Efficient computation of aliasing noise in down-sampling filters

The author describes an efficient algorithm for evaluating the frequency response of the aliased noise in FIR (finite impulse response) down-sampling filters. The algorithm uses Parseval´s theorem and an index-mapped DFT (discrete Fourier transform) decomposition to obtain the resolution of an MK-point transform using only K transforms of length M, where K is the down-sampling factor and 1/M is the desired frequency resolution in the down-sampled domain. For real symmetric FIR filters the symmetries in the spectrum can be exploited to reduce the computation by another factor of four. The algorithm was used to evaluate the frequency response and expected aliasing noise for a low-pass filter designed to be decimated by 128