Fundamental Properties of Non-Negative Impulse Response Filters

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 57; no. 6; pp. 1338 - 1347
• Main Authors: Yuzhe Liu, Bauer, Peter H
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2010; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Attenuation; Character recognition; Charge coupled devices; Circuits; Constrictions; Digital filters; Filter; Finite impulse response filter; Frequency domain analysis; Frequency domains; Frequency response; Frequency spectrum; frequency-domain bounds; Gain; Impulse response; non-negative impulse response (NNIR); Passband; Time domain analysis; time-domain bounds
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2009.2031708

This paper provides insights into some fundamental properties of non-negative impulse response (NNIR) digital filters. In particular, performance restrictions in the frequency domain due to the non-negativity constraint are investigated. It is shown that the gain drop in the frequency response near zero frequency affects the response over the entire frequency spectrum. The passband and stopband gains are shown to be severely limited. It is further shown that stopband and passband locations can be chosen freely with the exception of a mandatory passband around zero. Extensions of the presented results to the continuous-time (C-T) domain as well as duality results are also briefly presented.