How to preprocess such signals?

I am interested in denoising accerelation measurements, recorded in ambient vibration tests. Such tests consist in recording the vibrations of a mechanical structure, say a table for example. So say I put an accelerometer on the table and measure the signal without touching the table. The objective is to retrieve the dynamical properties of the table, i.e. its dominant natural frequencies.

The signal is a combination of the table dynamics response under a random excitation, plus some measurement noise. The sought frequencies correspond to peaks in the PSD, but for some other reason I would like to denoise the measurements.

The typical range of frequency can be estimated for a structure. Let's assume it is [10,20]Hz in the present case. The first thing I do is bandpass the signal with a bandpass of [10,20]Hz. Then, I decimate the measurements down to 50Hz, so that 20Hz is below the Nyquist frequency. But this does not suffice for my needs, so I am wondering how I could improve the preprocessing / denoising.

I am considering using wavelets to denoise the signals (i.e. have nice peaks in the |DFT| vs frequency plot), but I am not sure if it's a good idea. It would probably be if the input was highly unstationnary, but that's not very likely. Another possibility could be using correlation with some sines of appropriate frequencies, maybe... So the question is to the experienced DSP people, can you think of anything which I could use to improve the denoising?

Please do not hesitate do ask for clarifications. I tried to make my question simple enough to not discourage readers, but had to remove some details.

• How long is your signal? is it stationary (i.e. are the frequencies changing in time or constant)? – ThP Sep 26 '16 at 16:52
• @ThP Typically 50 000 to 300 000 points. It is "quite" stationary, meaning that the stationary assumptions is reasonable, even though it is not perfect. I'll add a spectrogram later. – anderstood Sep 26 '16 at 17:49
• Have you tried Welch's method or something similar for PSD estimation? – ThP Sep 26 '16 at 17:52
• @ThP Yes, that's exactly what I used (with 60% overlapping). – anderstood Sep 26 '16 at 18:45