# does aliasing occur always if i sample a vibration in real world applications?

I was reading about the aliasing effect and nyquist. I understand that aliasing effect occurs if the sampling rate is lower than twice the maximum frequency in the signal I want to sample.

So I was wondering if aliasing is always in signal measurements. Example: If I have a vibrations sensor that has a max sample rate of 8kHz -> It can reconstruct signals till 4kHZ perfectly right? But what about frequencies which occur also in the measurements with much higher frequencies? If there is a vibration with 16 kHz and because I sample with much lower rate, there could be aliasing in my measurement and false signals I don't know about? is this possible? That means i could have peaks in my measurements which are because of aliasing?

• A recent news story highlighted the risk of not adhering to Nyquist by proper lowpass filtering of (in this case) fuel flow, even when operating at a high (?) sample rate of 2200 samples/sec: arstechnica.com/cars/2020/03/… Mar 19 '20 at 12:36

If I have a vibrations sensor that has a max sample rate of 8kHz -> It can reconstruct signals till 4kHZ perfectly right?

Theoretically, yes. Though I would like to add that all the noise signals beyond $$+/-4kHz$$ will alias back into your sampled signal.

But what about frequencies which occur also in the measurements with much higher frequencies? If there is a vibration with 16 kHz and because I sample with much lower rate, there could be aliasing in my measurement and false signals I don't know about? is this possible?

The signal at $$16kHz$$ will fold back to $$0Hz$$ $$(16k - 2 \times f_s, where f_s=8kHz)$$.

That means i could have peaks in my measurements which are because of aliasing?

As mentioned above, yes, there could be unexpected peaks inside your sampled signal spectrum because of aliasing. It is difficult to say how much they will affect the measurement. It depends on nature of the aliased signal. But definitely you need to account for aliasing distortion due to under-sampling.

That is why, before sampling, a (steep) lowpass filter with cutoff frequency $$f_c \leq \frac{f_s}{2}$$ shall be applied. Thus, the amount of aliasing will be insignificant.

• Steep filter also add either a lot of phase distortion or time domain ringing. It's not quite as simple Mar 19 '20 at 14:03

does aliasing occur always if i sample a vibration in real world applications?

Yes. The aliasing always occurs. The sampling theorem assumes band limited signals, but these strictly band limited signal do not exist in reality (as they would be infinitely long).

Of course any signal can be low pass filtered to be reduce the aliasing to an acceptable level but the choice of good lowpass filter is not trivial and depends a lot on your specific requirements.