64点基-4FFT的matlab仿真

% - Fast Fourier Transform [64FFT] clear;clc;clf; N=64; n=0:63; x=0.5*cos(15/200*pi*n)+cos(6/200*pi*n); x1 = zeros(64,1); x2 = zeros(64,1); x3 = zeros(64,1); y = zeros(64,1); % stage 1 for mm = 0:1:15 %radix-4 twiddle1=exp(-2*pi*j*mm*1/64); twiddle2=exp(-2*pi*j*mm*2/64); twiddle3=exp(-2*pi*j*mm*3/64); x1(mm+1) =x(mm+1) +x(mm+17)+x(mm+33) +x(mm+49); x1(mm+17)=(x(mm+1)-j*x(mm+17)-x(mm+33)+j*x(mm+49))*twiddle1; x1(mm+33)=(x(mm+1) -x(mm+17)+x(mm+33) -x(mm+49))*twiddle2; x1(mm+49)=(x(mm+1)+j*x(mm+17)-x(mm+33)-j*x(mm+49))*twiddle3; end; % stage 2 for nn = 0:16:48 for mm = 0:1:3 %radix-4 twiddle1=exp(-2*pi*j*mm*4*1/64); twiddle2=exp(-2*pi*j*mm*4*2/64); twiddle3=exp(-2*pi*j*mm*4*3/64); x2(mm+nn+1) =x1(mm+nn+1) +x1(mm+nn+5)+x1(mm+nn+9) +x1(mm+nn+13); x2(mm+nn+5) =(x1(mm+nn+1)-j*x1(mm+nn+5)-x1(mm+nn+9)+j*x1(mm+nn+13))*twiddle1; x2(mm+nn+9) =(x1(mm+nn+1) -x1(mm+nn+5)+x1(mm+nn+9) -x1(mm+nn+13))*twiddle2; x2(mm+nn+13)=(x1(mm+nn+1)+j*x1(mm+nn+5)-x1(mm+nn+9)-j*x1(mm+nn+13))*twiddle3; end; end; % stage 3 for nn = 0:4:60 x3(nn+1) = x2(nn+1) +x2(nn+2)+x2(nn+3) +x2(nn+4); x3(nn+2) = x2(nn+1)-j*x2(nn+2)-x2(nn+3)+j*x2(nn+4); x3(nn+3) = x2(nn+1) -x2(nn+2)+x2(nn+3) -x2(nn+4); x3(nn+4) = x2(nn+1)+j*x2(nn+2)-x2(nn+3)-j*x2(nn+4); end; % reorder for n2 = 0:3 for n1 = 0:3 for n0 = 0:3 y(16*n0+4*n1+n2+1)=x3(16*n2+4*n1+n0+1); end; end; end; X=fft(x); real1=abs(y); imag1=angle(y); k=0:length(real1)-1; subplot(221); stem(k,real1,'.'); title('64点-基4'); xlabel('k');ylabel('|X(k)|'); k=0:length(imag1)-1; subplot(222); stem(k,imag1,'.'); xlabel('k');ylabel('θ(k)'); real2=abs(X); imag2=angle(X); k=0:length(real2)-1; subplot(223); stem(k,real2,'.'); title('64点FFT'); xlabel('k');ylabel('|X(k)|'); k=0:length(imag2)-1; subplot(224); stem(k,imag2,'.'); xlabel('k');ylabel('θ(k)');