# What are some suitable methods for removing low-frequency line noise from measured data prior to system identification/deconvolution?

I am performing a system identification by striking an experimental model with an instrumented impact hammer and measuring the strain response.

The timebase for the recorded signals is 5 microseconds and the hammer pulse width is typically around 200 microseconds. The data are recorded for 20 milliseconds prior to the hammer hit and for 60 milliseconds after.

An example of the recorded data is provided here. A close-up of the pre-trigger strain signal is provided here.

Prior to the hammer hit, the strain signal is non-zero with both low and high frequency noise present. The low frequency noise is of most concern as this affects the quality of the system impulse response function that I subsequently compute.

Unfortunately when completing the tests I did not record a zero-reference prior to each hammer hit. Thus my questions are:

1) What methods are available for removing the low-frequency line noise from the entire signal given that the strain response is also of low-frequency.

2) Is is possible to use the first 20 milliseconds to construct a longer zero-reference signal that I may then subtract from the recorded data? If so, how?

Taking a quick look at your acquisition: this doesn't look too terrible in terms of noise, however, the acquisition window looks way too short. With a 60ms window your frequency resolution is only 160 Hz. From the looks of it, you will also get a massive truncation error. As a rough rule of thumb, you want the acquisition window long enough so that the impulse response visually disappears in the noise.

Specific answers (although they may not help given the truncation error)

1. If it's really line (like in AC supply voltage hum) noise you can measure the exact location and notch it out for the fundamental and the harmonics.
2. Sure. Take the mean and subtract. However, again, the window is way too short to get decent low frequency resolution.

A bunch of tips

1. Make the acquisition window long enough to capture the complete impulse response
2. Take an acquisition with no excitation. That's your noise floor
3. Take an acquisition with excitation. That's your signal
4. Compare signal spectrum to noise floor spectrum. Calculate SNR as a function of frequency
5. You want at least 10 dB SNR for a decent measurement. Frequencies must either meet that or be so low in level that they don't matter (< at least 20 dB of "the bulk")

If that can't be done there are more esoteric methods like Wiener filtering and/or reconstructive modelling, but it's certainly preferable to clean up the measurement process.