Aliasing: tutorial question

[sherpa]

Hi everyone,

I have a question about a NI tutorial "Aliasing and Sampling at Frequencies Above the Nyquist Frequency"

Somewhere in the text the author wrote:

"Although sampling at twice the Nyquist frequency will ensure that you measure the correct frequency of your signal, it will not be sufficient to capture the shape of the waveform. If the shape of the waveform is desired, you should sample at a rate approximately 10 times the Nyquist theory."

I'm asking this question because I'm trying to model impedance data. I perturbate an electric voltage and measure a current, at different frequencies. So I get a impedance curve in function of the frequency. The fmax is 2250 Hz, sampling frequency 5000 S/s, according to the Nyquist theorema. So good so far. Only the cost function between the real measurements and the model isn't that good. Is it possible that the acquisition of the shape of the waveform, the magnitude of the current, ... aren't correct due to the low sample freq (only twice the max freq)?

I do understand the thing of twice the Nyquist frequency, but why 10 times? Is there a good, scientific answer? And could this solve my problem?

Thanks a lot for reading!

Regards, Sherpa

[gwd]

Suppose you impose a sinusoidal voltage, and you sample at twice the frequency to monitor the voltage. Let's sample at the minima and maxima to get a good amplitude number.

Now measure the current through a resistor, sampling at the same times. Works great, gives the right resistance. Now insert a capacitor with reactance exactly equal to the resistor. Now when you sample you get zero, because current is 90 degrees out of phase with voltage.

To do an impedance measurement you need both magnitude and phase. To get both you need enough data to make sure you get a good measurement.

[sherpa]

Hi,

Thanks for replying.

I`m switching from time domain to frequency domain with FFT when processing the measurments --> impedance is complex number --> magnitude and phase.

The impedance (and phase) is OK, I assume. The only thing I don`t understand is the part I mentioned in https://www.ni.com/en/shop/data-acquisition/measurement-fundamentals/analog-fundamentals/acquiring-a... .
Why ten times the highest frequency?

Regards,

Sherpa

[gwd]

1) Nothing magic about ten. It's more than two and less than a thousand.

2) I would NOT use FFT. What you want to do is determine the magnitude ratio and phase difference. The most noise-tolerant way is to multiply a reference waveform with the measured current waveform and determine the DC level (to get real part) and a 90 degree phase shifted refererence with the current waveform and determine that DC level (to get the imaginary part). Then calculate magnitude and phase. This is the DAQ equivalent to what is done in some flavors commercial impedance meters.

Thinking about the math, this is essentially the same as calculating the FFT at just one frequency. If you do go the FFT route you will have to think very hard about windowing.