Design of low complexity variable digital filters using first order all pass transformation and improved coefficient decimation method

Digital filters that provide variable frequency responses by controlling a small set of parameters are desired in numerous signal processing applications. In this paper, we present a new design technique to obtain variable lowpass, highpass, bandpass and bandstop frequency responses using a single lowpass prototype filter. The proposed variable digital filter (VDF) design technique employs first order all pass transformation and the improved coefficient decimation method (ICDM). ICDM is used to generate the four types of frequency responses and frequency warping using first order all pass transformation is performed to achieve variable cutoff frequencies for the obtained responses. In the proposed VDF, the nature of obtained frequency responses and their cutoff frequencies can be changed on-the-fly without the need of updating the filter coefficients. With the help of a design example, we show that the proposed VDF has a significantly lower implementation complexity when compared with other relevant VDF design methods in literature.