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I am new to signal processing world. I am working on a project where we have to find change points using spectral densities. I am running some simulations where in I created a wave which is a linear combination of a few sinusoidals of frequency ranges (3.5-7.5, 7.5-9, 9-12, 12-14). I find the periodogram of these sinusoidals using the usual formula which goes from 0 to pi.

My understanding is, I will be able to observe peaks in the periodograms which corresponds to the frequencies of the signal. But since the x axis in a periodogram ranges only from -pi to pi, how can I compare my input frequencies and the frequencies I got in periodogram?

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  • $\begingroup$ What is your sampling frequency? The periodogram assumes the time step between samples is 1 unit. If it is in fact 1/1000 for example, you will have to scale the x axis appropriately $\endgroup$ – geometrikal Apr 13 '16 at 3:47
  • $\begingroup$ @geometrikal Can you explain a little bit more on what you mean by scaling the samples? My sample rate is 50 samples per second. I have generated samples for 40 seconds (2000 samples) in total. How exactly should I scale this samples? $\endgroup$ – Anirudhan J Apr 13 '16 at 4:43
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    $\begingroup$ -$\pi$ to $\pi$ on the x-axis represents frequencies from -1/2 to 1/2 (period 2 seconds) assuming that the samples are 1 second apart. If the samples are actually 1/50 second apart, then -pi to pi on the x-axis represents frequencies from -50/2 to 50/2 $\endgroup$ – geometrikal Apr 13 '16 at 6:06
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The output you get from the periodogram are the power spectral density for the angular frequencies W in the range from 0 to pi. With the sampling rate Fs you can compute the frequencies f from W with: f = W * Fs / (2pi).

Be aware that you can only display frequencies from 0 to Fs/2 due to the Nyquist criterium which states that you need at least two points of a signal to be able to detect it.

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