What's the correct way to align two signals downsampled at 10 Hz?

Question

I'm trying to build a dataset where one of the features is a signal which has originally been sampled at 500 Hz, while another feature is a signal which was sampled at 100 Hz. I want to downsample both of them at 10 Hz and then align them (they start at different times).

What should I do after low-pass filtering them at 5 Hz? And what would be the most correct filter to use?

e.g. I have two signals, signal1 and signal2:

signal1: Sampled at 500 Hz, the first sample is at time signal1_t0. signal2: Sampled at 100 Hz, the first sample is at time signal2_t0.

Once that I have filtered the data as described above, would it be ok to firstly set t0 = max(signal1_t0,signal1_t0) and then get e.g. the closest sample to t0*n + 0.1 from all the samples in the interval (t0*n, t0*n + 0.1) for each signal?

Answer 1

To align the signals precisely fractional delay all-pass filters are used for time delay correction. This is assuming that the different processing channels each have a different time delay which in many cases won't conveniently be an integer of the final output sample rate. Fractional delay filters are resampling structures and include Farrow Filters and Polyphase Filters.

There is more info on Farrow Filters here:

Coefficients of Farrow structure?

And general fractional delay filters here:

How to pick coefficients for Fractional Delay Filters?