Electrical – A question on aliasing and sampling in a measurement system

aliasingsamplingvoltage measurement

Before asking my question here is the scenario how the voltage signals are used:

Where I work some are performing data acquisition of four DC signals through four channels by a daq device at a particular sampling rate. The DC signals are coming from transducers devices measuring temperature, air pressure, force transducer ect. All of these transducers have calibration certificates which have linear calibration equations for voltage to temperature conversion as Temperature = A*Voltage + B where A and B are the slope and offset of the calibration equation. So by looking at a certificate one can say "I measure this voltage so this corresponds to this temperature" ect. After sampling and logging the data, the engineers use software like MATLAB where they can do several transforms like FFT ect.

Here comes my question:

Imagine an analog DC signal coming from a force transducer in a time interval as below:

enter image description here

And imagine the maximum frequency of interest is 50Hz.
So according to Nyquist theorem the sampling frequency should be at least 100Hz.

But if this signal has many frequency components higher than 50Hz we will be face to face with a situation called aliasing. So we will be undersampling some of the frequency components. So far this is what understand form aliasing.

And below represents this:

enter image description here

I encounter some tutorials which suggest anti-aliasing filters like RC low-pass filters between the transducer and the daq so that we remove high freq. components and avoid undersampling and aliasing.

1-) Do you think in my case this type of filtering is necessary if the tools like MATLAB can do post signal processing like low-pass filtering? Or an analog anti-aliasing filter is still needed?

2-) If they don't do any FFT and filtering, is there a possibility the signal's mean values or low freq. components might be affected significantly by aliasing?

3-) How can I know that if a filter is needed or not? (I know how to use a scope)

My concern is if I use a low pass filter I don't want to affect the calibration equation of the transducer.

Best Answer

To answer your questions in order:

  1. Once the signal is aliased it's like cream in your coffee, you can't really get it back out again. If there was just one strong signal you could notch it out (losing whatever real signal happens to exist at that frequency), but generally once it's mixed in you're scuppered.

  2. The signals aliasing into different frequencies should not affect the mean if everything behaves linearly and your averaging period does not include an undue amount of aliased very low frequency component. For example, if you had a signal that was being aliased down to 0.01Hz and took a 1 second sample, the mean could be greatly affected. Low frequency components, of course, can be directly affected.

  3. Ideally the high frequency components (those above the Nyquist frequency) would be negligible. The closer you get to the Nyquist frequency the better your filter has to be. For a high accuracy measurement and a simple single or 2-pole RC frequency you might need to sample at 200 or even 2000x higher than the highest frequency of interest (that's what I came up with in a recent design).

You would want the passband flatness of your filter to not affect the desired signals. It may be easy to test this with a signal generator. You want the stopband attenuation to be such that negligible signal exists to be aliased down into your signal band. Again you can test this with a signal generator, and compare with actual signal components if you have them available (many oscilloscopes will do a crude FFT- ADC resolution is typically very low on oscilloscopes- that gives you an idea of what is going on). In between the filter rolls off if you have many decades for that to happen it is much easier. You can probably test the DC accuracy much better than you can create an accurate AC signal but if you know the DC accuracy and the passband flatness you can get a pretty good idea of what is going on.