A unified approach to the fast FIR filtering algorithms

Many different fast FIR (finite-impulse response) algorithms are known either based on fast transforms or on fast aperiodic convolution algorithms. Both types of algorithms make use of overlap-add or overlap-save on large data blocks. They lose the multiply-accumulate structure of the FIR filtering process which is best suited for many implementations. To overcome these two problems, a class of fast FIR algorithms, allowing various compromises between arithmetic complexity and regularity of the resulting algorithms, was proposed. It is shown that, by using the Chinese Remainder Theorem on different data lengths, and with different interpolation points, all the main types of algorithms are found, in a unified manner, as special cases of the new one