Amplitude modulation as a function of signal frequency and sampling rate

For an overview of the topic I create a stream of signals with frequencies 100:100:10k.

I set the sampling rate at 19990, on purpose, to demonstrate the strange amplitude modulation across all frequencies (At this rate it appears quite trippy to me).

This effect of course can be reduced by increasing sampling rate, however it is still present at any higher sampling rate too.

Can someone tell me how this effec is called and where it can be found in the literature. It must be kind a repeating pattern according to common multiples of frequency and sampling rate.

I heard of the nyquist-shannon theorem in terms of acquiring time-series data. But what about generating a data stream just like here?

Many thanks in advance!

CODE:

> fs = 19990;

> duration = 100;

> values = 0:1/fs:(duration*1e-3);

> stimsignal = [];

> for i= 1:100

> stimsignal = [stimsignal zeros(1,round(fs*0.01)) ((amp*sin(2*pi*i*1e2*values)))];

> end

> plot(stimsignal');

Answer 1

[Mathieu NOE]

hello Florian

maybe you should have a reading on signal processing - see for example dspguide / chapter 3

http://www.dspguide.com/pdfbook.htm/

in the chapter 3 , page 7 , see graph c)

eventhough the sine wave frequency and the sampling frequency do respect shannon criteria, there is a clearly visible distorsion of the signal. That may be a bit shocking in first place, but remember that sampling creates some amplitude modulation that is more or less pronounced depending of the ration f the sine frequency and sampling frequency

IMHO, there is no rule to say that you can find a suitable sampling frequency so that xx sine waves of YY frequencies will appear undistorted. Otherwise you have to select your test frequencies so that the peaks always fall on existing time stamps. that limit the choices of frequencies.

I remember in my young age , when music and test signals records were available on CDs, there was usually some tracks of sine waves with "special" frequencies (with Fs = 44.1 kHz) that showed silly waveforms. Nothing else as the stroboscopic effect - this time on signals.

[florian schertenleib]

Dear Mathieu

thank you so much for your kind and informative answer! That's exactly what I was looking for.

Best regards!

[Mathieu NOE]

you're welcome !