Digital filters for sample-rate reduction

The design of bandwidth-limiting filters for the purpose of sample-rate reduction is considered. Realization of linear-phase finite-duration impulse-response (FIR) filters for this application by direct convolution is shown to be more efficient than the recursive realization [1]. The degree to which the Nyquist rate (relative to the desired signal bandwidth) must be exceeded at the filter output in order to avoid aliasing is suggested as a measure of filter effectiveness. Direct convolution is faster than the fast convolution for FIR equiripple [2] filters designed to operate within 10 percent of the Nyquist rate with 60- to 70-dB stopband attenuation at a 2:1 sample-rate reduction. This advantage improves with the log of the sample-rate reduction ratio. Several comparisons made with recursive realizations of elliptic filters give the advantage to direct convolutional realization of FIR filters for sampling within about 20 percent of the Nyquist rate at 60- to 70-dB attenuation. Elliptic filters become more efficient at higher complexities (of about eight poles and eight zeros). Two design techniques that exploit the reduced output sample rate in the design of FIR filters by direct convolution are suggested. The effects of quantization of FIR filter coefficients on the frequency response are considered and several examples illustrated.