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  2. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    In digital signal processing, convolution is ... the joint distribution function can be obtained using the convolution theory. ... A collection of 18 lectures in pdf ...

  3. Circular convolution - Wikipedia

    en.wikipedia.org/wiki/Circular_convolution

    Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT). In particular, the DTFT of the product of two discrete sequences ...

  4. Convolution theorem - Wikipedia

    en.wikipedia.org/wiki/Convolution_theorem

    In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain).

  5. Overlap–add method - Wikipedia

    en.wikipedia.org/wiki/Overlap–add_method

    The following is a pseudocode of the algorithm: (Overlap-add algorithm for linear convolution) h = FIR_filter M = length(h) Nx = length(x) N = 8 × 2^ceiling( log2(M) ) (8 times the smallest power of two bigger than filter length M.

  6. Overlap–save method - Wikipedia

    en.wikipedia.org/wiki/Overlap–save_method

    where:. DFT N and IDFT N refer to the Discrete Fourier transform and its inverse, evaluated over N discrete points, and; L is customarily chosen such that N = L+M-1 is an integer power-of-2, and the transforms are implemented with the FFT algorithm, for efficiency.

  7. Algebraic signal processing - Wikipedia

    en.wikipedia.org/wiki/Algebraic_signal_processing

    Algebraic signal processing (ASP) is an emerging area of theoretical signal processing (SP). In the algebraic theory of signal processing, a set of filters is treated as an (abstract) algebra, a set of signals is treated as a module or vector space, and convolution is treated as an algebra representation.

  8. Nyquist–Shannon sampling theorem - Wikipedia

    en.wikipedia.org/wiki/Nyquist–Shannon_sampling...

    The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.

  9. Matched filter - Wikipedia

    en.wikipedia.org/wiki/Matched_filter

    Though we most often express filters as the impulse response of convolution systems, as above (see LTI system theory), it is easiest to think of the matched filter in the context of the inner product, which we will see shortly. We can derive the linear filter that maximizes output signal-to-noise ratio by invoking a geometric argument.