## [39b069]: gabor / tfmat.m  Maximize  Restore  History

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 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201``` ```function F=tfmat(ttype,p2,p3,p4,p5) %TFMAT Matrix of transform / operator % Usage: F=tfmat('fourier',L); % F=tfmat('dcti',L); % F=tfmat('dgt',g,a,M); % F=tfmat('dwilt',g,M); % F=tfmat('wmdct',g,M); % F=tfmat('zak',L,a); % F=tfmat('gabmul',sym,a); % F=tfmat('spread',c); % % `tfmat` returns a matrix *F* containing the basis functions / atoms of % one of the transforms in the toolbox. The atoms are placed as column % vectors in the matrix. A forward transform (analysis) can be done by:: % % c=F'*f; % % and a backwards or adjoint transform (synthesis) can be done by:: % % r=F*c; % % The possibilities are: % % `tfmat('fourier',L)` returns the matrix of the unitary Fourier % transform of length *L*. See |dft|_. % % `tfmat('dcti',L)` returns the matrix of the DCTI transform of length % *L*. Similarly for `'dctii'`, `'dctiii'`, `'dctiv'`, `'dsti'`, `'dstii'`, % `'dstiii'` or `'dstiv'`. % % `tfmat('dgt',g,a,M)` returns a matrix containing all the atoms of the % Gabor frame with window g and lattice constants *a* and *M*. % `tfmat('dgt',g,a,M,L)` will do the same for a FIR window *g*. % % `tfmat('dwilt',g,M)` returns a matrix containing all the atoms of the % Wilson basis with window *g* and *M* channels. `tfmat(g,M,L)` will do the % same for a FIR window *g*. % % `tfmat('wmdct',g,M)` and `tfmat('wmdct',g,M,L)` does the same for an WMDCT % with *M* channels. % % `tfmat('gabmul',sym,a)` return the matrix of the Gabor multiplier with % symbol sym and time shift *a*. `tfmat('gabmul',c,g,a)` does the same using % the window *g* for both analysis and % synthesis. `tfmat('gabmul',sym,ga,gs,a)` does the same using *ga* as % analysis window and *gs* as synthesis window. % % `tfmat('spread',c)` returns the matrix of the spreading operator with % symbol *c*. % % `tfmat('zak',L,a)` returns the transform matrix for a Zak transform of % length *L* and parameter *a*. % % This function should mainly be used for educational purposes or for % experimenting with systems, as the generated matrix can % become very large. % % See also: dft, dcti, dsti, dgt, dwilt, wmdct, gabmul, spreadop if (nargin<1) || ~ischar(ttype) error('You must specify the transform type') end; switch(lower(ttype)) case {'fourier','dft'} error(nargchk(2,2,nargin)); F=idft(eye(p2)); case {'dcti'} error(nargchk(2,2,nargin)); F=dcti(eye(p2))'; case {'dctii'} error(nargchk(2,2,nargin)); F=dctii(eye(p2))'; case {'dctiii'} error(nargchk(2,2,nargin)); F=dctiii(eye(p2))'; case {'dctiv'} error(nargchk(2,2,nargin)); F=dctiv(eye(p2))'; case {'dsti'} error(nargchk(2,2,nargin)); F=dsti(eye(p2))'; case {'dstii'} error(nargchk(2,2,nargin)); F=dstii(eye(p2))'; case {'dstiii'} error(nargchk(2,2,nargin)); F=dstiii(eye(p2))'; case {'dstiv'} error(nargchk(2,2,nargin)); F=dstiv(eye(p2))'; case {'gabor','dgt'} error(nargchk(4,5,nargin)); g=p2; if nargin==4 L=length(g); else L=p5; end; a=p3; M=p4; N=L/a; c=reshape(eye(M*N),M,N,M*N); F=idgt(c,g,a); case {'wilson','dwilt'} error(nargchk(3,4,nargin)); g=p2; if nargin==3 L=length(g); else L=p4; end; M=p3; N=L/M; c=reshape(eye(M*N),2*M,N/2,M*N); F=idwilt(c,g); case {'wmdct'} error(nargchk(3,4,nargin)); g=p2; if nargin==3 L=length(g); else L=p4; end; M=p3; N=L/M; c=reshape(eye(M*N),M,N,M*N); F=iwmdct(c,g); case {'spread','spreadop'} error(nargchk(2,2,nargin)); c=p2; L=size(c,2); F=spreadop(eye(L),c); case {'gabmul'} error(nargchk(3,5,nargin)); sym=p2; M=size(sym,1); N=size(sym,2); switch(nargin) case 3 a=p3; L=a*N; F=gabmul(eye(L),sym,a); case 4 g=p3; a=p4; L=a*N; F=gabmul(eye(L),sym,g,a); case 5 ga=p3; gs=p4; a=p5; L=a*N; F=gabmul(eye(L),sym,ga,gs,a); end; case {'ndgt'} error(nargchk(5,5,nargin)); g=p2; a=p3; M=p4; L=p5; %!!! the computation using eye matrix doesn't work if M>sigLen N=length(a); % number of time positions MN=sum(M); % total number of frame elements F=zeros(L,MN); jj=0; for ii=1:N c={eye(M(ii))}; F(:,jj+(1:M(ii)))=indgt(c,g(ii),a(ii),L); jj=jj+M(ii); end case {'zak'} error(nargchk(3,5,nargin)) L=p2; a=p3; N=L/a; c=reshape(eye(L),a,N,L); F=izak(c); otherwise error('Unknown transform.'); end; ```