LINEAR PHASE FIR APPROXIMATION OF MAGNITUDE RESPONSE |1/ω| FOR MAXIMAL FLATNESS AT AN ARBITRARY FREQUENCY ω_o, O<ω_o<π*

摘要

In may signal processing situations, the desired (ideal) magnitude response of the filter is rational function: H(ω)=|1/ω| (a digital integrator). The requirements of a linear phase response and guaranteed stable performance limit the design to finite impulse response (FIR) structure. In may 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 frequency ω _o in the spectrum (0,π). No techniques for meeting such requirements with respect to approximation of H(ω) are known in the literature. This paper suggests a design by which the linear phase magnitude response |H(ω| can be approximated by an FIR configuration viving a maximally flat (in the Butterworth sense) response at an arbitrary frequency ω_o, O<ω_o <π. A technique to compute exact weights for the design has also been given.