Here is another implementation of the Chirp-Z transform in Python,
that handles complex numbers.
Regards
Stéfan
On Thu, Mar 15, 2007 at 11:53:49AM +0200, Nadav Horesh wrote:
> A long time ago I translated a free code of chirp z transform (zoom fft) into
> python.
> Attached here the source and two translations (probably one of the is right)
>
> Nadav.
>
> On Wed, 2007-03-14 at 14:02 -0800, Ray S wrote:
>
> We'd like to do what most call a "zoom FFT"; we only are interested
> in the frequencies of say, 6kHZ to 9kHz with a given N, and so the
> computations from DC to 6kHz are wasted CPU time.
> Can this be done without additional numpy pre-filtering computations?
"""Chirp z-Transform.
As described in
Rabiner, L.R., R.W. Schafer and C.M. Rader.
The Chirp z-Transform Algorithm.
IEEE Transactions on Audio and Electroacoustics, AU-17(2):86--92, 1969
"""
import numpy as np
def chirpz(x,A,W,M):
"""Compute the chirp z-transform.
The discrete z-transform,
X(z) = \sum_{n=0}^{N-1} x_n z^{-n}
is calculated at M points,
z_k = AW^-k, k = 0,1,...,M-1
for A and W complex, which gives
X(z_k) = \sum_{n=0}^{N-1} x_n z_k^{-n}
"""
A = np.complex(A)
W = np.complex(W)
if np.issubdtype(np.complex,x.dtype) or np.issubdtype(np.float,x.dtype):
dtype = x.dtype
else:
dtype = float
x = np.asarray(x,dtype=np.complex)
N = x.size
L = int(2**np.ceil(np.log2(M+N-1)))
n = np.arange(N,dtype=float)
y = np.power(A,-n) * np.power(W,n**2 / 2.) * x
Y = np.fft.fft(y,L)
v = np.zeros(L,dtype=np.complex)
v[:M] = np.power(W,-n[:M]**2/2.)
v[L-N+1:] = np.power(W,-n[N-1:0:-1]**2/2.)
V = np.fft.fft(v)
g = np.fft.ifft(V*Y)[:M]
k = np.arange(M)
g *= np.power(W,k**2 / 2.)
return g
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