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?
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.