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Impulse Invariance
Impulse invariance is a technique for designing discrete-time infinite-impulse-response (IIR) filters from continuous-time filters in which the impulse response of the continuous-time system is sampled to produce the impulse response of the discrete-time system. The frequency response of the discrete-time system will be a sum of shifted copies of the frequency response of the continuous-time system; if the continuous-time system is approximately band-limited to a frequency less than the Nyquist frequency of the sampling, then the frequency response of the discrete-time system will be approximately equal to it for frequencies below the Nyquist frequency. Discussion The continuous-time system's impulse response, h_c(t), is sampled with sampling period T to produce the discrete-time system's impulse response, h /math>. :h Th_c(nT)\, Thus, the frequency responses of the two systems are related by :H(e^) = \frac \sum_^\infty\, If the continuous time filter is approximately band-l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinite-impulse-response
Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response h(t) which does not become exactly zero past a certain point, but continues indefinitely. This is in contrast to a finite impulse response (FIR) system in which the impulse response ''does'' become exactly zero at times t>T for some finite T, thus being of finite duration. Common examples of linear time-invariant systems are most electronic and digital filters. Systems with this property are known as ''IIR systems'' or ''IIR filters''. In practice, the impulse response, even of IIR systems, usually approaches zero and can be neglected past a certain point. However the physical systems which give rise to IIR or FIR responses are dissimilar, and therein lies the importance of the distinction. For instance, analog electronic filters composed of resistors, capacitors, and/or inductors (and perhaps linear amplifiers) are generally IIR filters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nyquist Frequency
In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), its value is one-half of the sampling rate (samples per second). When the highest frequency (bandwidth) of a signal is less than the Nyquist frequency of the sampler, the resulting discrete-time sequence is said to be free of the distortion known as aliasing, and the corresponding sample rate is said to be above the Nyquist rate for that particular signal. In a typical application of sampling, one first chooses the highest frequency to be preserved and recreated, based on the expected content (voice, music, etc.) and desired fidelity. Then one inserts an anti-aliasing filter ahead of the sampler. Its job is to attenuate the frequencies above that limit. Finally, based on the characteristics of the filter, one chooses a sample rate (and corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilinear Transform
The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa. The bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used to convert a transfer function H_a(s) of a linear, time-invariant ( LTI) filter in the continuous-time domain (often called an analog filter) to a transfer function H_d(z) of a linear, shift-invariant filter in the discrete-time domain (often called a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters). It maps positions on the j \omega axis, \mathrm 0 , in the s-plane to the unit circle, , z, = 1 , in the z-plane. Other bilinear transforms can be used to warp the frequency response of any discrete-time linear system (for example to approximate the non-linear frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matched Z-transform Method
The matched Z-transform method, also called the pole–zero mapping or pole–zero matching method, and abbreviated MPZ or MZT, is a technique for converting a continuous-time filter design to a discrete-time filter (digital filter) design. The method works by mapping all poles and zeros of the Laplace transform, ''s''-plane design to Z-transform, ''z''-plane locations z=e^, for a sample interval T=1 / f_\mathrm. So an analog filter with transfer function: :H(s) = k_ \frac is transformed into the digital transfer function : H(z) = k_ \frac The gain k_ must be adjusted to normalize the desired gain, typically set to match the analog filter's gain at DC by Final value theorem, setting s=0 and z=1 and solving for k_. Since the mapping wraps the ''s''-plane's j\omega axis around the ''z''-plane's unit circle repeatedly, any zeros (or poles) greater than the Nyquist frequency will be mapped to an aliased location. In the (common) case that the analog transfer function has more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilinear Transform
The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa. The bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used to convert a transfer function H_a(s) of a linear, time-invariant ( LTI) filter in the continuous-time domain (often called an analog filter) to a transfer function H_d(z) of a linear, shift-invariant filter in the discrete-time domain (often called a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters). It maps positions on the j \omega axis, \mathrm 0 , in the s-plane to the unit circle, , z, = 1 , in the z-plane. Other bilinear transforms can be used to warp the frequency response of any discrete-time linear system (for example to approximate the non-linear frequency ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matched Z-transform Method
The matched Z-transform method, also called the pole–zero mapping or pole–zero matching method, and abbreviated MPZ or MZT, is a technique for converting a continuous-time filter design to a discrete-time filter (digital filter) design. The method works by mapping all poles and zeros of the Laplace transform, ''s''-plane design to Z-transform, ''z''-plane locations z=e^, for a sample interval T=1 / f_\mathrm. So an analog filter with transfer function: :H(s) = k_ \frac is transformed into the digital transfer function : H(z) = k_ \frac The gain k_ must be adjusted to normalize the desired gain, typically set to match the analog filter's gain at DC by Final value theorem, setting s=0 and z=1 and solving for k_. Since the mapping wraps the ''s''-plane's j\omega axis around the ''z''-plane's unit circle repeatedly, any zeros (or poles) greater than the Nyquist frequency will be mapped to an aliased location. In the (common) case that the analog transfer function has more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Signal
In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next. This view of time corresponds to a digital clock that gives a fixed reading of 10:37 for a while, and then jumps to a new fixed reading of 10:38, etc. In this framework, each variable of interest is measured once at each time period. The number of measurements between any two time periods is finite. Measurements are typically made at sequential integer values of the variable "time". A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigma Delta
Sigma Delta () is a collegiate sorority at Dartmouth College Dartmouth College (; ) is a private research university in Hanover, New Hampshire. Established in 1769 by Eleazar Wheelock, it is one of the nine colonial colleges chartered before the American Revolution. Although founded to educate Native A ... in the United States. Founded in May 1977 by national sorority Sigma Kappa as its ''Zeta Lambda chapter'', it was the first sorority to be founded on Dartmouth's campus. Women were not permitted to enroll at Dartmouth until 1972, and women-only slots were an imperative experience for the newly matriculated women. This sorority fulfilled the gap well with this new establishment where women could meet anytime in the course of the week. By the late 1980s Dartmouth's student population had diversified. With this diversification of the student body, the sisterhood of Dartmouth's chapter of Sigma Kappa experienced an influx of women of minorities who wished to have not only a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signal Processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. DSP can involve linear or nonli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
