# Frequency analysis to determine low-pass cut off frequency

I collected some data for a practical application, where the signal represents force data obtained from an impact of a punch against a force plate attached to a quasi-rigid rig (it moves once the impact occurs). I have a few questions to understand how to deal with my data.

Features of the signal:

the signal (sampling 1000Hz) has a length of 2 seconds, but the impact last about 60ms. The recording is 2s for practical reasons though. Therefore, before the impact a baseline is recorded (values close to zero), and after the impact vibrations occur until data set back to baseline levels. I need to figure out a reasonable cut-off frequency to use combined with a 4th order butterworth filter to properly filter the signal.

1. When exploring (FFT) the frequency of that signal should I use the whole 5s long signal or only the 30ms of interest? Due to sampling frequency, data points over 30ms maybe not enough?
2. Vibrations occurring due to the impact are not of interest, but the frequency is likely to be in part similar to the frequency of the portion of the signal of interest. How to deal with this? I could select from before the impact (arbitrary) to when the signal becomes zero after the impact. Then use from that point onwards to explore frequency of the unwanted signal only?
3. Impacts are at least 10 per subject, when exploring the frequency of that signal, should I average all trials and all subjects out to obtain an average frequency content or should I perform the analysis for each trial and subject indepedently?

Attached a figure of a typical signal (x = time; y = Newtons)

• Out of interest: why do you need to do this with a fourth order butterworth? Jul 17, 2018 at 16:21
• and, much more importantly: "to properly filter the signal" for which purpose? What is it that you need to do with it afterwards? That defines all your needs! Jul 17, 2018 at 16:23
• In the literature force data are usually fitlered using a 4th order butterworth, but the low pass cut off frequency depends on a residual analysis. Thus, I just refer to other studies for the butterworth. However, for that signal, the typical frequency content is not well known in the literature. With this signal I need to look at peak value, impulse and time to peak value. These parameters are my outcome once the signal will be filtered. Jul 17, 2018 at 17:29
• Basically I need a good compromise to preserve both the signal magnitude and time domains. Jul 17, 2018 at 17:35
• what do you mean with "preserve time domains"? That's a bit of an uncommon thing to say, and honestly, I still don't know what's important for you about the signal. Jul 17, 2018 at 18:24

1. I think you will get almost the same amount of frequency content for both the cases (fft of 60 ms and fft of 2 sec). The time series indicates that only from 0.6 to 1.2 sec there is vibration. But it's better to use the full signal while doing the FFT as there is no fear of losing any data. If you cut some portion from the time series, you have to be careful about choosing the window (use cosine tapering not rectangular window) as edging effect may be introduced into your frequency content.

2. Sorry, I didn't get the question. Could you please rephrase it?

3. I think that for all the trials, the time series would be different. Therefore, it is not recommended to average all the time series. It is better to analyze all the time sequences and obtain the frequency contents. If dominant frequencies for all the trials are similar, then the average frequency can be calculated. If not, you can try to find out the reason e.g. inconsistency in the sample material etc.

• 2. I meant that the natural frequency of the system may overlap the frequency of the signal generated by an external factor (i.e. impact of an object). Is this a problem? Am I adding noise in this case? Jul 17, 2018 at 22:58
• 1. Thanks that is of help. It practically helps understanding how to procede with the raw signals. Jul 17, 2018 at 22:59
• I don't think that the frequency of the system is modified by this impact. Because impact means you are initiating the vibration of the system by only imparting an initial velocity. Jul 17, 2018 at 23:02
• 3. As for answer 1., very helpful for those like me unfamiliar with signal processing. Yes time series will be slighlty different for each trial/subject. However, a further question promoted by your answer... how to determine objectively the dominant frequency? What is for you the dominant frequency of the signal showed above based on the power spectrum plots attached? Jul 17, 2018 at 23:02
• Correct, I initiate the vibration with the impact and I was wondering whether I should make sure that I cut off the frequency of the system when the impact is over but the system will keep vibrating? This because I just care about the signal from beginning of impact till its end, nothing else. But apparently it is not a problem if I got you right. Jul 17, 2018 at 23:05