以下の Octave radix-4
FFT コードは、(xp) 値の累乗を4
ケースバイケースで設定すると正常に動作します。
$ octave fft4.m
ans = 1.4198e-015
ただし、ループコードのコメントを外すと、次のエラーが発生します
$ octave fft4.m
error: `stage' undefined near line 48 column 68
error: evaluating argument list element number 1
error: evaluating argument list element number 2
error: called from:
error: r4fftN at line 48, column 22
error: c:\Users\david\Documents\Visual Studio 2010\Projects\mv_fft\fft4.m at line 80, column 7
the "error" refers to a line the in fft function code which otherwise works correctly when xp is not set by a loop ... very strange.
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;
% Radix-4 Algorithm
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);
% assemble output
Z = [A B C D];
end % radix4bfly()
% radix-4 DIF FFT, input signal must be floating point, real or complex
%
function S = r4fftN(s)
% Initialize variables and signals: length of input signal is a power of 4
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 % r4fftN(s)
% test FFT code
%
xp = 2;
% ERROR if I uncomment loop!
%for xp=1:8
N = 4^xp; % must be power of: 4 16 64 256 1024 4086 ....
x = 2*pi/N * (0:N-1);
x = cos(x);
Y_ref = fft(x);
Y = r4fftN(x);
Y = digitrevorder(Y,4);
%Y = bitrevorder(Y,4);
abs(sum(Y_ref-Y)) % compare fft4 to built-in fft
%end