This is a cross posting from the crossvalidated stack exchange as I thought this may be a better forum to ask.
I have a dataset consisting of respiratory time series signals of different lengths obtained from different groups of patients. I want to either classify or cluster the patients using these timeseries by using the commonalities of the time series of each group. However, I have no experience in dsp.
Firstly, I am confused if I am supposed to filter my signals to get rid of any frequencies above the Nyquist frequency. My sampling frequency is 32Hz and my time series is somewhat noisy and has some artifacts. I am also unsure of which filter to select for this.
Secondly, I wanted to look at the periodogram and the average power spectral density at each frequency within a group - but I am not sure if I understand the periodogram very well - if I have different time series lengths then my periodogram length will vary too, so I am not sure how this comparison can be made.
Being from Pure Math, I know Fourier analysis purely from the perspective of functions and using Fourier transforms to obtain the coefficients that describe the projection of these functions onto an orthonormal system. With periodograms however, I noticed that the x-axis represents sample frequencies. I am confused with the distinction between sampling frequencies vs. underlying frequencies of the generating function (say I have $\sin(2\pi x)$ sampled at 10Hz, does the periodogram characterize the 1Hz underlying frequency of the function?)
Any resources on understanding how to analyze and remove noisy components of time signals from a machine learning perspective would be much appreciated! Due to time constraints, I have shied away from long textbooks on digital signal processing. Thanks a lot.