The frequency-sampling form is developed using (9.50) which uses complex arithmetic.
(a) Using the symmetry conditions of the DFT and root locations, show that (9.50) can be expressed by (9.51) and (9.52) which use real arithmetic.
(b) Develop a MATLAB function [G,sos]=firdf2fs(h) that determines frequency sampling form parameters given in (9.51) and (9.52) given the impulse response in h. The matrix sos should contain second-order section coefficients in the form similar to the tf2sos function while G array should contain the respective gains of second-order sections. Incorporate the coefficients for the H[0] and H[N/2] terms in sos and G arrays.
(c) Verify your function using the frequency-sampling form developed in Example 9.6.
Example 9.6
The samples of the frequency response of a causal narrowband lowpass FIR filter of length N = 33 are given by
