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Next Article What is the role of an art conservator? In general, signals can be classified into three broad categories, power signals, energy signals, or neither. Deterministic signals which are made up of sinusoids, are an example of power signals , which have infinite energy but finite average power. Random signals also have finite average power and fall into the category of power signals. A transient signal is an example of energy signals , which start and end with zero amplitude.
There are still other signals that cannot be characterized as either power signals or energy signals. As a first example, estimate the average power of a sinusoidal signal with a peak amplitude of 1 and a frequency component at Hz.
To measure the average power of the signal, call periodogram and specify the 'power' option. As you can see from the zoomed-in portion of the plot, each complex sinusoid has an average power of roughly —6 dB. Another way to calculate the average power of a signal is by "integrating" the area under the PSD curve.
In this plot, the peaks of the spectrum plot do not have the same height as in the power spectrum plot. The heights are different because it is the area under the curve — which is the measure of the average power — that matters when taking power spectral density PSD measurements. To verify that statement, use the bandpower function, which calculates the average power using the rectangle approximation to integrate under the curve.
According to Parseval's theorem, the total average power of a sinusoid is the same in both the time domain and the frequency domain. Use that fact to check the value of the signal's estimated total average power by summing up the signal in the time domain. For the second example, estimate the total average power of a signal containing energy at multiple frequency components: one at DC with amplitude 1.
The DC average power of the signal is equal to its peak power since it is constant and therefore is given by A 0 2. Calculate the average power of each unique frequency component in dB to see that the theoretical results match the mean-square spectrum plot below.
To measure once again the average power of the signal, use the periodogram function once more to calculate and plot the power spectrum of the signal. As in the first example, estimate the total average power of the signal by "integrating" under the PSD curve.
Once again the height of the peaks of the spectral density plot at a specific frequency component may not match the ones of the plot of the power spectrum. The difference is due to the reasons noted in the first example.
Again verify the estimated average power of the signal by invoking Parseval's theorem and summing up the signal in the time domain.
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