Design of high-speed digital filters suitable for multi-DSP implementation

Abstract

A multipath signal processing scheme is proposed to overcome the limitation on the throughput rate of present day available LSI devices which is specifically suitable for implementation using a number of Digital Signal Processors (DSP). Two methods are proposed to realize a given transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(z)</tex> of digital filter, with a throughput rate speed up factor of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> , over the conventional methods. The first method, called Delayed Multipath Approach here, uses an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -path structure as a building element. These <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> elements are connected successively with increasing delay units to realize a given transfer function. The second method preprocesses the input signal sequence by an FFT processor and follows it up by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> of constituent transfer functions derived from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H(z)</tex> having real coefficients. The output of these <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> constituent transfer functions are finally postprocessed by inverse FFT processor to obtain the desired output signal. The number of the constituent transfer functions are double for a special case when the transfer function to be implemented has complex valued coefficients. These two methods serve as complementary approaches, because the first method is better suited for small values of the speed-up factor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> and the second one has distinct advantage for larger values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> . The discussion of the first design method is organized in two parts: FIR filter design and IIR filter design, for each of which 2-path and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> -path structures are separately explained. The second design method is discussed under the headings of real transfer function and complex transfer function. Design examples are also given to illustrate both of these two methods. Finally, a multi-DSP hardware system is outlined which is specifically designed for implementing the multipath structures discussed here.