Frequency Domain Limitations in the Design of Nonnegative Impulse Response Filters

This paper provides a fundamental characterization of nonnegative impulse response (NNIR) filters. The analysis is performed in terms of both geometrically and equidistantly spaced frequencies. Various inferences on the frequency domain limitations in NNIR filter design are analyzed. It is found that a performance boundary exists for NNIR lowpass filters independent of the system order. A specification test procedure is also provided for NNIR lowpass filters based on these analyses. The results are presented for systems in the discrete-time (D-T) domain, although equivalent results exist for systems in the continuous-time domain.