Smoothening Noisy FFT

Question

I've got the following FFT with a sampling frequency of 192 kHz that has around 17.000.000 samples. The signal is a hiss of escaping gas. This looks noisy and i want to determine the characteristic "hiss frequency" that should lie between ±40 kHz (according to other studies).

Since most of the noise in industrial areas is broadband, and the hissing characteristics can be observed accross a wide frequency band including lower frequencies (e.g. from 0-10 kHz an), I can filter out anything below 20 kHz. This is done with a bandpass designed with the help of scipy's cookbook on Butterworth. I've used a 30th order Bandpass. Below is the resulting FFT.

Using a "noise-only" (leakage-free) measurement I have determined the FFT of the noise level.

Now, according to the noise level 3, the noise should exist mainly under 20 kHz. However, this can change with the environment such that the leakage can be "consumed" by noise. How can I solve this issue?

I have plotted the PSD 4 of the non-filtered data using Welch's algorithm with a Tukey window (which is apparently good for transient data). The plot can be examined below.

Am I using the correct window for this? How can I smoothen the FFT and reduce the noise, such that I get a better understanding of the overall data, since I have other measurements that i have to compare with each other?

Answer 1

The Tukey window seems like it would be a good window choice for your application.

In terms of smoothing out your FFT, PSD estimates are a good place to start if you only need to observe the spectrum. If you need to get back to the time domain signal, you cannot do that from a PSD (at least not easily).

PSD estimates have a couple tradeoffs that could be advantageous for you. PSD estimates, like FFTs, typically employ windowing. Windowing reduces the sidelobes, but also broadens the mainlobe. This can have a smoothing effect. The other tradeoff has to do with time-averaging that most PSDs use. This can also help to smooth the FFT by reducing the noise, as often the time averaging causes destructive interference in the noise and constructive interference in the signal, assuming your signal is stationary.

If you’re looking for a better PSD estimate, you can try a more modern approach, like burg’s, which is built into Matlab. These approaches typically are able to keep better resolution despite time averaging.