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Identify discrete-time filter parameters from frequency response data
[b,a] = invfreqz(h,w,n,m)
[b,a] = invfreqz(h,w,n,m,wt)
[b,a] = invfreqz(h,w,n,m,wt,iter)
[b,a] = invfreqz(h,w,n,m,wt,iter,tol)
[b,a] = invfreqz(h,w,n,m,wt,iter,tol,'trace')
[b,a] = invfreqz(h,w,'complex',n,m,...)
invfreqz is the inverse operation of freqz; it finds a discrete-time transfer function that corresponds to a given complex frequency response. From a laboratory analysis standpoint, invfreqz can be used to convert magnitude and phase data into transfer functions.
[b,a] = invfreqz(h,w,n,m) returns the real numerator and denominator coefficients in vectors b and a of the transfer function
$$H(z)=\frac{B(z)}{A(z)}=\frac{b(1)+b(2){z}^{-1}+\cdots +b(n+1){z}^{-n}}{a(1)+a(2){z}^{-1}+\cdots +a(m+1){z}^{-m}}$$
whose complex frequency response is given in vector h at the frequency points specified in vector w. Scalars n and m specify the desired orders of the numerator and denominator polynomials.
Frequency is specified in radians between 0 and π, and the length of h must be the same as the length of w. invfreqz uses conj(h) at -w to ensure the proper frequency domain symmetry for a real filter.
[b,a] = invfreqz(h,w,n,m,wt) weights the fit-errors versus frequency, where wt is a vector of weighting factors the same length as w.
[b,a] = invfreqz(h,w,n,m,wt,iter) and
[b,a] = invfreqz(h,w,n,m,wt,iter,tol) provide a superior algorithm that guarantees stability of the resulting linear system and searches for the best fit using a numerical, iterative scheme. The iter parameter tells invfreqz to end the iteration when the solution has converged, or after iter iterations, whichever comes first. invfreqz defines convergence as occurring when the norm of the (modified) gradient vector is less than tol, where tol is an optional parameter that defaults to 0.01. To obtain a weight vector of all ones, use
invfreqz(h,w,n,m,[],iter,tol)
[b,a] = invfreqz(h,w,n,m,wt,iter,tol,'trace') displays a textual progress report of the iteration.
[b,a] = invfreqz(h,w,'complex',n,m,...) creates a complex filter. In this case no symmetry is enforced, and the frequency is specified in radians between -π and π.