Notes regarding invfreqsmethod listing in Fig.D.22:

• The basic method is to use invfreqs to find the coefficients of a second-order analog filter having a frequency response close to what we measured. Then, we calculate the and resonance frequency from the simple formulas relating these quantities to the transfer-function coefficients:
  
  where is an arbitrary finite zero location near dc. Finally, using the impulse invariant method (§R.1.1), we map the estimated and to digital biquad coefficients, as shown in the code.

• A useful quantitative measure of filter approximation error can be defined as follows (insert after the call to freqs):

    err = norm(wt(:) .* (db(Hp(:))-db(Hph(:))))/norm(wt(:) .* Hp(:));
    disp(sprintf(['Relative weighted L2 norm of frequency ',
                  'db-magnitude response error = %f'],err));
  

• The minphaseir function for converting a spectrum to its minimum-phase counterpart is listed in Fig.D.23 and discussed in [460].