From signal theory we know that a very useful representation of some power signals is that of its power spectral density, whose curve represents how the total power of the signal is distributed at all frequencies. For instance, it is a couple of dirac pulses for a sine wave of frequency f0 because its power is concentrated at frequencies f0 and -f0.
But in some different situations I have seen that we often use not exactly the power spectral density representation, but the power representation.
EXAMPLE 1: Measurements with Spectrum Analyzer
If we use a spectrum analyzer, we see in abscissa the different frequencies, and in ordinate the power of the signal. For instance, this is a measurement I have done:
I have sent to the instrument a sine wave of -13dBm of power, and its total power is represented in ordinate of the peak. What does it mean from a math point of view?
I think this representation has no sense: the ordinate should be the power spectral density, not its integral in a neighborhood around the frequency considered!
Example 2: simulink
This is the representation of the power spectral density of a certain noise:
This is the representation of the power of the same noise:
What is the link between them? Power should not be function of frequency (it is the integral on all frequencies of power spectral density), power spectral density yes! So what does it mean that we see the "power spectrum"?