# Why is sampling frequency/rate typically abbreviated Fs and not Sf in English?

This is not a technical question, it is rather a question about the implicit notation used in MATLAB and multiple digital signal processing books to refer to sampling frequency/sampling rate.

Why is sampling frequency/rate typically abbreviated Fs and not Sf in English? Is it because of a particular historical reason? Was the term imported from another language?

• By convention. There's really no "rational reasoning" behind naming conventions, it's just what a group of people does. And by that convention, you use indices to specify the quantity. The quantity is a frequency, so it's "main" letter is an f , and the index specifies that it's not the frequency of hamsters wheel turnings, but the frequency of samples. This has been true in math and physics for a loooooong time, much predating signal processing. Commented Apr 29 at 22:34
• It's a frequency. So it's $f$ for "frequency". "What kind of frequency?" one might ask? It's a frequency of kind "sampling". So it has a qualifier $\mathrm{s}$ and that qualifier is put in the subscript. Qualifiers ain't the main thing. So like all other frequencies (not angular frequency), it's $f_\mathrm{something}$. Commented Apr 30 at 2:09
• It's a very unfortunate choice - easily confused with FrameSize. Commented Apr 30 at 7:20
• @MSalters FrameSize of course being Sf for Size: Frame!
– pipe
Commented Apr 30 at 10:26
• "and the index specifies that it's not the frequency of hamsters wheel turnings" -- which could get confusing if you're working on a system who's behavior depends on how often a snake passes by. Commented May 1 at 3:33

DSP is in the end a field of math, mostly living on the intersection of analysis, linear algebra and maybe stochastics. As it describes signals, it's also a daughter of Physics.

So, it uses the dominant notation of these fields; I find that in math and physics, you always find

$$\text{q}_{\text{d}},$$

where $$\text{q}$$ names the quantity described (here: a frequency, hence using the letter $$f$$), and $$\text{d}$$ gives a more detailed insight on what the quantity describes. This is by no means an English thing at all – all French, German, Russian and as far as I found and, not even hoping to glimpse known words from the text, Japanese publications in math adhere to that.

So, we need to look at the very beginnings of modern math and physics if we want to figure out where this came from. From the top of my head, I opened Leonhard Euler's wikipedia page, navigated to his works, and found indices describing the direction of a differential, the differential being signified by the "main" letter, in his Latin book from 1755!

So, this has neither anything to do with DSP nor with English. It's mathematical tradition, from German mathematicians, over English physicist, through enlightenment era French philosophers through Swiss physicist, Hungarian Algebraicians, to American signal processers:

The "main" letter defines the kind of quantity, the subscript tells you what the quantity describes.

You wouldn't write

$$\text{Hamsters}_N,$$

but

$$N_{\text{Hamsters}}\text{!}$$

• $N_{Hamsters}!$ looks like a very large number to me. Commented Apr 30 at 6:57
• @SimonRichter and for some reasons, it keeps growing! Commented Apr 30 at 9:20