Improving the response of a symmetric nonrecursive digital filter by multiple use of the same filter through ACF shifting/scaling

Abstract

A method is suggested for improving the response of a symmetric nonrecursive digital filter using identical blocks. This is based on shifting and/ or scaling of the Amplitude Change Function (ACF). A new generalized ACF has been derived which has similar characteristics to that of the Kaiser-Hamming Chebyshev ACF but does not require additional correction filters for its implementation. Shifting and scaling of the new ACF are shown to result in further improvement of the response. A method is suggested for varying the cut-off frequency of a digital filter without modifying the coefficients of the prototype filter. This is achieved by interconnecting several copies of the prototype filter and adjusting a few gain factors. A modular hardware implementation scheme and its advantages are illustrated with the help of an example. The concept of ACF is also used for the frequency transformation of digital filters, viz transforming a lowpass filter into a high pass, bandpass or a bandstop filter. The method is extended to obtain variable cut-off and variable centre frequency bandpass/bandstop filters.