Fundamental properties of non-negative impulse response filters — Theoretical bounds I

This paper presents several fundamental frequency-domain bounds for a non-negative impulse response (NNIR) filter. Upper-bounds on power spectral attenuation and power spectral gain in geometrically spaced frequency regions are derived, when power spectral attenuation near frequency zero is limited. By analyzing the tightnesses of these bounds, the relationship between the maximally allowable power attenuation and gain is also treated. All results hold for both continuous and discrete-time domains.