Fixed-step size: why doesn't the Nyquist-Shannon sampling theorem work?

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Zahara 2024-3-27

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评论： Zahara 2024-3-30，17:08

采纳的回答： David Goodmanson

Hello,

My problem concerns the choice of fixed-step size (Model Settings > Solver details).

I have a sinusoidal signal of amplitude 3 and frequency 5Hz.

According to Shanon's theorem, I should choose a fixed-step size of 5Hz*2 = 10Hz. So I assigned 0.1 to fixed-step size. I chose "auto" solver.

But as you can see, I get a flat curve:

I have a much more better curve if I choose, for example, 0.01 as fixed-step size:

Thank you in advance for your help. I've been struggling this problem for a few hours now.

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Answer 1

David Goodmanson 2024-3-27

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编辑：David Goodmanson 2024-3-27

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Hello Zahara,

The Nyquist theorem gives you the bare minimum number of points to describe the oscillation. More points are better, as you are finding out. Taking your case of 5 Hz, Nyquist frequency 10 Hz, then

t = 0:.1:1;
cos(2*pi*5*t)
ans = 1    -1     1    -1     1    -1     1    -1     1    -1

showing that there is a steady oscillation, but at just two points per oscillation, you can't see the shape of the cosine waveform at all

And

sin(2*pi*5*t)
1.0e-14 *  [0  0.0122  -0.0245 -0.1409  -0.0490  0.0612  0.2818 -0.2695 -0.0980  0.1102]

which is essentially 0 since the time points match up with the zeros of the sine function. In practical terms, the Nyquist criterion is no help at all here. This may or may not be why you are obtaining the flat line.