Basic Sampling (Nyquist) Question 2

[EngineeringNewbie]

Hi,

I'm 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). My question relates to the resultant periodic waveform - how many plot points (i.e. time values) should I plot?

After doing a little research into the Nyquist Theorem I think I have stumbled on the answer - but am still a little unsure as I am no expert in this field.

The fundamental frequency is 50Hz. My dataset has 5 harmonics: 1st, 5th, 7th, 11th, 13th. Am I right in saying that I should 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 I am to display one cycle/period of the periodic waveform (i.e. time values from 0 to 1/50 sec) does this mean I need to plot 1300 points?

Your help would be much appreciated!

 

[Skogsgurra]

No.

You need only to plot one period. 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.

I think that you should 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. I would go for more than that - say five times the Nyquist frequency - which increases the sample rate to 6500 Hz.

Why? Do you ask. The answer is that Nyquist is right, but only if there is a "brick-wall" filter in the circuit. That is a filter that eliminates all frequencies above the 13th harmonic. Such filters do not exist and you shall not expect to find anything even close to it in your application. That's why I recommend you to sample between 5000 and 10 000 Sa/s. It will also make your plotted curve look a lot better. 26 points will look very "dotty".

 

[EngineeringNewbie]

Thank you - your answer provides the clarification I needed!