posted 05 September 2005 13:21            

So if we had instead keeped two sets of levels (one that represented the level of sine and one that represented the level of cos) then we could reconstruct the original signal. One set of levels is called the real and the other set is called the imaginary.

But phase is a relative thing, so relative to what, I hear you say. Normaly it's the begining of the frame that the FFT is analising. If we have a sin wave and a cos wave (a cos wave is a sine wave 90 degs out of phase ) of the same frequency we can make a sine/cos wave of the same frequency of any phase and level we choose , just by adjusting those two signals levels and mixing the results. Don't forget that the levels could be positive or negative . Yes a sine wave (0 degs) and a cos wave (90Deg) mixed together make a single wave 45degs out of phase but with exactly the same shape. BTW there is no other wavefrom that has this feature as any other waveform would produce something entirely different.

So in an FFT, if we analised just a single sine wave of level one that was at its peek at the time the frame started , our FFT would give a value of 1 in the cos represening levels (real), and a value of zero in the sine representing levels (imaginary). If the wave form was passing through zero at the time the frame started the FFT would give a value of zero in the cos represening levels (real) and a value of one in the sine representing levels (imaginary). If it started the frame at negative peek then the cos value would be minus one and the sine value would be zero.

If you start playing with FFTs and inverse FFTs ( the ones we stick on the output to get your original signal back) you find that they are almost identical. So you find that the an FFTs input also has two space for two signals in the same way as the output, but in most cases the second input signal is silent. If we are analising real input signals, then it gets feed into the FFTs real input, In this case the other input is purely imaginary.

I hope this makes some form of sence

Pete