Search results
Results from the WOW.Com Content Network
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 ...
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 ...
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.
which gives rise to the interpretation as a circular convolution of and . [7] [8] It is often used to efficiently compute their linear convolution. (see Circular convolution, Fast convolution algorithms, and Overlap-save) Similarly, the cross-correlation of and is given by:
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.
There are many terms in mathematics that begin with cyclic: Cyclic chain rule, for derivatives, used in thermodynamics; Cyclic code, linear codes closed under cyclic permutations; Cyclic convolution, a method of combining periodic functions; Cycle decomposition (graph theory) Cycle decomposition (group theory)
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).
And for any parameter +, [A] it is equivalent to the -point circular convolution of [] with [] in the region [,]. The advantage is that the circular convolution can be computed more efficiently than linear convolution, according to the circular convolution theorem :