# understand short time fourier transform

I am reading this paper for signal denoising. In the paper, the authors says

The core concept in this paper is to compute a regression between a noisy signal frame and a clean signal frame in the frequency domain. To do so we start with the obvious choice of using frames from a magnitude short-time Fourier transform (STFT). Using these features allows us to abstract many of the phase uncertainties and to focus on turning off" parts of the input spectral frames that are purely noise.

I don't understand the last sentence and hopefully, someone could explain it to me.

To understand:

Using these features allows us to abstract many of the phase uncertainties and to focus on turning off" parts of the input spectral frames that are purely noise.

check out reference 6 in the linked paper.

That reference contains the image:

As you can see, this paper uses the DFT of the noisy signal, and the spectrum of the noise and "turns off" (subtracts) the one from the other. The phase information from the original signal’s DFT is applied to the results before synthesis of the estimated speech signal is done with the inverse DFT.

Added to answer rb-j's comment: $$\hat{P}$$ is just the power spectrum estimate and $$\gamma$$ can be chosen for any number, but they suggest $$1$$ for power processing or $$0.5$$ for magnitude processing.

• Do the hats, $\hat{P}$, mean magnitude? And is $\gamma$ somewhere around 2? Commented May 16, 2022 at 4:59
• So $P_x[k] = |X[k]|^2$, right Peter? Or proportional? Commented May 16, 2022 at 23:42