Fundamental Properties of Non-Negative Impulse Response Filters

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.