FREQUENCY-RESPONSE MASKING APPROACH FOR THE SYNTHESIS OF SHARP LINEAR PHASE DIGITAL FILTERS.

Abstract

If each delay element of a linear-phase, low-pass digital filter is replaced by M delay elements, an (M plus 1)-band filter is produced. The transition-width of this (M plus 1)-band filter is 1/M that of the prototype low-pass filter. A complementary filter can be obtained by subtracting the output of the (M plus 1)-band filter from a suitably delayed version of the input. The complementary filter is an (M plus 1)-band filter whose passbands and stopbands are the stopbands and passbands, respectively, of the original (M plus 1)-band filter. If the frequency responses of the original (M plus 1)-band filter and its complementary filter are properly masked and recombined, a narrow transition-band filter can be obtained. This techniques can be used to design sharp low-pass, high-pass, bandpass, and bandstop filters with arbitrary passband bandwidth.