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  2. 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 ...

  3. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    The most common fast convolution algorithms use fast Fourier transform (FFT) algorithms via the circular convolution theorem. Specifically, the circular convolution of two finite-length sequences is found by taking an FFT of each sequence, multiplying pointwise, and then performing an inverse FFT. Convolutions of the type defined above are then ...

  4. Circulant matrix - Wikipedia

    en.wikipedia.org/wiki/Circulant_matrix

    Using the circular convolution theorem, we can use the discrete Fourier transform to transform the cyclic convolution into component-wise multiplication = () = so that = [((()) (()))]. This algorithm is much faster than the standard Gaussian elimination , especially if a fast Fourier transform is used.

  5. Overlap–add method - Wikipedia

    en.wikipedia.org/wiki/Overlap–add_method

    Hence the cost of the overlap–add method scales almost as (⁡) while the cost of a single, large circular convolution is almost (⁡). The two methods are also compared in Figure 3, created by Matlab simulation.

  6. Discrete Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Discrete_Fourier_transform

    As seen above, the discrete Fourier transform has the fundamental property of carrying convolution into componentwise product. A natural question is whether it is the only one with this ability. It has been shown [9] [10] that any linear transform that turns convolution into pointwise product is the DFT up to a permutation of coefficients ...

  7. Multidimensional discrete convolution - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_discrete...

    The premise behind the circular convolution approach on multidimensional signals is to develop a relation between the Convolution theorem and the Discrete Fourier transform (DFT) that can be used to calculate the convolution between two finite-extent, discrete-valued signals. [7]

  8. 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.

  9. 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 ).