Higher radix aperiodic-convolution algorithms

Two alternative methods are proposed which can be used to derive efficient aperiodic-convolution algorithms for all filter lengths up to 36. A nesting technique is then described by which algorithms of this class can be used to derive efficient aperiodic-convolution algorithms for over 60 percent of the filter lengths in the range 37-1296. The computational complexity of the new algorithms is studied and formulas are derived for the required numbers of multiplications and additions. The contribution concludes with a comparison which clearly illustrates that the new methods lead to algorithms which are more efficient than algorithms based on the fast Fourier transform or rectangular transform for filter lengths up to 1296 for the case where the data block length is equal to the filter length.