FIR linear-phase approximations of frequency response 1/(jω) for maximal flatness at an arbitrary frequency ω0,0<ω0<π

In a host of signal processing situations, the desired (ideal) frequency response of the filter is a rational function H˜(ω)=1/(jω) (a digital integrator). In such cases, IIR filters can be exploited but at the sacrifice of linearity of the phase response. However, FIR structures are preferred to the IIR ones due to well-known advantages of the former. We may also essentially require the FIR filter with its magnitude response having maximal flatness at an arbitrary frequency ω₀ in the spectrum (0,π). This article suggests mathematical formulas through which the frequency response H˜(ω) may be approximated by design of a linear-phase, FIR configuration. The approximation may be made maximally flat (in the Butterworth sense) at an arbitrary frequency ω₀ ,0<ω₀<π. A technique to compute the exact weights needed in the design has been given. No fractional delays are used in the proposed design. The application of such designs have also been indicated