# How to take inverse fft of windowed and callibrated fft data? [closed]

I have done windowing and fft on a signal but when I try to recover original raw signal ,I am unable to do it .Can anybody help me. How to take inverse fft of windowed and callibrated fft data? Thanks in advance....

## closed as unclear what you're asking by Marcus Müller, MBaz, lennon310, jojek♦Mar 19 at 8:37

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• It's a bit unclear what you need help with. The IFFT is nearly the same operation as the FFT, and if you've done the FFT with some existing library, that library most definitely brings an IFFT itself. – Marcus Müller Mar 13 at 10:45
• BTW, $\text{IFFT} \lbrace W(f) \ast X(f) \rbrace \neq x(t)$. Windowing modifies the signal, so you can't get the "original raw" signal $x(t)$ back. – MBaz Mar 13 at 13:42

## 1 Answer

When using quantized data formats, applying a window function is a lossy process, and arbitrary original data cannot be recovered, either before or after an FFT/IFFT process.

You could try multiplying by the reciprocal of the window (being careful to avoid divide-by-zero), and get a noisy reconstruction (except perhaps for an end point or two). And noisier at the ends, where the window tapers to near zero, thus potentially adding a huge amount of quantization noise.

Or you could overlap Hamming/Von_Hann windows by 50%, where the sum of the sequence of overlapped windows has a gain of 1.0 (except at the very ends), and thus is not lossy (or as lossy, but still with some amount of tiny numerical or rounding noise).