invfreqz() - Signal Processing

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 functionH(z)=B(z)A(z)=b(1)+b(2)z−1+⋯+b(n+1)z−na(1)+a(2)z−1+⋯+a(m+1)z−mwhose 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, useinvfreqz(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.

Syntax

[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,...)

Example

invfreqz(h,w,n,m,[],iter,tol)

Output / Return Value

Limitations

Alternatives / See Also

Reference