Low Pass Filters and Sampling Frequency

Question

I am trying to understand the relationship between low pass filters and sampling frequency. Let's say I have a signal data with sampling frequency (sampling rate 500Hz), and the data represent a signal with a (0-200Hz) frequency. I am trying to get rid off the frequencies over 50Hz ( removing the part from 50-200Hz). In butterworth filter they are talking about sampling frequency. The frequency bands formulas are based on the sampling frequency, like f_cut/f_sampling. These are all related to sampling frequency although I need remove the extra noise with respect to physical frequency which signal has. How does it work?

Answer 1

When doing digital filter design you normally work with normalised frequency, which is just the actual frequency divided by the sample rate. So in your example where you want to specify a cut-off of 50 Hz at a sample rate of 500 Hz then you would specify this as a normalised frequency of 0.1. (Note that if you later changed your sample rate to say 1 KHz then your filter would have a cut-off frequency of 100 Hz.)