Editing Discrete Fourier transform (section)

==== Convolution ====
When data is [[Convolution|convolved]] with a function with wide support, such as for downsampling by a large sampling ratio, because of the [[Convolution theorem]] and the FFT algorithm, it may be faster to transform it, multiply pointwise by the transform of the filter and then reverse transform it.  Alternatively, a good filter is obtained by simply truncating the transformed data and re-transforming the shortened data set.