What is wrong with this IDFT trick?

Question

In this section from Wikipedia about IDFT, three methods are given for expressing the Inverse Discrete Fourier Transform in terms of the direct transform.

Being curious, I implemented the three methods in Octave:

% define TD signal
N = 1024; n = [1:N]-1; f = [4 8];
x0 = sin(2*pi*n'*f/N);
x0 = sum(x0');

% calculate FD spectrum
y0 = fft(x0);

% trick #1
y1 = fliplr(y0);
x1 = fft(y1) / N;

% trick #2
y2 = conj(y0);
x2 = conj(fft(y2)) / N;

% trick #3
y3 = imag(y0) + i*real(y0);
x3 = fft(y3) / N;
x3 = imag(x3) + i*real(x3);

% plot results
plot(n,x0,'m-o', n,x1,'r-*', n,x2,'g-^', n,x3,'bxo');
axis tight

If happens that tricks #2 and #3 work well, while trick #1 fails to generate the correct result.

Am I missing something in the explanation, or is there an error in Wikipedia?

UPDATE: It seems like the magnitude of the y1 result is actually OK, it is just that the angle is doing funny things. Replacing the plot line with:

plot(n,abs(x0),'m-o', n,abs(x1),'r-*', n,abs(x2),'g-^', n,abs(x3),'bxo');

shows the overlap.

Answer 1

I found my mistake. According to Wikipedia, using the 1st method, the indices of the reversed series are modulo N. So the correct code is:

% trick #1
y1 = [y0(1) fliplr(y0(2:N))];
x1 = fft(y1) / N;

and not as posted in the question.