In physics, frequency is simply \$f\$.

I mean,
Frequency: \$f\$ (with unit Hz = s-1)
Angular frequency: \$\omega = 2\pi f\$ (with unit rad/s)

However, when I read EE textbooks, they use `frequency' for both of them.

For example, when they say something like RF, they use frequency in Hz ― so \$f\$.
However, in textbook Signals & Systems 2th Ed. by A. V. Oppenheim et al,
they introduce fundamental frequency as \$\omega_0 = 2 \pi f_0\$.
When I try to solve problems like `find the frequency' without any appearance of \$f\$, \$\omega\$, or units, this drives me crazy.

How to differentiate them? Only by the context? I hope not...

  • 2
    \$\begingroup\$ Well, frequency and angular frequency have the same units, since radians are not an unit (they are dimensionless), see: physics.stackexchange.com/questions/11500 . Btw, many (most?) physicists mix frequency and angular frequency. So answer using whichever you want. \$\endgroup\$ – jinawee Jun 27 '14 at 16:56
  • \$\begingroup\$ Jinawee is right. The word does double duty in physics as well. It's only a problem if it's used in a context where (a) the context doesn't eliminate the ambiguity, and (b) the ambiguity matters. \$\endgroup\$ – Ben Crowell Jun 27 '14 at 22:06
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    \$\begingroup\$ As long as you include units in your answer (either Hz or rad/s), which you always should, there won't be any problem. \$\endgroup\$ – Emmet Jun 27 '14 at 23:31

Generally, frequency is measured in Hz, or 1/second. If a variable named "f" or "Fsomething" is used, then its unit is generally understood to be Hz.

Sometimes it is mathematically more convenient to use radians/second instead of full rotations per second. If a variable is named "ω", then its unit is generally understood to be radians/second.

All that said, it's really sloppy not to specify the units. Mostly you'll run into rad/s in texts and papers. Look carefully at the beginning of a paper, the start of a chapter in a book or maybe in a definitions section, and you should find a definition of the terms used. Or, something like your example of introducing the fundamental frequency as "ω0 = 2πf0" makes it quite clear. That basically defines how variables "ω" and "f" will be used subsequently, which is also the overwhelming convention.

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    \$\begingroup\$ Yes - I agree with O. Lathrop. However - I am afraid, there are some (sloppy?) exceptions. For example, for a transfer function the pole location is given in the complex s-plane (based on ω). From this location the so called "pole frequency" ωp is derived (magnitude of the pointer to the pole). It is very uncommon to use - in this context - the term "pole angular frequency". Hence, it is always necessary to watch the units. \$\endgroup\$ – LvW Jun 27 '14 at 12:24
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    \$\begingroup\$ @LvW: All "s" variables in Laplace transformed equations are always based on radians. Otherwise you'd have to carry factors of 2Pi around all over the place. This is one of those cases I mentioned where its mathematically more convenient to use rad/sec. Of course this is universally done, so in the case of s-variables in Laplace transforms (often even called the s-domain), it is not ambiguous. \$\endgroup\$ – Olin Lathrop Jun 27 '14 at 13:20
  • \$\begingroup\$ No doubt about it. Nevertheless, all I wanted to point out is that the symbol ωp in most (all ?) cases is used in conjunction with the term "frequency" (rather than angular frequency). \$\endgroup\$ – LvW Jun 27 '14 at 14:07

Radians per second and Hertz are both units of frequency, much like centimeters and inches are both units of length. If you saw a geometry book using both centimeters and inches, you wouldn't say "my book uses 'length' for both of them". Same applies here. As Olin says, its sloppy (I'd say "wrong") not to say which units you're using in any given context, but sometimes the overall trend with respect to frequency is what's being highlighted, and the actual units are of secondary importance.

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    \$\begingroup\$ Radian is not a unit of frequency. It is meant for measuring angles but interestingly it has no "unit". (it's a ratio...) \$\endgroup\$ – Blup1980 Jun 27 '14 at 13:00
  • \$\begingroup\$ You're right -- a should have said radians per second. I'll edit. \$\endgroup\$ – Scott Seidman Jun 27 '14 at 13:18

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