New designs of frequency selective FIR digital filters

Fourier series expansion is used to explore the relationship between the coefficients of halfband lowpass and general bandpass FIR digital filters. This relationship is used to derive new designs of band pass/stop and low/high pass MAXFLAT FIR digital filters, from an available design of halfband lowpass MAXFLAT FIR digital filters. The presented designs have explicit formulas for the filter coefficients, and can give infinite number of distinct filters of any finite length. The formulas are modified to obtain a new class of filters, which allow a reduction in the transition bandwidth at the expense of smoothness of the magnitude response, and have a performance comparable to that of the minimax filters.