# Is it better to use sampling rates which are a power of 2? 32-64-128-256-512Hz? instead of using for example 30- 60-100-250-500Hz?

I am recently working with a sensor that I its sampling frequency can only be configured to either 32hz- 64hz- 128hz-256hz... and I was wondering whether using such sampling frequencies have any benefits. For example is it better to use 128 Hz than use 100 Hz? or 64Hz rather than 60 Hz?

• In many cases this will be constrained anyway by whatever HW you are using. Apr 11 '20 at 12:10

There's a lot of things that influence your choice of sampling rate.

First of all, of course, the Nyquist theorem, which says you need to sample at more than twice of the signal's single-sided bandwidth $$B$$ (for real signals)¹.

Then, you often choose a sampling rate that is useful for your system. For example, a lot of 3G/4G/5G systems use sampling rates of 30.72 MHz (or multiples thereof). That's not an elegant multiple of anything (as far as I know) – it just happens to be what the symbol rates in the standard suggests, so it's very useful if you're already sampling at rate that is rational relative to what you'll be using in the end.

That's a generally important rule: Pick a sampling rate that makes sense for what you'll be doing to the signal afterwards.

Then, especially in audio and lower-frequency sampling, you choose sampling rates that are multiples of other rates, so that it's easy to keep multiple subsystems in synchronization. For example, your CD audio sampling rate is 44100 Hz – first of all, that's an integer multiple of 100 Hz, and that's good, because it means it's easy to keep not only the second counter on your CD player correct by simply counting the samples and dividing by 44100, but also things like studio hardware, which tends to have higher "human-readable" time resolution. But, why the strange rate 44100? Well, that rate happens to be $$44100=2\cdot2\cdot3\cdot3\cdot5\cdot5\cdot7\cdot7$$. Back in the 1980s, when that rate came up, it was harder than it is now to derive good clocks from each other, unless they had an integer factor between them. So, a clock with "all" the small integer factors was chosen. A curious choice!

Another reason to pick a specific sampling rate is noise alignment, or intentional non-alignment. While it's not a sampling rate itself, the NTSC frame rate of 29.97 frames a second is still something that you find in video systems today, so you find a lot of video capturing ADCs that run at a high multiple of 29.97 Hz. And that frequency was chosen so that the zeros of the color information shaping filter didn't interfere with the brightness info.

In the very same motivation, you'll find noise-sensitive systems where the ADC rate is as far as possible from being rationally related to the other dominant digital clocks in the system – so that the noise from these clocks distributes more evenly to the digitized signal.

In other systems, you painstakingly try to align all these clocks – so that clock noise ends up being narrow interferers in the digital signal, and thus can be digitally filtered out using notch filters.

Of course, you also need to be able to get any rate you'd want to use – you can't just by a 876.543 kHz oscillator, even if you wanted to, these don't exist commercially. Sure, you can synthesize one with either a lot of jitter or a lot of effort, but in the end, complexity and cost restraints are relevant for almost any system design.

As you can see, a lot of conflicting reasons!

¹ that's not necessarily twice the maximum frequency in the signal! A lot of systems, especially superheterodyne systems, i.e. systems that have a strictly bandslimited signal on an intermediate frequency (IF) use subsampling, i.e. the sample rate is $$> 2\cdot B$$, but $$\ll 2\cdot f_\text{max}$$. The aliasing that occurs doesn't distort the information content, but aliases the signal down from the IF to the Nyquist band. It's a very useful, very common technique.

Only requirement for sampling frequency is that it should be more than twice the maximum frequency component in desired signal. Any other constraint can only be because of the oscillator design of the ADC circuit. So, the sensor you are working with might be able to generate a fundamental frequency of 32Hz and, using squaring non-linearity to produce 2x, 4x, 8x, ...so on That is why it can be configured only to sample at 32Hz - 64Hz - 128Hz - 256Hz.

Aside from the good points mentioned in the answer by @Marcus Müller, some other considerations are the required oversampling in Rx (for noise suppression in discrete time domain), similarly oversampling in Tx to ease the design of the analog front end filters.

It is not unusual to get sampling rates in practical wirless deployments that are not a power of 2, but if it possible it makes sense to have it as a power of two for other things like windowing, spectral estimation etc etc.