Nonrecursive digital filtering using cascade fast Fourier transformers

Abstract

The organization of a special-purpose digital processor for performing nonrecursive digital filtering is described. The processor uses two complementary cascade fast Fourier transformers. Each transformer can simultaneously transform two independent data blocks of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> words using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\log_{2} N</tex> arithmetic units and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3/2 N</tex> complex words of digital storage. Continuous filtering is achieved by sectioning the input signal, performing a fast transform on each section, multiplying by the frequency characteristics of the desired filter, and inverse transforming. The cascade organization of the processor allows processing at very high speeds. Word rates in excess of 3 MHz are possible with currently available hardware.