will provide 360 degrees of RF phase shift that can be modulated at 100 kHz. The communications configuration, meanwhile, must support 10 gigabits per second of modulation on each of the in-phase and quadrature components of a lightwave.Russian Company RTIhttps://itech.aorti.ru/%20No.%201%20(20)%20of%202018As for semiconductormodulators in microchipperformance, then in 2019 the researchwork on this topic in whichOKB-Planeta OJSC is an industrial partner.Within three to five years is possibleorganization of the development, design and production of photonicintegrated circuits (FIS) both in packageless execution, and in the case.The implementation of these plans will allowJSC "RTI" take a leading positionin development and productionadvanced domestic radio systems based on componentradiophotonic bases.Acquiring PICs To Be Two Generations AheadRussia had demonstrated photonic radar antennas with the image above showing them to be very thin but a little thicker than paint. They also have a set mass production date somewhere in 2022–2024. RTI stated in 2019 that in a few years their photonic radar prototype will be tested on a multifunctional fighter and there is a new Su-57 receiving new weapons, engines and avionics from 2022–2024. Yakhroma radars frequency range sets it as another possibility of being a photonic radar.Quantum Radar QIC SourcesКогда начнется эра российских квантовых компьютеров?Первый кубит в России получили в 2015 году. Новое устройство созданное в лаборатории искусственных квантовых систем МФТИ уже сейчас может быть использовано в квантовом машинном обучении — области науки…https://naukatehnika.com/era-rossijskih-kvantovyh-kompyuterov.htmlExperts of the Moscow Institute of Physics and Technology (MIPT) and the Laboratory of Artificial quantum systems (LYCS) claim that the new quantum integrated circuit is unique and fully controlled. According to them, even at the current stage of development it can be applied in quantum machine learning.Representatives of MIPT noted that the creation of the Russian multi-cubit integrated circuit was made possible by four factors, and the first among them is a significant improvement in the control of the geometric and electrical parameters of tunnel contacts. According to the representatives of the university, these contacts can be considered the "heart" of superconducting qubits, as the quality and reproducibility of their manufacture directly depends on the performance of the entire quantum scheme. The second factor is the setting up of the technology of making microwave resonators, the goodness of which in a single photon mode is hundreds of thousands. This is also a very important part of quantum integrated circuits - they are needed to read the quantum state of qubits. The third factor is the debugging of the process of making "air bridge" (air bridge) necessary to suppress parasitic resonant mods, which positively affects the goodness of structures. But the most important component that allowed MIPT specialists to create a multi-cobit scheme, in their opinion, is their experience in this area over the past few years. THE IFTI does not specify when the era of Russian quantum computers will begin, as well as do not disclose their future plans to develop new multi-cubit integrated circuits and their implementation. For any further action in this area, it is necessary to modernize both the CCP and the IX laboratory within the IFTI. Of Russia's large companies, Rosatom is particularly interested in quantum computing. In 2020, they were offered a plan of work - a "road map" of the development of quantum technologies in RussiaAcquiring QICs to be Three Generations AheadAFAIK Russia only has photonic integrated circuit production planned dates but they dont have any planned dates for quantum integrated circuit production dates. Rather if Quantum radars are the end of all stealth. The next concern is their radar shadowing method.«Колоссальный прорыв»: российские учёные разработали новый способ обнаружения самолётов-невидимокВ России разработан новый метод селекции движущихся объектов, изготовленных по технологии «стелс». Как сообщили в Радиотехническом институте имени академика А.Л. Минца, он позволяет фиксировать так называемую радиолокационную тень, которую оставляет на экране радара самолёт-невидимка. По словам экспертов, сегодняшние локаторы не всегда могут своевременно обнаружить подобную цель. В связи с этим изобретение российских специалистов имеет большое значение для укрепления противовоздушной обороны страны, указывают аналитики.https://russian.rt.com/russia/article/760838-stels-tehnologii-radar-rti"Now it is too early to talk about the imminent implementation of a new method of breeding moving objects. To date, it has been proven that it is theoretically possible. There's still a lot of work to do. I think it's going to take about seven years. But if all goes well, this method will give Russia a noticeable advantage on the battlefield," Denisentsev said.So we will see in 2027.

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal).A sample is a value or set of values at a point in time and/or space.A sampler is a subsystem or operation that extracts samples from a continuous signal.A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.Contents[hide]1Theory2Practical considerations3Applications3.1Audio sampling3.1.1Sampling rate3.1.2Bit depth3.1.3Speech sampling3.2Video sampling3.33D sampling4Undersampling5Oversampling6Complex sampling7See also8Notes9Citations10Further reading11External linksTheory[edit]See also: Nyquist–Shannon sampling theoremSampling can be done for functions varying in space, time, or any other dimension, and similar results are obtained in two or more dimensions.For functions that vary with time, let s(t) be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every T seconds, which is called the sampling interval or the sampling period.[1]Then the sampled function is given by the sequence:s(nT), for integer values of n.The sampling frequency or sampling rate, fs, is the average number of samples obtained in one second (samples per second), thus fs= 1/T.Reconstructing a continuous function from samples is done by interpolation algorithms. The Whittaker–Shannon interpolation formula is mathematically equivalent to an ideal lowpass filter whose input is a sequence of Dirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant (T), the sequence of delta functions is called a Dirac comb. Mathematically, the modulated Dirac comb is equivalent to the product of the comb function with s(t). That purely mathematical abstraction is sometimes referred to as impulse sampling.[2]Most sampled signals are not simply stored and reconstructed. But the fidelity of a theoretical reconstruction is a customary measure of the effectiveness of sampling. That fidelity is reduced when s(t) contains frequency components whose periodicity is smaller than two samples; or equivalently the ratio of cycles to samples exceeds ½ (see Aliasing). The quantity ½ cycles/sample × fssamples/sec = fs/2 cycles/sec (hertz) is known as the Nyquist frequency of the sampler. Therefore, s(t) is usually the output of a lowpass filter, functionally known as an anti-aliasing filter. Without an anti-aliasing filter, frequencies higher than the Nyquist frequency will influence the samples in a way that is misinterpreted by the interpolation process.[3]Practical considerations[edit]In practice, the continuous signal is sampled using an analog-to-digital converter (ADC), a device with various physical limitations. This results in deviations from the theoretically perfect reconstruction, collectively referred to as distortion.Various types of distortion can occur, including:Aliasing. Some amount of aliasing is inevitable because only theoretical, infinitely long, functions can have no frequency content above the Nyquist frequency. Aliasing can be made arbitrarily small by using a sufficiently large order of the anti-aliasing filter.Aperture error results from the fact that the sample is obtained as a time average within a sampling region, rather than just being equal to the signal value at the sampling instant. In a capacitor-based sample and hold circuit, aperture error is introduced because the capacitor cannot instantly change voltage thus requiring the sample to have non-zero width.Jitter or deviation from the precise sample timing intervals.Noise, including thermal sensor noise, analog circuit noise, etc.Slew rate limit error, caused by the inability of the ADC input value to change sufficiently rapidly.Quantization as a consequence of the finite precision of words that represent the converted values.Error due to other non-linear effects of the mapping of input voltage to converted output value (in addition to the effects of quantization).Although the use of oversampling can completely eliminate aperture error and aliasing by shifting them out of the pass band, this technique cannot be practically used above a few GHz, and may be prohibitively expensive at much lower frequencies. Furthermore, while oversampling can reduce quantization error and non-linearity, it cannot eliminate these entirely. Consequently, practical ADCs at audio frequencies typically do not exhibit aliasing, aperture error, and are not limited by quantization error. Instead, analog noise dominates. At RF and microwave frequencies where oversampling is impractical and filters are expensive, aperture error, quantization error and aliasing can be significant limitations.Jitter, noise, and quantization are often analyzed by modeling them as random errors added to the sample values. Integration and zero-order hold effects can be analyzed as a form of low-pass filtering. The non-linearities of either ADC or DAC are analyzed by replacing the ideal linear function mapping with a proposed nonlinear function.Applications[edit]Audio sampling[edit]Digital audio uses pulse-code modulation and digital signals for sound reproduction. This includes analog-to-digital conversion (ADC), digital-to-analog conversion (DAC), storage, and transmission. In effect, the system commonly referred to as digital is in fact a discrete-time, discrete-level analog of a previous electrical analog. While modern systems can be quite subtle in their methods, the primary usefulness of a digital system is the ability to store, retrieve and transmit signals without any loss of quality.Sampling rate[edit]A commonly seen measure of sampling is S/s, which stands for "samples per second". As an example, 1 MS/s is one million samples per second.When it is necessary to capture audio covering the entire 20–20,000 Hz range of human hearing,[4]such as when recording music or many types of acoustic events, audio waveforms are typically sampled at 44.1 kHz (CD), 48 kHz, 88.2 kHz, or 96 kHz.[5]The approximately double-rate requirement is a consequence of the Nyquist theorem. Sampling rates higher than about 50 kHz to 60 kHz cannot supply more usable information for human listeners. Early professional audio equipment manufacturers chose sampling rates in the region of 50 kHz for this reason.There has been an industry trend towards sampling rates well beyond the basic requirements: such as 96 kHz and even 192 kHz[6]This is in contrast with laboratory experiments, which have failed to show that ultrasonic frequencies are audible to human observers; however in some cases ultrasonic sounds do interact with and modulate the audible part of the frequency spectrum (intermodulation distortion).[7]It is noteworthy that intermodulation distortion is not present in the live audio and so it represents an artificial coloration to the live sound.[8]One advantage of higher sampling rates is that they can relax the low-pass filter design requirements for ADCs and DACs, but with modern oversampling sigma-delta converters this advantage is less important.The Audio Engineering Society recommends 48 kHz sampling rate for most applications but gives recognition to 44.1 kHz for Compact Disc (CD) and other consumer uses, 32 kHz for transmission-related applications, and 96 kHz for higher bandwidth or relaxed anti-aliasing filtering.[9]A more complete list of common audio sample rates is:Sampling rateUse8,000 HzTelephone and encrypted walkie-talkie, wireless intercom and wireless microphone transmission; adequate for human speech but without sibilance (ess sounds like eff (/s/, /f/)).11,025 HzOne quarter the sampling rate of audio CDs; used for lower-quality PCM, MPEG audio and for audio analysis of subwoofer bandpasses.[citation needed]16,000 HzWideband frequency extension over standard telephone narrowband 8,000 Hz. Used in most modern VoIP and VVoIP communication products.[10]22,050 HzOne half the sampling rate of audio CDs; used for lower-quality PCM and MPEG audio and for audio analysis of low frequency energy. Suitable for digitizing early 20th century audio formats such as 78s.[11]32,000 HzminiDV digital video camcorder, video tapes with extra channels of audio (e.g. DVCAM with four channels of audio), DAT (LP mode), Germany's Digitales Satellitenradio, NICAM digital audio, used alongside analogue television sound in some countries. High-quality digital wireless microphones.[12]Suitable for digitizing FM radio.[citation needed]37,800 HzCD-XA audio44,056 HzUsed by digital audio locked to NTSC color video signals (3 samples per line, 245 lines per field, 59.94 fields per second = 29.97 frames per second).44,100 HzAudio CD, also most commonly used with MPEG-1 audio (VCD, SVCD, MP3). Originally chosen by Sony because it could be recorded on modified video equipment running at either 25 frames per second (PAL) or 30 frame/s (using an NTSC monochrome video recorder) and cover the 20 kHz bandwidth thought necessary to match professional analog recording equipment of the time. A PCM adaptor would fit digital audio samples into the analog video channel of, for example, PAL video tapes using 3 samples per line, 588 lines per frame, 25 frames per second.47,250 Hzworld's first commercial PCM sound recorder by Nippon Columbia (Denon)48,000 HzThe standard audio sampling rate used by professional digital video equipment such as tape recorders, video servers, vision mixers and so on. This rate was chosen because it could reconstruct frequencies up to 22 kHz and work with 29.97 frames per second NTSC video - as well as 25 frame/s, 30 frame/s and 24 frame/s systems. With 29.97 frame/s systems it is necessary to handle 1601.6 audio samples per frame delivering an integer number of audio samples only every fifth video frame.[9]Also used for sound with consumer video formats like DV, digital TV, DVD, and films. The professional Serial Digital Interface (SDI) and High-definition Serial Digital Interface (HD-SDI) used to connect broadcast television equipment together uses this audio sampling frequency. Most professional audio gear uses 48 kHz sampling, including mixing consoles, and digital recording devices.50,000 HzFirst commercial digital audio recorders from the late 70s from 3M and Soundstream.50,400 HzSampling rate used by the Mitsubishi X-80 digital audio recorder.88,200 HzSampling rate used by some professional recording equipment when the destination is CD (multiples of 44,100 Hz). Some pro audio gear uses (or is able to select) 88.2 kHz sampling, including mixers, EQs, compressors, reverb, crossovers and recording devices.96,000 HzDVD-Audio, some LPCM DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, HD DVD (High-Definition DVD) audio tracks. Some professional recording and production equipment is able to select 96 kHz sampling. This sampling frequency is twice the 48 kHz standard commonly used with audio on professional equipment.176,400 HzSampling rate used by HDCD recorders and other professional applications for CD production. Four times the frequency of 44.1 kHz.192,000 HzDVD-Audio, some LPCM DVD tracks, BD-ROM (Blu-ray Disc) audio tracks, and HD DVD (High-Definition DVD) audio tracks, High-Definition audio recording devices and audio editing software. This sampling frequency is four times the 48 kHz standard commonly used with audio on professional video equipment.352,800 HzDigital eXtreme Definition, used for recording and editing Super Audio CDs, as 1-bit DSD is not suited for editing. Eight times the frequency of 44.1 kHz.2,822,400 HzSACD, 1-bit delta-sigma modulation process known as Direct Stream Digital, co-developed by Sony and Philips.5,644,800 HzDouble-Rate DSD, 1-bit Direct Stream Digital at 2× the rate of the SACD. Used in some professional DSD recorders.11,289,600 HzQuad-Rate DSD, 1-bit Direct Stream Digital at 4× the rate of the SACD. Used in some uncommon professional DSD recorders.22,579,200 HzOctuple-Rate DSD, 1-bit Direct Stream Digital at 8× the rate of the SACD. Used in rare experimental DSD recorders. Also known as DSD512.Bit depth[edit]See also: Audio bit depthAudio is typically recorded at 8-, 16-, and 24-bit depth, which yield a theoretical maximum signal-to-quantization-noise ratio (SQNR) for a pure sine wave of, approximately, 49.93 dB, 98.09 dB and 122.17 dB.[13]CD quality audio uses 16-bit samples. Thermal noise limits the true number of bits that can be used in quantization. Few analog systems have signal to noise ratios (SNR) exceeding 120 dB. However, digital signal processing operations can have very high dynamic range, consequently it is common to perform mixing and mastering operations at 32-bit precision and then convert to 16- or 24-bit for distribution.Speech sampling[edit]Speech signals, i.e., signals intended to carry only human speech, can usually be sampled at a much lower rate. For most phonemes, almost all of the energy is contained in the 100 Hz–4 kHz range, allowing a sampling rate of 8 kHz. This is the sampling rate used by nearly all telephony systems, which use the G.711 sampling and quantization specifications.Video sampling[edit]This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.(June 2007)(Learn how and when to remove this template message)Standard-definition television (SDTV) uses either 720 by 480 pixels (US NTSC 525-line) or 704 by 576 pixels (UK PAL 625-line) for the visible picture area.High-definition television (HDTV) uses 720p (progressive), 1080i (interlaced), and 1080p (progressive, also known as Full-HD).In digital video, the temporal sampling rate is defined the frame rate – or rather the field rate – rather than the notional pixel clock. The image sampling frequency is the repetition rate of the sensor integration period. Since the integration period may be significantly shorter than the time between repetitions, the sampling frequency can be different from the inverse of the sample time:50 Hz – PAL video60 / 1.001 Hz ~= 59.94 Hz – NTSC videoVideo digital-to-analog converters operate in the megahertz range (from ~3 MHz for low quality composite video scalers in early games consoles, to 250 MHz or more for the highest-resolution VGA output).When analog video is converted to digital video, a different sampling process occurs, this time at the pixel frequency, corresponding to a spatial sampling rate along scan lines. A common pixel sampling rate is:13.5 MHz – CCIR 601, D1 videoSpatial sampling in the other direction is determined by the spacing of scan lines in the raster. The sampling rates and resolutions in both spatial directions can be measured in units of lines per picture height.Spatial aliasing of high-frequency luma or chroma video components shows up as a moiré pattern.3D sampling[edit]The process of volume rendering samples a 3D grid of voxels to produce 3D renderings of sliced (tomographic) data. The 3D grid is assumed to represent a continuous region of 3D space. Volume rendering is common in medial imaging, X-ray computed tomography (CT/CAT), magnetic resonance imaging (MRI), positron emission tomography (PET) are some examples. It is also used for seismic tomography and other applications.The top two graphs depict Fourier transforms of two different functions that produce the same results when sampled at a particular rate. The baseband function is sampled faster than its Nyquist rate, and the bandpass function is undersampled, effectively converting it to baseband. The lower graphs indicate how identical spectral results are created by the aliases of the sampling process.Undersampling[edit]Main article: UndersamplingWhen a bandpass signal is sampled slower than its Nyquist rate, the samples are indistinguishable from samples of a low-frequency alias of the high-frequency signal. That is often done purposefully in such a way that the lowest-frequency alias satisfies the Nyquist criterion, because the bandpass signal is still uniquely represented and recoverable. Such undersampling is also known as bandpass sampling, harmonic sampling, IF sampling, and direct IF to digital conversion.[14]Oversampling[edit]Main article: OversamplingOversampling is used in most modern analog-to-digital converters to reduce the distortion introduced by practical digital-to-analog converters, such as a zero-order hold instead of idealizations like the Whittaker–Shannon interpolation formula.[15]Complex sampling[edit]Complex sampling (I/Q sampling) is the simultaneous sampling of two different, but related, waveforms, resulting in pairs of samples that are subsequently treated as complex numbers.[note 1]When one waveform[math]{\displaystyle ,{\hat {s}}(t),}[/math] is the Hilbert transform of the other waveform[math]{\displaystyle ,s(t),\,}[/math] the complex-valued function, [math]{\displaystyle s_{a}(t)\ {\stackrel {\text{def}}{=}}\ s(t)+i\cdot {\hat {s}}(t),}[/math] is called an analytic signal, whose Fourier transform is zero for all negative values of frequency. In that case, the Nyquist rate for a waveform with no frequencies ≥ B can be reduced to just B (complex samples/sec), instead of 2B (real samples/sec).[note 2]More apparently, the equivalent baseband waveform, [math]{\displaystyle s_{a}(t)\cdot e^{-i2\pi {\frac {B}{2}}t},}[/math] also has a Nyquist rate of B, because all of its non-zero frequency content is shifted into the interval [-B/2, B/2).Although complex-valued samples can be obtained as described above, they are also created by manipulating samples of a real-valued waveform. For instance, the equivalent baseband waveform can be created without explicitly computing [math]{\displaystyle {\hat {s}}(t),}[/math] by processing the product sequence[math]{\displaystyle ,\left[s(nT)\cdot e^{-i2\pi {\frac {B}{2}}Tn}\right],}[/math][note 3]through a digital lowpass filter whose cutoff frequency is B/2.[note 4]Computing only every other sample of the output sequence reduces the sample-rate commensurate with the reduced Nyquist rate. The result is half as many complex-valued samples as the original number of real samples. No information is lost, and the original s(t) waveform can be recovered, if necessary.See also[edit]DownsamplingUpsamplingMultidimensional samplingSample rate conversionDigitizingSample and holdBeta encoderKell factorBit rateNotes[edit]Jump up^ Sample-pairs are also sometimes viewed as points on a constellation diagram.Jump up^ When the complex sample-rate is B, a frequency component at 0.6 B, for instance, will have an alias at −0.4 B, which is unambiguous because of the constraint that the pre-sampled signal was analytic. Also see Aliasing#Complex sinusoids.Jump up^ When s(t) is sampled at the Nyquist frequency (1/T = 2B), the product sequence simplifies to [math]{\displaystyle \left[s(nT)\cdot (-i)^{n}\right].}[/math]Jump up^ The sequence of complex numbers is convolved with the impulse response of a filter with real-valued coefficients. That is equivalent to separately filtering the sequences of real parts and imaginary parts and reforming complex pairs at the outputs.Citations[edit]Jump up^ Martin H. Weik (1996). Communications Standard Dictionary. Springer. ISBN 0412083914.Jump up^ Rao, R. Signals and Systems. Prentice-Hall Of India Pvt. Limited. ISBN 9788120338593.Jump up^ C. E. Shannon, "Communication in the presence of noise", Proc. Institute of Radio Engineers, vol. 37, no.1, pp. 10–21, Jan. 1949. Reprint as classic paper in: Proc. IEEE, Vol. 86, No. 2, (Feb 1998)Jump up^ "Frequency Range of Human Hearing". The Physics Factbook.Jump up^ Self, Douglas (2012). Audio Engineering Explained. Taylor & Francis US. pp. 200, 446. ISBN 0240812735.Jump up^ "Digital Pro Sound". Retrieved 8 January 2014.Jump up^ Colletti, Justin (February 4, 2013). "The Science of Sample Rates (When Higher Is Better—And When It Isn't)". Trust Me I'm A Scientist. Retrieved February 6, 2013.Jump up^ David Griesinger. "Perception of mid frequency and high frequency intermodulation distortion in loudspeakers, and its relationship to high-definition audio". Archived from the original (Powerpoint presentation) on 2008-05-01.^ Jump up to:a b AES5-2008: AES recommended practice for professional digital audio - Preferred sampling frequencies for applications employing pulse-code modulation, Audio Engineering Society, 2008, retrieved 2010-01-18Jump up^ http://www.voipsupply.com/cisco-hd-voice[unreliable source?]Jump up^ "The restoration procedure - part 1". http://Restoring78s.co.uk. Archived from the originalon 2009-09-14. Retrieved 2011-01-18. For most records a sample rate of 22050 in stereo is adequate. An exception is likely to be recordings made in the second half of the century, which may need a sample rate of 44100.Jump up^ "Zaxcom digital wireless transmitters". Zaxcom. Retrieved 2011-01-18.Jump up^ "MT-001: Taking the Mystery out of the Infamous Formula, "SNR=6.02N + 1.76dB," and Why You Should Care" (PDF).Jump up^ Walt Kester (2003). Mixed-signal and DSP design techniques. Newnes. p. 20. ISBN 978-0-7506-7611-3. Retrieved 8 January 2014.Jump up^ William Morris Hartmann (1997). Signals, Sound, and Sensation. Springer. ISBN 1563962837.Further reading[edit]Matt Pharr, Wenzel Jakob and Greg Humphreys, Physically Based Rendering: From Theory to Implementation, 3rd ed., Morgan Kaufmann, November 2016. ISBN 978-0128006450. The chapter on sampling (available online) is nicely written with diagrams, core theory and code sample.External links[edit]Journal devoted to Sampling TheoryI/Q Data for Dummies – a page trying to answer the question Why I/Q Data?Sampling of analog signals – an interactive presentation in a web-demo at the Institute of Telecommunications, University of Stuttgart