Quick question, I'm testing one of my own FFT routines with an input as a complex waveform, I'm not sure what kind of output i'm suppose to get, but one of the most obvious features is that the real part of the result is not symmetrical ... is it possible to get a FFT result with such a feature or is my routine incorrect? (This may seem like a really silly question!) If I input some samples with just the real part set, it behaves as I would expect, and if I perform a Inverse FFT I get the original complex samples returned, with no errors. The input is generated from something called a gabor waveform, the real input is (16 samples); -0.04321392, -0.03453337, 0.12078786, 0.27080447, 0.00000000, -0.59395005, -0.58104729, 0.36435210, 1.00000000, 0.36435210, -0.58104729, -0.59395005, 0.00000000, 0.27080447, 0.12078786, -0.03453337, and the imag. part is; 0.00000000, -0.08337094, -0.12078786, 0.11217089, 0.45593813, 0.24602216, -0.58104729, -0.87962379, 0.00000000, 0.87962379, 0.58104729, -0.24602216, -0.45593813, -0.11217089, 0.12078786, 0.08337094, Any help / input greatly appreciated :)
FFT result not symetrical?
Started by ●July 7, 2006
Reply by ●July 7, 20062006-07-07
moosedude wrote:> Quick question, I'm testing one of my own FFT routines with an input as a > complex waveform, I'm not sure what kind of output i'm suppose to get, but > one of the most obvious features is that the real part of the result is not > symmetrical ... is it possible to get a FFT result with such a feature or > is my routine incorrect? (This may seem like a really silly question!) > > If I input some samples with just the real part set, it behaves as I would > expect, and if I perform a Inverse FFT I get the original complex samples > returned, with no errors.Yes, what you see is expected. The reason is that Euler's equations no longer apply for complex-valued signals. As you know, real-valued sines and cosines can be expressed as 2*i*sin(x) = exp(ix) - exp(-ix) 2* cos(x) = exp(ix) + exp(-ix) i.e. the complex exponentials come in conjugate symmetric pairs. These relations are only valid for real-valued signals, and are the reasons why the DFT of a real-valued signals is conjugate symmetric. Rune
Reply by ●July 8, 20062006-07-08
On Fri, 07 Jul 2006 09:34:11 -0500, "moosedude" <phill_holland@hotmail.com> wrote:>(snipped)> >Any help / input greatly appreciated :)Hello moosehead, Rune Allnor is, of course, correct. Maybe the following website will help you a little. Who knows. www.dspguru.com/info/tutor/QuadSignals.pdf Good Luck, [-Rick-]