THE COMPLEX DIGITAL FILTER AND ITS APPLICATIONS IN DIGITAL SIGNAL PROCESSING

Abstract

Digital computer simulation of communication systems have been gaining wide acceptance and usage as a tool for analysis. In some cases, when the number of independent parameters is large or the processes are highly nonlinear, it is the only viable technique. In most digital computer simulations, the digital representation of bandpass filters can impose serious synthesis problems when conventional digital filter synthesis techniques are utilized. It is shown that the use of a complex (real and imaginary) technique of digital filter synthesis can eliminate several of the synthesis problems associated with conventional techniques. Three applications of the com lex technique are described in this paper. The three applications discussed in this paper are listed below with a short description of each. 1. A lowpass-to-bandpass transformation is described that preserves all lowpass characteristics of the filter. For instance the gain and group delay functions remain symmetrical for any center frequency and bandwidth. 2. The synthesis of analytic representations of real signals can be easily achieved by the use of a complex digital filter. An important advantage of analytic signals is that their envelope and phase are instantaneously available. 3. Equalization of bandpass characteristics can be effected at lowpass and then shifted to the proper frequency without any undesirable warping effects. Complex digital filter synthesis has been described previously, but very little emphasis has been placed on the application of this technique. Advances in the art of miniature high speed digital circuitry will allow the advantages of complex filtering to be realized in actual systems as well as digital simulations.