求:分数阶傅里叶变换的matlab程序,请各位帮帮忙

求:分数阶傅里叶变换的matlab程序,请各位帮帮忙,第1张

function Faf = frft(f, a)

% The fast Fractional Fourier Transform

% input: f = samples of the signal

%a = fractional power

% output: Faf = fast Fractional Fourier transform

error(nargchk(2, 2, nargin))

f = f(:)

N = length(f)

shft = rem((0:N-1)+fix(N/2),N)+1

sN = sqrt(N)

a = mod(a,4)

% do special cases

if (a==0), Faf = freturnend

if (a==2), Faf = flipud(f)returnend

if (a==1), Faf(shft,1) = fft(f(shft))/sNreturnend

if (a==3), Faf(shft,1) = ifft(f(shft))*sNreturnend

% reduce to interval 0.5 <a <1.5

if (a>2.0), a = a-2f = flipud(f)end

if (a>1.5), a = a-1f(shft,1) = fft(f(shft))/sNend

if (a<0.5), a = a+1f(shft,1) = ifft(f(shft))*sNend

% the general case for 0.5 <a <1.5

alpha = a*pi/2

tana2 = tan(alpha/2)

sina = sin(alpha)

f = [zeros(N-1,1) interp(f) zeros(N-1,1)]

% chirp premultiplication

chrp = exp(-i*pi/N*tana2/4*(-2*N+2:2*N-2)'.^2)

f = chrp.*f

% chirp convolution

c = pi/N/sina/4

Faf = fconv(exp(i*c*(-(4*N-4):4*N-4)'.^2),f)

Faf = Faf(4*N-3:8*N-7)*sqrt(c/pi)

% chirp post multiplication

Faf = chrp.*Faf

% normalizing constant

Faf = exp(-i*(1-a)*pi/4)*Faf(N:2:end-N+1)

function xint=interp(x)

% sinc interpolation

N = length(x)

y = zeros(2*N-1,1)

y(1:2:2*N-1) = x

xint = fconv(y(1:2*N-1), sinc([-(2*N-3):(2*N-3)]'/2))

xint = xint(2*N-2:end-2*N+3)

function z = fconv(x,y)

% convolution by fft

N = length([x(:)y(:)])-1

P = 2^nextpow2(N)

z = ifft( fft(x,P) .* fft(y,P))

z = z(1:N)

fs=1000%采样频率

N=1024 %采样点数

n=0:N-1

t=n/fs

f0=100 %信号频率

x=sin(2*pi*f0*t)

y=abs(fft(x,N)) %傅里叶变换后画出幅度谱

plot(y)


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