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zoomfft

PURPOSE ^

ZOOMFFT DTFT evaluated over a linear frequency range Y=(X,N,M,S,D)

SYNOPSIS ^

function [y,f]=zoomfft(x,n,m,s,d)

DESCRIPTION ^

ZOOMFFT    DTFT evaluated over a linear frequency range Y=(X,N,M,S,D)
 Inputs:
    x    vector (or matrix)
    n    reciprocal of normalized frequency increment (can be non-integer).
         The frequency increment is fs/n where fs is the sample frequency
         [default n=size(x,d)]
    m    mumber of output points is floor(m) [default m=n]
    s    starting frequency index (can be non-integer).
         The starting frequency is s*fs/n [default s=0]
    d    dimension along which to do fft [default d=first non-singleton]

 Outputs:
    y       Output dtft coefficients. y has the same dimensions as x except
            that size(y,d)=floor(m).
    f(1,m)  normalized frequencies (1 corresponds to fs)

 This routine allows the evaluation of the DFT over an arbitrary range of
 frequencies; as its name implies this lets you zoom into a narrow portion
 of the spectrum.
 The DTFT of X will be evaluated along dimension D at the M frequencies
 f=fs*(s+(0:m-1))/n where fs is the sample frequency. Note that N and S
 need not be integers although M will be rounded down to an integer.
 Thus zoomfft(x,n,n,0,d) is equivalent to fft(x,n,d) for n>=length(x).

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function [y,f]=zoomfft(x,n,m,s,d)
0002 %ZOOMFFT    DTFT evaluated over a linear frequency range Y=(X,N,M,S,D)
0003 % Inputs:
0004 %    x    vector (or matrix)
0005 %    n    reciprocal of normalized frequency increment (can be non-integer).
0006 %         The frequency increment is fs/n where fs is the sample frequency
0007 %         [default n=size(x,d)]
0008 %    m    mumber of output points is floor(m) [default m=n]
0009 %    s    starting frequency index (can be non-integer).
0010 %         The starting frequency is s*fs/n [default s=0]
0011 %    d    dimension along which to do fft [default d=first non-singleton]
0012 %
0013 % Outputs:
0014 %    y       Output dtft coefficients. y has the same dimensions as x except
0015 %            that size(y,d)=floor(m).
0016 %    f(1,m)  normalized frequencies (1 corresponds to fs)
0017 %
0018 % This routine allows the evaluation of the DFT over an arbitrary range of
0019 % frequencies; as its name implies this lets you zoom into a narrow portion
0020 % of the spectrum.
0021 % The DTFT of X will be evaluated along dimension D at the M frequencies
0022 % f=fs*(s+(0:m-1))/n where fs is the sample frequency. Note that N and S
0023 % need not be integers although M will be rounded down to an integer.
0024 % Thus zoomfft(x,n,n,0,d) is equivalent to fft(x,n,d) for n>=length(x).
0025 
0026 % [1] L.R.Rabiner,  R.W.Schafer and C.M.Rader, "The chirp z-transform algorithm"
0027 %     IEEE Trans. Audio Electroacoustics 17 (2), 8692 (1969).
0028 
0029 %      Copyright (C) Mike Brookes 2007
0030 %      Version: $Id: zoomfft.m 8556 2016-09-22 08:17:18Z dmb $
0031 %
0032 %   VOICEBOX is a MATLAB toolbox for speech processing.
0033 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
0034 %
0035 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0036 %   This program is free software; you can redistribute it and/or modify
0037 %   it under the terms of the GNU General Public License as published by
0038 %   the Free Software Foundation; either version 2 of the License, or
0039 %   (at your option) any later version.
0040 %
0041 %   This program is distributed in the hope that it will be useful,
0042 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0043 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0044 %   GNU General Public License for more details.
0045 %
0046 %   You can obtain a copy of the GNU General Public License from
0047 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0048 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0049 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0050 persistent n0 k0 s0 m0 b c h g
0051 e=size(x);
0052 p=prod(e);
0053 if nargin<5
0054     d=find(e>1);
0055     if ~isempty(d)
0056         d=d(1);
0057     else
0058         d=1;
0059     end
0060 end
0061 k=e(d);
0062 q=p/k;
0063 if d==1
0064     z=reshape(x,k,q);
0065 else
0066     z=shiftdim(x,d-1);
0067     r=size(z);
0068     z=reshape(z,k,q);
0069 end
0070 if nargin<2 || isempty(n)
0071     n=k;
0072 end
0073 if nargin<3 || isempty(m)
0074     m=floor(n);
0075 else
0076     m=floor(m);
0077 end
0078 if nargin<4 || isempty(s)
0079     s=0;
0080 end
0081 l=pow2(nextpow2(m+k-1));    % round up to next power of 2
0082 if n==fix(n) && s==fix(s) && n<2*l && n>=k
0083     a=fft(z,n,1);           % quickest to do a normal fft
0084     y=a(1+mod(s:s+m-1,n),:);
0085 else
0086     % can precaluclate all this for fixed n, k, s and m
0087     if isempty(b) || n~=n0 || k~=k0 || s~=s0 || m~=m0
0088         n0=n;
0089         k0=k;
0090         s0=s;
0091         m0=m;
0092         b=exp(1i*pi*mod((s+(1-k:m-1)').^2,2*n)/n);
0093         c=conj(b(k:k+m-1));
0094         h=fft(b,l,1);
0095         g=exp(-1i*pi*mod(((0:k-1)').^2,2*n)/n);
0096     end
0097     a=ifft(fft(z.*repmat(g,1,q),l,1).*repmat(h,1,q)); % calculate correlation
0098     y=a(k:k+m-1,:).*repmat(c,1,q);
0099 end
0100 if d==1
0101     e(d)=m;
0102     y=reshape(y,e);
0103 else
0104     r(1)=m;
0105     y=shiftdim(reshape(y,r),length(e)+1-d);
0106 end
0107 f=(s+(0:m-1))/n;

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