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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 ...
In graph theory, a graph or digraph whose adjacency matrix is circulant is called a circulant graph/digraph. Equivalently, a graph is circulant if its automorphism group contains a full-length cycle. The Möbius ladders are examples of circulant graphs, as are the Paley graphs for fields of prime order.
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 ...
Graph theory: Cyclic function, a periodic function Cycle graph, a connected, 2-regular graph; Cycle graph (algebra), a diagram representing the cycles determined by taking powers of group elements; Circulant graph, a graph with cyclic symmetry; Cycle (graph theory), a nontrivial path in some graph from a node to itself
The overlap-add method involves a linear convolution of discrete-time signals, whereas the overlap-save method involves the principle of circular convolution. In addition, the overlap and save method only uses a one-time zero padding of the impulse response, while the overlap-add method involves a zero-padding for every convolution on each ...
The advantage is that the circular convolution can be computed more efficiently than linear ... Figure 2 is a graph of the values of that minimize ...
English: Circular convolution can be expedited by the FFT algorithm, so it is often used with an FIR filter to efficiently compute linear convolutions. These graphs illustrate how that is possible. Note that a larger FFT size (N) would prevent the overlap that causes graph #6 to not quite match all of #3.
Circulant graphs can be described in several equivalent ways: [2] The automorphism group of the graph includes a cyclic subgroup that acts transitively on the graph's vertices. In other words, the graph has an automorphism which is a cyclic permutation of its vertices. The graph has an adjacency matrix that is a circulant matrix.