Method of two-stage FRM filter

A method of constructing a two-stage FRM filter, comprising the following steps of:

• determining, with a processor, a transfer function H(z) of a two-stage FRM filter as follows:
• H(z)=G(z)Hma(1)(z)+(1−G(z))Hmc(1)(z),
• wherein G(z)=Ha(2)(zM)Hma(2)(zP)+(1−Ha(2)(zM))Hmc(2)(zQ), without any constraint among interpolation factors M, P, Q;
• Ha(2)(zM) represents a prototype filter, while Hma(1)(z) and Hmc(1)(z) represent first-stage masking filters, respectively, and Hma(2)(zP) and Hmc(2)(zQ) represent second-stage masking filters, respectively;
• storing the interpolation factors M, P, Q in a memory;
• searching, with a processor, within a search range for [M, P, Q], and for a certain set [M, P, Q], calculating passband and stopband edge parameters of the prototype filter Ha(2)(z), passband and stopband edge parameters of the second-stage masking filters and passband and stopband edge parameters of the first-stage masking filters in Case A and Case B, respectively, on the basis that a transition band of the whole filter is provided by Ha(2)(zM) or a complement of Ha(2)(zM);
• calculating calculating, with a processor, the complexity of the FRM filter according to the calculated passband and stopband edge parameters, and finding out one or more sets [M, P, Q] having the lowest complexity within the search range;
• optimizing, with a processor, an improved FRM filter according to the calculated filter parameters, by determining a number of multipliers implementing the improved FRM filter and a group time delay performed by the improved FRM filter, and
• constructing the improved FRM filter by arranging the multipliers, based on the calculated filter parameters.