# Choosing minimum sampling frequency of a filtered signal

I have a time series of acceleration sampled at 1000Hz to capture random impacts on a structure. The ringing of the structure (not of interest) produces noise which a 50Hz filter seems to eliminate while preserving the impulses' amplitude and width. I'd like to downsample the filtered data to reduce data volume. What is the minimum sample rate I could choose? Based on this article, I should choose a sample frequency higher than 2*50Hz (Nyquist) since 50Hz is just the filter cutoff and there is still energy at higher frequencies that I don't want to alias. Is 10*50Hz = 500Hz reasonable?

As you say, you should select a sampling frequency at least at twice the largest frequency you wish to keep.

What you'll do is called downsampling: going from a higher to a lower sampling frequency. This process usually starts by filtering, so there is no energy above the new Nyquist frequency, and any aliasing is negligible.

Many numerical programs, such as Matlab, include the filtering step in commands such as downsample and resample. In any case, you should always look at the spectrum before and after downsampling, and make sure the process meets your requirements.

• Very helpful! I checked the Matlab help and I believe decimate and resample apply the filter as you mention, but downsample does not. We will play around with these functions. – KAE Nov 23 '15 at 19:00
• @KAE You are correct about the downsample command; my memory failed me. I was thinking of decimate, which does include the low-pass filter. – MBaz Nov 23 '15 at 22:11