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
|
function c=ref_dgt_3(f,g,a,M)
%-*- texinfo -*-
%@deftypefn {Function} ref_dgt_3
%@verbatim
%REF_DGT_3 DGT algorithm 3
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/reference/ref_dgt_3.html}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.2.0
%
% 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 3 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, see <http://www.gnu.org/licenses/>.
L=size(g,1);
N=L/a;
b=L/M;
[c,h_a,h_m]=gcd(-a,M);
p=a/c;
q=M/c;
d=N/q;
w=zeros(M,N);
if 0
% This version uses the definition.
F=zeros(c,d,p,q);
G=zeros(c,d,p,q);
for r=0:c-1
for s=0:d-1
for k=0:p-1
for l=0:q-1
for st=0:d-1
F(r+1,s+1,k+1,l+1)=F(r+1,s+1,k+1,l+1)+f(mod(r+k*M+st*p*M-l*h_a*a,L)+1)*exp(-2*pi*i*s*st/d);
G(r+1,s+1,k+1,l+1)=G(r+1,s+1,k+1,l+1)+g(mod(r+k*M-l*a+st*p*M,L)+1)*exp(-2*pi*i*s*st/d);
end;
end;
end;
end;
end;
for r=0:c-1
for l=0:q-1
for u=0:q-1
for s=0:d-1
for v=0:d-1
for k=0:p-1
w(r+l*c+1,mod(u+s*q-l*h_a,N)+1)=w(r+l*c+1,mod(u+s*q-l*h_a,N)+1)+...
1/d*F(r+1,v+1,k+1,l+1)*conj(G(r+1,v+1,k+1,u+1))*exp(2*pi*i*v*s/d);
end;
end;
end;
end;
end;
end;
else
% This version uses matrix-vector products and ffts
F=zeros(c,d,p,q);
G=zeros(c,d,p,q);
C=zeros(c,d,q,q);
% Set up the matrices
for r=0:c-1
for s=0:d-1
for k=0:p-1
for l=0:q-1
F(r+1,s+1,k+1,l+1)=f(mod(r+k*M+s*p*M-l*h_a*a,L)+1);
G(r+1,s+1,k+1,l+1)=sqrt(M*d)*g(mod(r+k*M-l*a+s*p*M,L)+1);
end;
end;
end;
end;
% fft them
F=dft(F,[],2);
G=dft(G,[],2);
% Multiply them
for r=0:c-1
for s=0:d-1
GM=reshape(G(r+1,s+1,:,:),p,q);
FM=reshape(F(r+1,s+1,:,:),p,q);
C(r+1,s+1,:,:)=GM'*FM;
end;
end;
% Inverse fft
C=idft(C,[],2);
% Place the result
for r=0:c-1
for l=0:q-1
for u=0:q-1
for s=0:d-1
w(r+l*c+1,mod(u+s*q-l*h_a,N)+1)=C(r+1,s+1,u+1,l+1);
end;
end;
end;
end;
end;
c=dft(w);
|
