# Alignment of 2 Set of Samples from Different Sensors

If we measure the heart rate of a subject with two different devices, which have big different sampling rates then how we can compare their outcomes. For instance, one of the devices has the sampling rate of 1000 while the other one has sampling rate of 32.

• HR stands for Heart Rate. – Reza Sadeghi Mar 21 '19 at 15:55

There are 2 main factors here:

• Aligned timeline
Namely each sample has time stamp taken with the same reference time.
• The lower sampling rate is high enough according to the sampling theorem
Namely even the lowest sampling rate, in your case 32 [Hz] is high enough to reconstruct the original signal.

If both (1) and (2) hold you'll be able easily to compare them by interpolating both into a shared time grid.
If (1) doesn't hold you may be able, by interpolation and some other DSP techniques (Such as Matched Filter and Dynamic Time Warping), to align both to the same grid.
Yet it would be harder (And in some cases, not achievable).

As long as the sampling rate is large enough, theoretically there is no difference. You can interpolate the slower sampled signal into the higher sampled signal, so they are in essence equivalent.

You need to take care that the sampling rate is high enough. For example, sampling at a rate of 32 samples per second limits you to signals with zero energy above 16 Herz in theory, and maybe 10 Herz or so in practice.

In practice, when signals are quantized, the quantization noise can depend on the sampling frequency; see for example the paper - Relationship Between Sampling Rate and Quantization Noise. See also the answer to Sampling Rate Effect on Quantizer SNR and the comments below it.