Design of cut off-frequency fixing filters by error compensation of maxflat fir filters

Maximally-flat (MAXFLAT) finite impulse response (FIR) filters often face a problem of the cutoff-frequency error due to approximation of the desired frequency response by some closed-form solution. So far, there have been plenty of efforts to design such a filter with an arbitrarily specified cut off-frequency, but this filter type requires extensive computation and is not MAXFLAT anymore. Thus, a computationally efficient and effective design is needed for highly accurate filters with desired frequency characteristics. This paper describes a new method for designing cutoff-frequency-fixing FIR filters through the cutoff-frequency error compensation of MAXFLAT FIR fil-ters. The proposed method provides a closed-form Chebyshev polynomial containing a cutoff-error compensation function, which can characterize the “cutoff-error-free” filters in terms of the degree of flatness for a given order of filter and cut off-frequency. This method also allows a computationally efficient and accurate formula to directly determine the degree of flatness, so that this filter type has a flat magnitude characteristic both in the passband and the stopband. The remarkable effec-tiveness of the proposed method in design efficiency and accuracy is clearly demonstrated through various examples, indicating that the cutoff-fixing filters exhibit amplitude distortion error of less than 10⁻¹⁴ and no cut off-frequency error. This new approach is shown to provide significant ad-vantages over the previous works in design flexibility and accuracy.