# why nonperiodic signals still has the concept of frequency?

I'm new to EE from CS background, just a question on nonperiodic signals. I don't understand why nonperiodic signals still has the concept of frequency/frequency domain? The definition is :

Period refers to the amount of time, in seconds, a signal needs to complete 1 cycle. Frequency refers to the number of periods in 1 s

Since nonperiodic signal doesn't have cycle(does't form a pattern), therefore it shouldn't have the concept of Frequency neither?

• How familiar are you with the concept of the Fourier or Laplace transforms? Commented Oct 4, 2019 at 2:50
• A non-periodic signal (or any signal really) is made up of a combination of periodic signals (sinusoids) of varying amplitudes, frequencies, and phase shifts. Any signal you can imagine can be produced by superimposing the right combination of sinusoids of the appropriate amplitude, frequencies, and phase shifts. Commented Oct 4, 2019 at 2:55
• @Hearth not at all. Commented Oct 4, 2019 at 3:46
• frequency is just the periodicity of the best-correlating basis function Commented Oct 4, 2019 at 4:29
• 'not at all' ? But you were talking about Frequency domain. Whats the representation of a signal in Frequency domain called ? Commented Oct 4, 2019 at 6:16

## 1 Answer

I don't understand why nonperiodic signals still has the concept of frequency/frequency domain?

Any absolutely integrable function can be represented as a sum of infinitely many periodic functions even though it is not periodic. These periodic functions are the frequencies making up the frequency spectrum of that function. You can compute them using the Fourier Transform.

Since nonperiodic signal doesn't have cycle(does't form a pattern), therefore it shouldn't have the concept of Frequency neither?

Musical notes are not periodic - periodic functions are infinitely long and all music notes have a finite duration - so would you say that music does not contain frequencies?

You don't actually have to have a period to be associated with a frequency. You just have to contain a periodic function. When you pluck a string or strike a drum the note eventually dies out and is therefore not periodic, but it does contain a series of periodic signals, including the frequency of the note, which sum to the (finite and thus not periodic) tone of the note.