A low-pass-bandpass transform for arithmetical symmetry in digital filters

Abstract

For shaped filter functions, such as Gaussian and raised cosine filter shapes, the bandpass digital filter design based on the wellknown low-pass-bandpass transformation shows asymmetry except for two choices of center frequency, thus making a filter bank of equal symmetrical filters or a bandpass filter with variable center not realizable. Another low-pass-bandpass transformation formulated by Broome can be shown to give either symmetrical bandpass filters or filters with a small but known symmetry error across the passband. It can also be shown that the bandpass recursive digital filters realized with the Broome transformation will have real coefficients and will always be stable filters, as the filter poles are obtained from the low-pass filter poles by rotation in the z-plane. The zero locations however, are to be evaluated, and a theorem has been developed on the minimum number of real zeros to be found.