# FFT/PSD/IFFT analysis on single axis piezoelectric accelerometer signals for curb impacts

I'm trying to denoise the signal by performing PSD analysis and followed by IFFT. Ultimately, I want to generate Force and Displacement plots from the denoised acceleration signal.

Noisy Acceleration Signal($$a_z$$ vs t):

PSD analysis of the signal:

Setting a PSD > 0.001 in the code to filter out frequencies having less power than 0.001.

After IFFT($$a_z$$ vs t):

The denoised signal makes sense since I'm recording z-acceleration on curb impacts which comes out to be a series of impulses.

I'm a novice in signal processing and I don't know whether a windowing would have given a better result or not?

Further questions: Is it possible to find force distribution from the acceleration signal? I've been searching to find answers but none have given me a good idea.

Filtering by zeroing out bins is not a recommended approach as it will introduce significantly more time domain ringing, as detailed here

Why is it a bad idea to filter by zeroing out FFT bins?

Consider using the firls function available in MATLAB / Octave or Python scipy.signal to design optimized multiband filters around your frequencies of interest.

However the frequency content will be driven by repetition in the data; if the actual application will repeat (or not) at unknown and variable intervals, any such filtering techniques will not be useful.

Your time series looks very regular: «big bump» followed by «small bump», then repeat. Is that representative of you application, or are you engaging the accelerometer in som kind of test setting? Do you expect this regularity in the final application? If not, then perhaps generate a more representative waveform? If this is your expected behaviour, perhaps you can look into (pitched) voice analysis for hints.

What is your «curb impact» physically (I am not a native English speaker). Is it about a car hitting a fence? If so, that would be a one-off event, right?

I am not familiar with «displacement plots». Sounds like you want to integrate acceleration twice in order to estimate position? That is sensitive to «dc errors» more than zero-mean noise in the measurement.