-1
$\begingroup$

Usually when we observe spectrum of a signal,we see multiple frequency components, each having different contribution to amplitude

But is it true that each and every signal has multiple frequency components? For example common AC power has frequency 60 Hz, if we observe its spectrum, will we observe only one frequency components or multiple components? Why if we observe multiple frequency components,despite the fact as we know beforehand that ac power has frequency 60 hz?

Improve this question
$\endgroup$
6
  • 1
    $\begingroup$ «frequency» is a somewhat constructed concept that aids us in analyzing certain problems. Like all analysis tools, it involves some preconditions and simplifications. This includes the idea of an «infinite duration signal», something that is hard to truely measure for us mortals. For the practical engineer this is something to be aware of but often not a big obstacle. $\endgroup$
    – Knut Inge
    Apr 1, 2020 at 9:40
  • $\begingroup$ What do you mean by "constructed concept"? $\endgroup$
    – DSP_CS
    Apr 1, 2020 at 10:01
  • $\begingroup$ really, have you read a signals and systems textbook by now? Also, this is essentially a duplicate of your previous "what is a spectrum" question. $\endgroup$
    – Marcus Müller
    Apr 1, 2020 at 12:41
  • 2
    $\begingroup$ Does this answer your question? Meaning of spectrum in simple words? $\endgroup$
    – Marcus Müller
    Apr 1, 2020 at 12:41
  • $\begingroup$ A stone or a tree are physical concepts. You can touch it, and it will exist long after man kind has disappeared. «Frequency» is like algebra. Or Swedish. It is made by men (and women) because it is useful. But you can’t touch a frequency, and when man kind is gone, there will be no frequencies :-) Sure, some things will vibrate naturally, and the time between each period might be something. But no-one will ponder about the frequency. $\endgroup$
    – Knut Inge
    Apr 1, 2020 at 13:34

1 Answer 1

Reset to default
4
$\begingroup$

The only signal, that really has just one frequency component, is an infinite sine signal. Limiting the signal duration in any way is bound to produce other frequency components, as time limiting can be thought of as multiplying with a rectangle window, which translates to convolution with an si-function in the frequency domain, thus introducing new frequency components, however infinitesimal.

As for your example: the 60Hz AC power "signal" is messed up with all kinds of stuff coming from devices connected to the grid, that "backfire" into it. Also, the 60Hz are not really constant, they vary ever so slightly around 60Hz.

Improve this answer
$\endgroup$
4
  • $\begingroup$ So in nutshsell you mean that each and every signal that is observed on spectrum analyzer will have multiple frequency components including 60 hz ac power signal? ? $\endgroup$
    – DSP_CS
    Apr 1, 2020 at 9:17
  • $\begingroup$ Essentially, yes. Although, depending on the analysis, there can be cases, where there won't be any additional components visible, although this is somewhat constructed. If you have a pure sine signal, that is windowed as to contain only full periods, with a circular fourier transform, you will not observe any additional components. Actually, this is virtually the case of an infinite sine signal, as described in the answer. So, no real exception to the rule. $\endgroup$
    – Max
    Apr 1, 2020 at 9:25
  • $\begingroup$ "Although this is somewhat constructed " what do you mean? Ideal? $\endgroup$
    – DSP_CS
    Apr 1, 2020 at 10:02
  • $\begingroup$ Yes, kind of ideal. Pure sine signals, that do not contain any fractions of full periods are interesting only for theoretical, mathematical purposes and do not appear as real signals. $\endgroup$
    – Max
    Apr 1, 2020 at 10:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.