# I Does the non-periodic signals have frequency or not?

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1. Mar 7, 2016

### Geek007

Can someone kindly explain , what is the frequency of non periodic signals? Periodic signals have frequency of number of cycles completed in one second and but non periodic signals don't have repeated pattern so what would be the frequency of non periodic signals. Kindly do explain it in simple words , as my background isn't of physics.I'm a CS students.

2. Mar 7, 2016

### Staff: Mentor

Non-periodic signals do not have "a frequency". If they are close to a periodic signal, but with some additional nonperiodic noise, you can still find frequencies that are relevant for the signal. Mathematically, that is done via a Fourier transformation. It will give you an amplitude for every frequency, which shows you how "relevant" that frequency is.

3. Mar 7, 2016

### BvU

Another way of looking at this: A perfectly periodic signal lasts forever and started an infinitely long time ago -- or else it would not be perfectly periodic. In practice, e.g. in music, a tone can be almost perfect (have one single frequency for all we know) and last only a short time. But it's clearly not exactly periodical.

The mathematical bottom line is that if we choose a time slice, for music e.g. 1 second, we can calculate a frequency spectrum for that one second of music. To do that we simply let this second repeat forever and calculate the aforementioned Fourier transform ( -- very useful for CS students too !) We don't get information on frequencies lower than 1 Hz but don't care about that.
That's what spectrum analyzers do (for example in media player visualizations).

4. Mar 7, 2016

### Geek007

Well, if non periodic signal donot have frequency then why we said this music is of 25khz etc? i mean to say , why should then we associate frequency with non peroidic signals such like music?

5. Mar 7, 2016

### BvU

If the frequency spectrum has a peak somewhere then that's the frequency we hear. But when the music is over, we don't hear that frequency anymore. So it's periodical for a while. Not periodical in the mathematical sense that $f(t + n \tau)\quad \forall n \quad$.

6. Mar 7, 2016

### Geek007

does the non periodic signal have period, as period and frequency are exactly of opposite of each other?

7. Mar 7, 2016

### BvU

Do you understand the answers that you got so far ? If not, what is your background ? I would expect some math for a CS student ( -- if CS means Computer Science ). Trigonometry ?

Last edited: Mar 7, 2016
8. Mar 7, 2016

### BvU

A non-periodic signal does not have a frequency as indicaterd in post #3. But we can calculate a frequency spectrum as indicated in post #4.

9. Mar 7, 2016

### sophiecentaur

We do it because it 'works' as a way of describing the signal to an adequate level of accuracy. (And that goes for any measurement of anything.)
The very first assumption in frequency analysis assumes that any continuous waveform exists for all time. The full Fourier Transform of such a signal will not consist of a 'comb' of frequency components - which is what we see on a spectrum analyser. It will be a continuous function in the Frequency Domain What we always see is a Discrete Fourier Transform, which takes a sequence of thousands or millions of signal values (samples) over a period of time and that will give a comb of components, spaced by a frequency equal to 1/(the sequence length). It 'assumes' that the signal repeats itself over the time of the whole number of samples. A FFT (Fast Fourier Transform is a cheeky / clever method that uses a set of samples that is 2n long and uses a process of reduction to give an answer with much less computing time.
So you may say that it is all a big con from the start! And, if you are not careful, you can get 'wrong' answers from the process. Using a long enough string of samples and a process of 'windowing' can reduce errors to an acceptable level. If you try to make a wrong analysis of a signal, you can end up losing some major components in your result.
Unfortunately, many people do not consider the small print involved in these signal processes and can come to false conclusions. Signal processing is hard stuff and you often have to take some things for granted (as long as you get them from a reputable source).