Undersampling
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Undersampling
In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass-filtered signal at a sample rate below its Nyquist rate (twice the upper cutoff frequency), but is still able to reconstruct the signal. When one undersamples a bandpass signal, the samples are indistinguishable from the samples of a low-frequency alias of the high-frequency signal. Such sampling is also known as bandpass sampling, harmonic sampling, IF sampling, and direct IF-to-digital conversion. Description The Fourier transforms of real-valued functions are symmetrical around the 0 Hz axis. After sampling, only a periodic summation of the Fourier transform (called discrete-time Fourier transform) is still available. The individual frequency-shifted copies of the original transform are called ''aliases''. The frequency offset between adjacent aliases is the sampling-rate, denoted by ''fs''. When the aliases are mutually exclusive (spectrally), the original transf ...
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Drizzle (image Processing)
Drizzle (or DRIZZLE) is a digital image processing method for the linear reconstruction of undersampled images. The method is normally used for the combination of astronomical images and was originally developed for the Hubble Deep Field observations made by the Hubble Space Telescope. The algorithm, known as variable-pixel linear reconstruction, or informally as "Drizzle", preserves photometry and resolution, can weight input images according to the statistical significance of each pixel, and removes the effects of geometric distortion on both image shape and photometry. In addition, it is possible to use drizzling to combine dithered images in the presence of cosmic rays. Drizzling is commonly used by amateur astrophotographers, particularly for processing large amounts of planetary image data (typically several thousand frames), drizzling in astrophotography applications can also be used to recover higher resolution stills from terrestrial video recordings. According to astropho ...
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Filter Bank
In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal. The process of decomposition performed by the filter bank is called ''analysis'' (meaning analysis of the signal in terms of its components in each sub-band); the output of analysis is referred to as a subband signal with as many subbands as there are filters in the filter bank. The reconstruction process is called ''synthesis'', meaning reconstitution of a complete signal resulting from the filtering process. In digital signal processing, the term ''filter bank'' is also commonly applied to a bank of receivers. The difference is that receivers also down-convert the subbands to a low center frequency that can be re-sa ...
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Sampling (signal Processing)
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 to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the term's usage in statistics, which refers to a set of such values. 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. The original signal can be reconstructed from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a reconstruction filter. Theory Functions of space, time, or any other dimension can be sampled, and similarly 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 ...
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Analog-to-digital Converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a Digital signal (signal processing), digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or Electric current, current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. There are several ADC hardware architecture, architectures. Due to the complexity and the need for precisely matched electronic component, components, all but the most specialized ADCs are implemented as integrated circuits (ICs). These typically take the form of metal–oxide–semiconductor (MOS) mixed-signal integrated circuit chips that integrate both Analogue electronics, anal ...
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Aliasing
In signal processing and related disciplines, aliasing is a phenomenon that a reconstructed signal from samples of the original signal contains low frequency components that are not present in the original one. This is caused when, in the original signal, there are components at frequency exceeding a certain frequency called Nyquist frequency, f_s / 2, where f_s is the sampling frequency ( undersampling). This is because typical reconstruction methods use low frequency components while there are a number of frequency components, called aliases, which sampling result in the identical sample. It also often refers to the distortion or artifact that results when a signal reconstructed from samples is different from the original continuous signal. Aliasing can occur in signals sampled in time, for instance in digital audio or the stroboscopic effect, and is referred to as temporal aliasing. Aliasing in spatially sampled signals (e.g., moiré patterns in digital images) is referre ...
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Igor Kluvánek
Igor Kluvánek (27 January 1931 – 24 July 1993) was a Slovak-Australian mathematician. Academic career Igor Kluvánek obtained his first degree in electrical engineering from the Slovak Polytechnic University, Bratislava, in 1953. His first appointment was in the Department of Mathematics of the same institution. At the same time he worked for his C.Sc. degree obtained from the Slovak Academy of Sciences. In the early 60's he joined the Department of Mathematical Analysis of the University of Pavol Jozef Šafárik in Košice. During 1967–68 he held a visiting position at The Flinders University of South Australia. The events of 1968 in Czechoslovakia made it impossible for him and his family to return to their homeland. The Flinders University of South Australia was able to create a chair in applied mathematics to which he was appointed in January 1969 and occupied until his resignation in 1986. Early years Kluvánek graduated in 1953 from the Slovak Polytechnic Universit ...
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Anti-aliasing Filter
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is zero, a brick wall filter is an idealized but impractical AAF. A practical AAF makes a trade off between reduced bandwidth and increased aliasing. A practical anti-aliasing filter will typically permit some aliasing to occur or attenuate or otherwise distort some in-band frequencies close to the Nyquist limit. For this reason, many practical systems sample higher than would be theoretically required by a perfect AAF in order to ensure that all frequencies of interest can be reconstructed, a practice called oversampling. Optical applications In the case of optical image sampling, as by image sensors in digital cameras, the anti ...
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Band-pass Filter
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects ( attenuates) frequencies outside that range. It is the inverse of a '' band-stop filter''. Description In electronics and signal processing, a filter is usually a two-port circuit or device which removes frequency components of a signal (an alternating voltage or current). A band-pass filter allows through components in a specified band of frequencies, called its ''passband'' but blocks components with frequencies above or below this band. This contrasts with a high-pass filter, which allows through components with frequencies above a specific frequency, and a low-pass filter, which allows through components with frequencies below a specific frequency. In digital signal processing, in which signals represented by digital numbers are processed by computer programs, a band-pass filter is a computer algorithm that performs the same function. The term band ...
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Aperture Uncertainty
In optics, the aperture of an optical system (including a system consisting of a single lens) is the hole or opening that primarily limits light propagated through the system. More specifically, the entrance pupil as the front side image of the aperture and focal length of an optical system determine the cone angle of a bundle of rays that comes to a focus in the image plane. An optical system typically has many structures that limit ray bundles (ray bundles are also known as ''pencils'' of light). These structures may be the edge of a lens or mirror, or a ring or other fixture that holds an optical element in place or may be a special element such as a diaphragm placed in the optical path to limit the light admitted by the system. In general, these structures are called stops, and the aperture stop is the stop that primarily determines the cone of rays that an optical system accepts (see entrance pupil). As a result, it also determines the ray cone angle and brightness at t ...
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Megahertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base units is 1/s or s−1, meaning that one hertz is one per second or the reciprocal of one second. It is used only in the case of periodic events. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. For high frequencies, the unit is commonly expressed in multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. The units are sometimes also used as a representation o ...
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FM Radio
FM broadcasting is a method of radio broadcasting that uses frequency modulation (FM) of the radio broadcast carrier wave. Invented in 1933 by American engineer Edwin Armstrong, wide-band FM is used worldwide to transmit high fidelity, high-fidelity sound over broadcast radio. FM broadcasting offers higher fidelity—more accurate reproduction of the original program sound—than other broadcasting techniques, such as AM broadcasting. It is also less susceptible to Electromagnetic interference, common forms of interference, having less static and popping sounds than are often heard on AM. Therefore, FM is used for most broadcasts of music and general audio (in the audio spectrum). FM radio stations use the very high frequency range of radio frequency, radio frequencies. Broadcast bands Throughout the world, the FM broadcast band falls within the VHF part of the radio spectrum. Usually 87.5 to 108.0 MHz is used, or some portion of it, with few exceptions: * In the Commo ...
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Sampling FM At 56MHz
Sampling may refer to: *Sampling (signal processing), converting a continuous signal into a discrete signal *Sample (graphics), Sampling (graphics), converting continuous colors into discrete color components *Sampling (music), the reuse of a sound recording in another recording **Sampler (musical instrument), an electronic musical instrument used to record and play back samples *Sampling (statistics), selection of observations to acquire some knowledge of a statistical population *Sampling (case studies), selection of cases for single or multiple case studies *Sampling (audit), application of audit procedures to less than 100% of population to be audited *Sampling (medicine), gathering of matter from the body to aid in the process of a medical diagnosis and/or evaluation of an indication for treatment, further medical tests or other procedures. *Sampling (occupational hygiene), detection of hazardous materials in the workplace *Sampling (for testing or analysis), taking a represent ...
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