Frequency response method and apparatus

An apparatus for filtering a temporal signal, the apparatus comprising a digital signal processing device comprising:

• a target magnitude frequency response specifier configured to specify a target magnitude frequency response HT(f) of frequency f in terms of a column vector l of a number K of weights lk where log HT(f)=lTW(f) where lT is a vector transpose of l and W(f) is a column vector of K magnitude basis functions Wk(f);
• a constrained frequency response determiner programmed to compute a constrained frequency response Hc(f) defined by log Hc(f)=gT V(f), where V(f) is a column vector of a number N of constrained basis functions Vn(f) for which each exp gnVn(f) satisfies a constraint preserved by concatenation, and g is a column vector of N coefficients satisfying a matching criterion between lTW(f) and gT V(f), where gT is a vector transpose of g;
• an input temporal signal receiver interface to receive an input temporal signal;
• a filter to filter the input temporal signal with the constrained frequency response Hc(f) to form a filtered temporal signal;
• and
• a filtered temporal signal output interface to output the filtered temporal signal.