APPENDIX
01 – CAPTURING A SIGNAL WITH DIFFERENT SAMPLING RATES
Introduction:
Consider a pure sine tone signal of frequency 3.999KHz. This signal will be acquired with different sampling rates. The sampling rates are 8KHz, 16KHz and 48KHz. The Nyquist theorem states that in order to capture a signal accurately, it has to be sampled at twice the signal frequency. However, practically it has to be sampled 2.5 times the signal frequency accounting for the roll-off of the anti-aliasing filter. The sampling frequencies 16KHz and 48KHz in this example satisfy the Nyquist criteria while 8KHz does not since it is not 2.5 times 3.999KHz. But the goal here is to demonstrate how the software interpolates and reconstructs the signal based on the available data points. Signal frequency of 3.999KHz is chosen instead of 4KHz so that it is possible to use 8KHz sampling rate in the software for demonstration purposes.
Graphs:
Time signal graphs of 3.999KHz with different sampling rates (zoomed for more clarity)
3.999KHz acquired with
8KHz sampling rate:
3.999KHz acquired with 16KHz
sampling rate:
3.999KHz acquired with 48KHz
sampling rate:
