# Is it true that each and every signal has multiple frequency components?

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?

• «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. Apr 1 '20 at 9:40
• What do you mean by "constructed concept"? Apr 1 '20 at 10:01
• 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. Apr 1 '20 at 12:41
• Does this answer your question? Meaning of spectrum in simple words? Apr 1 '20 at 12:41
• 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. Apr 1 '20 at 13:34

## 1 Answer

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.

• 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? ? Apr 1 '20 at 9:17
• 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.
– Max
Apr 1 '20 at 9:25
• "Although this is somewhat constructed " what do you mean? Ideal? Apr 1 '20 at 10:02
• 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.
– Max
Apr 1 '20 at 10:27