Periodogram frequencies not matching with signals

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?

• 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 – geometrikal Apr 13 '16 at 3:47
• @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? – Anirudhan J Apr 13 '16 at 4:43
• -$\pi$ 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 – geometrikal Apr 13 '16 at 6:06