dspdata.psd (Signal Processing Toolbox)

Power spectral density

Syntax

Hpsd = dspdata.psd(Data)
Hpsd = dspdata.psd(Data,Frequencies)
Hpsd = dspdata.psd(...,'Fs',Fs)
Hpsd = dspdata.psd(...,'SpectrumType',SpectrumType)
Hpsd = dspdata.psd(...,'CenterDC',flag)

Description

The power spectral density (PSD) is intended for continuous spectra. The integral of the PSD over a given frequency band computes the average power in the signal over that frequency band. In contrast to the mean-squared spectrum, the peaks in this spectra do not reflect the power at a given frequency. See the avgpower method of dspdata for more information.

A one-sided PSD contains the total power of the signal in the frequency interval from DC to half of the Nyquist rate. A two-sided PSD contains the total power in the frequency interval from DC to the Nyquist rate.

Hpsd = dspdata.psd(Data) uses the power spectral density data contained in Data, which can be in the form of a vector or a matrix, where each column is a separate set of data. Default values for other properties of the object are shown below:

.

Property
Default Value
Description

Name
'Power Spectral Density'
Read-only string

Frequencies
[]
type double
Vector of frequencies at which the power spectral density is evaluated. The range of this vector depends on the SpectrumType value. For one-sided, the default range is [0, pi) or [0, Fs/2) for odd length, and [0, pi] or [0, Fs/2] for even length, if Fs is specified. For two-sided, it is [0, 2pi) or [0, Fs).
If you do not specify Frequencies, a default vector is created. If one-sided is selected, then the whole number of FFT points (nFFT) for this vector is assumed to be even.

If onesided is selected and you specify Frequencies, the last frequency point is compared to the next-to-last point and to pi (or Fs/2, if Fs is specified). If the last point is closer to pi (or Fs/2) than it is to the previous point, nFFT is assumed to be even. If it is closer to the previous point, nFFT is assumed to be odd.

The length of the Frequencies vector must match the length of the columns of Data.

Fs
`Normalized'
Sampling frequency, which is 'Normalized' if NormalizedFrequency is true. If NormalizedFrequency is false Fs defaults to 1.

SpectrumType
'Onesided'
Nyquist interval over which the power spectral density is calculated. Valid values are 'Onesided' and 'Twosided'. A one-sided PSD contains the total signal power in half the Nyquist interval. See the onesided and twosided methods in dspdata for information on changing this property.

The range for half the Nyquist interval is [0 pi) or [0 pi] depending on the number of FFT points. For the whole Nyquist interval, the range is [0 2pi).

NormalizedFrequency
true
Whether the frequency is normalized (true) or not (false). This property is set automatically at construction time based on Fs. If Fs is specified, NormalizedFrequency is set to false. See the normalizefreq method in dspdata for information on changing this property.

Property	Default Value	Description
Name	'Power Spectral Density'	Read-only string
`Frequencies`	`[]` type `double`	Vector of frequencies at which the power spectral density is evaluated. The range of this vector depends on the `SpectrumType` value. For one-sided, the default range is [0, pi) or [0, `Fs`/2) for odd length, and [0, pi] or [0, `Fs`/2] for even length, if `Fs` is specified. For two-sided, it is [0, 2pi) or [0, `Fs`). If you do not specify `Frequencies`, a default vector is created. If one-sided is selected, then the whole number of FFT points (nFFT) for this vector is assumed to be even. If `onesided` is selected and you specify `Frequencies`, the last frequency point is compared to the next-to-last point and to pi (or `Fs`/2, if `Fs` is specified). If the last point is closer to pi (or `Fs`/2) than it is to the previous point, nFFT is assumed to be even. If it is closer to the previous point, nFFT is assumed to be odd. The length of the `Frequencies` vector must match the length of the columns of `Data`.
`Fs`	`Normalized'	Sampling frequency, which is `'Normalized'` if `NormalizedFrequency` is `true`. If `NormalizedFrequency` is `false` `Fs` defaults to `1`.
`SpectrumType`	`'Onesided'`	Nyquist interval over which the power spectral density is calculated. Valid values are `'Onesided'` and `'Twosided'`. A one-sided PSD contains the total signal power in half the Nyquist interval. See the `onesided` and `twosided` methods in `dspdata` for information on changing this property. The range for half the Nyquist interval is [0 pi) or [0 pi] depending on the number of FFT points. For the whole Nyquist interval, the range is [0 2pi).
`NormalizedFrequency`	`true`	Whether the frequency is normalized (`true`) or not (`false`). This property is set automatically at construction time based on `Fs`. If `Fs` is specified, `NormalizedFrequency` is set to `false`. See the `normalizefreq` method in `dspdata` for information on changing this property.

Hpsd = dspdata.psd(Data,Frequencies) uses the power spectral density estimation data contained in Data and Frequencies vectors.

Hpsd = dspdata.psd(...,'Fs',Fs) uses the sampling frequency Fs. Specifying Fs uses a default set of linear frequencies (in Hz) based on Fs and sets NormalizedFrequency to false.

Hpsd = dspdata.psd(...,'SpectrumType',SpectrumType) uses the SpectrumType string to specify the interval over which the power spectral density was calculated. For data that ranges from [0 pi) or [0 pi], set the SpectrumType to onesided; for data that ranges from [0 2pi), set the the SpectrumType to twosided.

Hpsd = dspdata.psd(...,'CenterDC',flag) uses the value of flag to indicate whether the zero-frequency (DC) component is centered. If flag is true, it indicates that the DC component is in the center of the two-sided spectrum. Set the flag to false if the DC component is on the left edge of the spectrum.

Methods

Methods provide ways of performing functions directly on your dspdata object. You can apply a method directly on the variable you assigned to your dspdata.psd object. You can use the following methods with a dspdata.psd object.

avgpower
centerdc
normalizefreq
onesided
plot
twosided

For example, to normalize the frequency and set the NormalizedFrequency parameter to true, use

```
Hpsd = normalizefreq(Hpsd)
```

For detailed information on using the methods and plotting the spectrum, see the dspdata reference page.

Examples

Resolving Signal Components

Use the periodogram to estimate the power spectral density of a noisy sinusoidal signal with two frequency components and then store the results in a PSD data object and plot it.

Fs = 32e3;
t = 0:1/Fs:2.96;
x = cos(2*pi*t*1.24e3)+ cos(2*pi*t*10e3)+ randn(size(t));
Pxx = periodogram(x);
Hpsd = dspdata.psd(Pxx,'Fs',Fs); % Create a PSD data object.
plot(Hpsd);                        % Plot the PSD data object.

dspdata.msspectrum dspdata.pseudospectrum