Code covered by the BSD License

# Fixed Point Radix-4 FFT

### Mike Donovan (view profile)

These functions compute a fixed point radix-4 FFT.You can generate C code from this m-code.

```function S = radix4FFT1_Float(s)
% This is a radix-4 FFT, using decimation in frequency
% The input signal must be floating point
% Works with real or complex input

% Initialize variables and signals
% NOTE: The length of the input signal should be a power of 4: 4, 16, 64, 256, etc.
N = length(s);
M = log2(N)/2;

% Initialize variables for floating point sim
W=exp(-j*2*pi*(0:N-1)/N);
S = complex(zeros(1,N));
sTemp = complex(zeros(1,N));

% FFT algorithm
% Calculate butterflies for first M-1 stages
sTemp = s;
for stage = 0:M-2
for n=1:N/4
S((1:4)+(n-1)*4) = radix4bfly(sTemp(n:N/4:end), floor((n-1)/(4^stage)) *(4^stage), 1, W);
end
sTemp = S;
end

% Calculate butterflies for last stage
for n=1:N/4
S((1:4)+(n-1)*4) = radix4bfly(sTemp(n:N/4:end), floor((n-1)/(4^stage)) * (4^stage), 0, W);
end
sTemp = S;

% Rescale the final output
S = S*N;

end

function Z = radix4bfly(x,segment,stageFlag,W)
% For the last stage of a radix-4 FFT all the ABCD multiplers are 1.
% Use the stageFlag variable to indicate the last stage
% stageFlag = 0 indicates last FFT stage, set to 1 otherwise

% Initialize variables and scale to 1/4
a=x(1)*.25;b=x(2)*.25;c=x(3)*.25;d=x(4)*.25;

A=a+b+c+d;
B=(a-b+c-d)*W(2*segment*stageFlag + 1);
C=(a-b*j-c+d*j)*W(segment*stageFlag + 1);
D=(a+b*j-c-d*j)*W(3*segment*stageFlag + 1);

Z = [A B C D];

end

```