Digital filters

A process for deriving a z-transform transfer function of a FIR digital filter comprising a plurality of cascaded subfilters, the process comprising the steps of:

• a) determining a target z-transform transfer function for the filter and evaluating therefrom a first set of z-values for which the transfer function is zero,
• b) generating a plurality of different n.sup.th -order polynomials in z.sup.-1 from different combinations of polynomials in z.sup.-1 derived from the zero values of said first set,
• c) quantizing the coefficients of said n.sup.th -order polynomials to generate a plurality of quantized n.sup.th -order polynomials in z.sup.-1,
• d) factorizing each quantized nth order polynomial to evaluate one or more new values of z for which the polynomial is zero,
• e) comparing the zero values of said first set with the new zero values derived from the quantized n.sup.th order polynomials,
• f) retaining or rejecting each quantized, n.sup.th -order polynomial on the basis of the comparison of zero values,
• g) using the retained polynomials to generate a plurality of different trial transfer functions having zero values substantially corresponding to the zero values of the target transfer function,
• h) comparing the trial transfer functions generated at step (g) with the target transfer function, and
• i) selecting one of the trial transfer functions generated in step (g) as a result of the comparison in step (h).