Symmetric Convolution - Advantages of Symmetric Convolutions

Advantages of Symmetric Convolutions

There are a number of advantages to computing symmetric convolutions in DSTs and DCTs in comparison with the more common circular convolution with the Fourier transform.

Most notably the implicit symmetry of the transforms involved is such that only data unable to be inferred through symmetry is required. For instance using a DCT-II, a symmetric signal need only have the positive half DCT-II transformed, since the frequency domain will implicitly construct the mirrored data comprising the other half. This enables larger convolution kernels to be used with the same cost as smaller kernels circularly convolved on the DFT. Also the boundary conditions implicit in DSTs and DCTs create edge effects that are often more in keeping with neighbouring data than the periodic effects introduced by using the Fourier transform.