import numarray as N import numarray.fft as F def czt(x, m=None, w=None, a=1.0, axis = -1): """ Copyright (C) 2000 Paul Kienzle This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 US usage y=czt(x, m, w, a) Chirp z-transform. Compute the frequency response starting at a and stepping by w for m steps. a is a point in the complex plane, and w is the ratio between points in each step (i.e., radius increases exponentially, and angle increases linearly). To evaluate the frequency response for the range f1 to f2 in a signal with sampling frequency Fs, use the following: m = 32; ## number of points desired w = exp(-2i*pi*(f2-f1)/(m*Fs)); ## freq. step of f2-f1/m a = exp(2i*pi*f1/Fs); ## starting at frequency f1 y = czt(x, m, w, a); If you don't specify them, then the parameters default to a Fourier transform: m=length(x), w=exp(2i*pi/m), a=1 Because it is computed with three FFTs, this will be faster than computing the Fourier transform directly for large m (which is otherwise the best you can do with fft(x,n) for n prime). TODO: More testing---particularly when m+N-1 approaches a power of 2 TODO: Consider treating w,a as f1,f2 expressed in radians if w is real """ # Convenience declarations ifft = F.inverse_fft fft = F.fft do_transpose = (axis != -1) and (x.rank > 1) # transpose data to make it equivalent to axis=-1 if axis < 0: axis += x.rank if do_transpose: axes = N.arange(x.rank) axes[[axis, x.rank-1]] = axes[[x.rank-1, axis]] x = N.transpose(x, axes) if m is None: m = x.shape[-1] if w is None: w = N.exp(2j*N.pi/m) n = x.shape[-1] k = N.arange(m, type=N.Float64) Nk = N.arange(-(n-1), m-1, type=N.Float64) nfft = next2pow(min(m,n) + len(Nk) -1) Wk2 = w**(-(Nk**2)/2) # length = m + len(x) AWk2 = a**(-k) * w**((k**2)/2) # length = m y = ifft(fft(Wk2,nfft) * fft(x * N.resize(AWk2, x.shape), nfft)); y = N.take(y, range(n,m+n), axis=-1) # [n:m+n] y = N.resize(w**((k**2)/2), y.shape) * y if do_transpose: y.transpose(axes) return y def next2pow(x): return 2**int(N.ceil(N.log(float(x))/N.log(2.0)))