Linear phase FIR approximation of magnitude response |1/ω| for maximal flatness at an arbitrary frequency ω₀, 0<ω₀<π^*

Abstract

In many signal processing situations, the desired (ideal) magnitude response of the filter is a rational function:$\tilde H(\omega ) = |1/\omega |$ (a digital integrator). The requirements of a linear phase response and guaranteed stable performance limit the design to a finite impulse response (FIR) structure. In many applications we require the FIR filter to yield a highly accurate magnitude response for a narrow band of frequencies with maximal flatness at an arbitrary frequencyω ₀ in the spectrum (0, π). No techniques for meeting such requirements with respect to approximation of$\tilde H(\omega )$ are known in the literature. This paper suggests a design by which the linear phase magnitude response$|\tilde H(\omega )|$ can be approximated by an FIR configuration giving a maximally flat (in the Butterworth sense) response at an arbitrary frequency ω₀, 0<ω₀<π^*. A technique to compute exact weights for the design has also been given.