Correct time signal after Inverse FFT

[JayZ]

I am using inverse FFT to rebuild the time signal from spectrum. Since Hanning window is applied during FFT, the rebuilt time signal is still windowed.

I am trying to divide this time signal directly by the hanning window. It works except two ends of the time data. Because Hanning function gives 0 at its two ends, I got infinity for these points when the data is divided by this 0. Is there anybody could tell me how to correct it?

Thanks!

[JLS]

Hello,

I'm not a signal processing expert, but it sounds like the correction in this case is going to be a design choice.  If the inversion operation you require happens to yield a division by 0, then your result isn't infinity - it's not even defined (division by 0 is not defined).  I suspect you'll want to play some numerical trick to get back your resulting time domain waveform, at least as best you can.  On the other hand, if you're using the fourier analysis and making decisions based on the windowed signals anyway, then perhaps it makes sense to simply look at the windowed signal in time as well.

Best Regards,

JLS

[JayZ]

I am trying to get the visual effect of the un-windowed time signal. If there is no other way, I will use part of the acquired data without two ends. It looks ok. For further analysis, yes, definitely I will use the windowed data. Thanks for the reply.

[Kevin_Price]

Also not an expert, but it seems to me that it'd be inherently impossible to recover those endpoints.  If X(i) is the original time domain data, H(i) is the hanning window function and Y(i) is the post-windowing data, then you've got a situation like:

Y(i) = X(i) * H(i).

At the 2 endpoints, this breaks down to:

0 = X(i) * 0

So I'd think your best bet is to characterize the values very near the endpoints so you can extrapolate some reasonable guesses for your endpoint values.

-Kevin P.

[JayZ]

yes, it looks like Windowing is a one-way stuff for the time signal. We can not recover something after it is applied.

[bassbuckeye]

I have noticed that, using similar methods, not only are the two endpoints not usuable, but usually a few values in from either endpoint are not useful either.  Symetrically folding the spectrum and zero padding lessens the distortion near the endopoints, and the time domain signal can easily be clipped after IFFTing.

[JayZ]

bassbuckeye, could you please give some detail about "Symetrically folding the spectrum and zero padding lessens the distortion near the endopoints"? Do you mean to remove the Hanning window effect, we should process the spectrum first (before IFFT) instead of directly working on the time signal after IFFT?