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[Guest]

Say you are writing a software application which applies Fourier Synthesis to some electrical frequency-domain data (i.e. harmonics comprising a harmonic number, amplitude and phase for each harmonic). With respect to the resultant periodic waveform, how many plot points (i.e. time values) should be plotted?

After digging up some info on the Nyquist Theorem you think you have stumbled on the answer, but are still a little unsure as you are no expert in this field.

The fundamental frequency is 50Hz. Your dataset has 5 harmonics: 1st, 5th, 7th, 11th, 13th. Should you first calculate the highest frequency (13 * 50Hz = 650Hz) then double this to get the sampling rate that Nyquist recommends (i.e. 650 * 2 = 1300Hz)?

If you are to display one cycle/period of the periodic waveform (i.e. time values from 0 to 1/50 sec) does this mean you need to plot 1300 points?

[daqmaster]

Answer:

Nope.

Only one period needs to be plotted. And one period is 0.02 seconds. So the number of points will not be more than 1300 times 0.02 and that is not more than 26 points.

Be aware of the fact that your signal probably has higher components, even if you do not have to record them. Most real-life signals need to be sampled at least twice the Nyquist frequency. Five times the Nyquist frequency -- which increases the sample rate to 6500 Hz -- is even better. The reason for this is that Nyquist is right, but only if there is a "brick-wall" filter in the circuit. That is, a filter which eliminates all frequencies above the 13th harmonic. Such filters do not exist and you should not expect to find anything even close to it in your application. That is why you should sample between 5000 and 10000 Sa/s. This will also make the plotted curve look a lot better. 26 points will look very "dotty".