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Is there a way to plot PSD of a signal which show true frequency amounts ( not normalized one) without having knowledge about frequency bandwidth or sampling frequency of the signal in matlab ?

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Without more information about the signal, it is not possible.

The set of samples is just a set of numbers with no further information associated with them. If you know the frequency at which the samples were taken, then you can associate "real-world" frequencies to their FFT bins. Otherwise, it may be impossible.

To give an example, consider the samples of $\cos(2\pi 100t)$ taken at $f_s=500\,\text{Hz}$, and the samples of $\cos(2\pi 200t)$ taken at $f_s=1000\,\text{Hz}$. They are exactly the same! There is no way to tell the two signals apart just from their samples.

It may be, however, that you have some extra piece of information that may help deduce $f_s$. For example, you may know that the signal's spectrum has a peak, or a particular phase, or some other property at a certain frequency. If you find the normalized FFT of the samples and identify this property, you can extrapolate from there to estimate the actual signal frequencies.

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  • $\begingroup$ This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. $\endgroup$ – jojek Oct 27 '15 at 8:15
  • $\begingroup$ @jojek The question is: is there a way to do this? The answer is no, there is no way. Why is this not an answer? Having said that, I'll try to provide a bit more detail later, but it's not like there is a lot more to say about the subject. $\endgroup$ – MBaz Oct 27 '15 at 13:00
  • $\begingroup$ @jojek, I added some information; I hope my answer is more useful now. $\endgroup$ – MBaz Oct 27 '15 at 15:26

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