基4 的FFT算法matlab代码

以下是一个基于MATLAB的基4 FFT算法的代码示例：

function y = fft4(x)

% Make sure x has length 4^n
n = length(x);
if mod(log2(n)/log2(4),1) ~= 0
error('Length of input vector is not a power of 4');
end

% Reshape x into a 4 x ... matrix
x = reshape(x, [4 n/4]);

% Compute the DFT of each column
for k = 1:n/4
% First stage of butterfly
a = x(1,k);
b = x(2,k);
c = x(3,k);
d = x(4,k);

% Second stage of butterfly
s1 = a + c;
s2 = b + d;
s3 = a - c;
s4 = b - d;

% Third stage of butterfly
x(1,k) = s1 + s2;
x(2,k) = 1i*(s1 - s2);
x(3,k) = s3 + 1i*s4;
x(4,k) = s3 - 1i*s4;
end

% Compute the DFT of each row
for k = 1:4
x(k,:) = fft(x(k,:));
end

% Reorder the entries
y = zeros(1,n);
for k = 1:n/4
y(4*k-3) = x(1,k);
y(4*k-2) = x(2,k);
y(4*k-1) = x(3,k);
y(4*k) = x(4,k);
end

end

% 示例用法：

x = [1 2 3 4 5 6 7 8];
y = fft4(x);
disp(y);