FFT response for noisy signal, averaging the response and

I try to analyze a system's state with acceleration sensors by measuring the frequencies and amplitudes.

Since a cheap sensor is used, I have a noisy signal in the beginning (up to 40Hz - see below). That is the first thing that I don't get. With another sensor (much higher resolution but also different position) this noise couldn't be observed.

1. Do you have any idea where this might come from?

Due to the noise and to reduce uncertainty, I perform multiple measurements which I intend to average afterwards. The second question would, therefore, be:

1. Where do I best average the measurements in order to obtain the "correct" amplitude/frequency? I have the following ideas:

• average the signals and perform a single fft. The maxima result from the maximum of the transformed signal
• average the signals after the transform and take the maxima of the resulting signal
• average only the maximum/frequency of the single transforms of each measurement

Furthermore, I observe a sort of frequency shift within the measurements (the left vertical line is the excitation frequency, while the right one is the response of the averaged fourier transoforms). Here, I excite the system with 183 Hz and expect the maximum at this very frequency (or in a really small bound around it). Instead, the responses occur to be around 189 Hz and sometimes even more. Due to my lack of experience I tried to conduct some tests to "check" if my algorithm works correctly:

I generated a sine wave and added different offsets and noises. The frequencies would be met with an accuracy of 0.15 Hz (see below). Therefore, I guess it's not the algorithm.

1. Do you have any experience with this procedure and how much shift in frequency is normal?

1. Do you have any suggestions for further (pre-) processing of the signal? I was thinking about a highpass-filter to get rid of the noise in the beginning. Also, I think it might be interesting to apply a bandpassfilter only around the "bound" and analyze the signal in the time-domain - what do you think about that?

2. I am curious to find out if it's possible to observe the switch of a valve position. Since this is a transient behaviour I am wondering which method to apply. I'd try a PSD and to cut the evaluation of the FFT into pieces and perform it for smaller periods. Do you have any ideas?

• Not just guys here, hence I've cut your question down on the colloquialism a bit, and tried to phrase it more concisely in a few places. – Marcus Müller Dec 5 '19 at 21:09
• fair enough, thanks! – Raz0r115 Dec 6 '19 at 7:31