by Dr. Jaydeep T. Vagh In mathematics, an integral transform maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain. The solution is then mapped back to the original domain using the inverse of the integral transform. General form An …
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Impulse invariance
by Dr. Jaydeep T. Vagh 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 …
Advanced z-transform
by Dr. Jaydeep T. Vagh In mathematics and signal processing, the advanced z-transform is an extension of the z-transform, to incorporate ideal delays that are not multiples of the sampling time. It takes the form where T is the sampling period m (the “delay parameter”) is a fraction of the sampling period [ 0,T.] It …
Constant-Q transform
by Dr. Jaydeep T. Vagh In mathematics and signal processing, the constant-Q transform transforms a data series to the frequency domain. It is related to the Fourier transform[1] and very closely related to the complex Morlet wavelet transform. The transform can be thought of as a series of logarithmically spaced filters fk, with the k-th …
Discrete-time Fourier transform
by Dr. Jaydeep T. Vagh In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose …
Discrete Fourier transform
by Dr. Jaydeep T. Vagh That mathematical knowledge only parpose in Signal processing In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the …
Bilinear transform(Signal processing)
by Dr. Jaydeep T. Vagh Discrete-time approximation The bilinear transform is a first-order approximation of the natural logarithm function that is an exact mapping of the z-plane to the s-plane. When the Laplace transform is performed on a discrete-time signal (with each element of the discrete-time sequence attached to a correspondingly delayed unit impulse), the …
Signal sampling(Signal processing)
by Dr. Jaydeep T. Vagh 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 …
Digital signal processing
by Dr. Jaydeep T. Vagh 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 signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain …
Discrete time and continuous time
by Dr. Jaydeep T. Vagh In mathematics and, in particular, mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time. 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 …
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