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Encyclopedia > Power spectrum

The power spectrum is a plot of the portion of a signal's power (energy per unit time) falling within given frequency bins. As opposed to the frequency spectrum, the power spectrum does not show spatial or phase angle information.

The most common way of generating a power spectrum is by using a Fourier transform and taking the square of the magnitude of the complex coefficients. Other techniques such as the maximum entropy method can also be used to estimate the power spectrum.

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## Existence of the power spectrum

The power spectrum of a signal exists if and only if the signal is stationary. If the signal is not stationary then the same methods used to calculate the power spectrum can still be used, but the result cannot be called the power spectrum.

## Spectral centroid

In acoustics, the spectral centroid of a sound is the midpoint of its spectral energy distribution, i.e. the frequency that divides the distribution into two parts of equal energy.

## Spectrogram

If the power spectrum is plotted in time then the graph is called the spectrogram. Results from FactBites:

 Displaying a Power Spectrum (403 words) ANSWER: The power spectrum is a representation of the the magnitude of the various frequency components of a 2D image that has been transformed with the FFT command from the spacial domain into the frequency domain. Different frequencies in the power spectrum are located at different distances and directions from the origin. The power at each location in the power spectrum is an indication of the frequency and orientation of a particular feature in the image.
 Power Spectrum Estimates :: Frequency Domain Signals ( Signal Processing Blockset) (1050 words) The power spectrum of a signal represents the contribution of every frequency of the spectrum to the power of the overall signal. In the previous topic, you have assembled the blocks needed to calculate the power spectrum of your speech signal. Use the Periodogram block to compute a nonparametric estimate of the power spectrum of the speech signal.
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