轉(zhuǎn)載一個(gè)實(shí)現(xiàn)分?jǐn)?shù)傅立葉變換的matlab程序,作者信息在程序中有。
j#7wyi5q IRlN++I! function FF=frft_PXJ(N,alpha);
FYp|oD2=1 %matrix
UedvA9$&; % FF is the kernel matrix of fractional Fourier transform
+R2^*
*< % \copyright: zjliu
<P|`7wfxE % Author's email:
zjliu2001@163.com -
P\S>G. Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
30A`\+^f variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
t9?R/:B% for k=3:N;
=$^Wkau HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
CWE Ejl end
f@wsSm HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
j5PaSk&o= for k=2:N;
%T`4!:vy HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
Ix*BI9E factorial(k-1)*sqrt(variance));
vh<]aiY end
"V*kOb&'*Z if mod(N,2)==1;
ATKYjhc _ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
4$0jz' else
jz|Wj W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
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