A general analysis for the time-invariant multirate digital filter

An analysis is presented for obtaining a general transfer function for a digital filter, with a number of shift sequences in each pulse-repetition interval, as initially described by Fjällbrant. This type of filter has been given the term "multirate filter." The analysis results in a complex convolution integral which is evaluated to produce the transfer function resulting from the multirate processing. Some examples of the use of this technique in certain quantization problems are given.