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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[n]. :h[n]=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-li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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) that 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 filter, 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 gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nyquist Frequency
In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a Sampling (signal processing), sampler, which converts a continuous function or signal into a discrete sequence. For a given Sampling (signal processing), sampling rate (''samples per second''), the Nyquist frequency ''(cycles per second'') is the frequency whose cycle-length (or period) is twice the interval between samples, thus ''0.5 cycle/sample''. For example, audio compact disc, CDs have a sampling rate of 44100 ''samples/second''. At ''0.5 cycle/sample'', the corresponding Nyquist frequency is 22050 ''cycles/second'' (hertz, Hz). Conversely, the Nyquist rate for sampling a 22050 Hz signal is 44100 ''samples/second''. When the highest frequency (Bandwidth (signal processing), 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 corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 for converting a transfer function H_a(s) of a linear, time-invariant ( LTI) filter in the continuous-time domain (often named an analog filter) to a transfer function H_d(z) of a linear, shift-invariant filter in the discrete-time domain (often named 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 for warping the frequency response of any discrete-time linear system (for example to approximate the non-linear f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 ''s''-plane design to ''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 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 poles than zeros, the zeros at s=\infty may optio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 for converting a transfer function H_a(s) of a linear, time-invariant ( LTI) filter in the continuous-time domain (often named an analog filter) to a transfer function H_d(z) of a linear, shift-invariant filter in the discrete-time domain (often named 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 for warping the frequency response of any discrete-time linear system (for example to approximate the non-linear f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 ''s''-plane design to ''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 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 poles than zeros, the zeros at s=\infty may optio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 quantiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sigma Delta
Sigma Delta () is a collegiate sorority at Dartmouth College in Hanover, New Hampshire in the United States. History Sigma Delta was founded in May 1977 at Dartmouth College as the ''Zeta Lambda chapter'' of Sigma Kappa national sorority. It was the first sorority to be founded on Dartmouth's campus. Women were not permitted to enroll at Dartmouth until 1972; the sorority provided a place where the college's coed students could meet. By the late 1980s, Dartmouth's student population had diversified and the Sigma Kappa chapter experienced an influx of minority women who wished to have not only a female space, but also a space that would embrace their personal identities as women regardless of age, class, religion, or ethnicity. In the fall of 1988, Dartmouth's Sigma Kappa chapter split from the national organization and became a local sorority. Its members made this decision to move away from "the patriarchal, puritanical and heteronormative conventions ingrained in sororities ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 Sampling (signal processing), 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 signal processing, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
