Inconsistency when using IFFT with a real signal

Hi,

I am having a strange problem with a small snippet of code that takes the fft of a real input signal, and using one half of its spectrum, recreates the signal by exploiting conjugate symmetry. The problem I'm facing is that I'm not getting a result identical to the input.

len = length(pi);
%Nyquist point for a signal of even length
halfLen = length(pi)/2 + 1;

PI = fft(pi);
PO(1:halfLen) = PI(1:halfLen);
%Exploit conjugate symmetry of the real input signal
PO(halfLen+1:len) = fliplr(conj(PO(2:halfLen-1)));
%Taking IFFT should give same signal as pi
po = ifft(PO);

Both po and pi should be identical, but they are within 1e-10 of each other which is causing colossal errors at high frequencies.

A simple bit of code but I have not been able to figure out why po ≠ pi. Any input is appreciated!

Thanks.

Answer 1

[Walter Roberson]

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

You are hitting round-off error.

[A B]

Thanks very much for identifying the problem.

Could you suggest any means by which I can reduce this effect?

It seems like I needn't do much for it to rear its head!