dsp.CrossSpectrumEstimator

Estimate cross-spectral density

Description

The dsp.CrossSpectrumEstimator System object™ computes the cross-spectrum density of a signal, using the Welch's averaged periodogram method.

To implement the cross-spectrum estimation object:

1. Create the dsp.CrossSpectrumEstimator object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

cse = dsp.CrossSpectrumEstimator

cse = dsp.CrossSpectrumEstimator(Name,Value)

Description

cse = dsp.CrossSpectrumEstimator returns a System object, cse, that computes the cross-power spectrum of real or complex signals using the periodogram method and Welch’s averaged, modified periodogram method.

cse = dsp.CrossSpectrumEstimator(Name,Value) returns a dsp.CrossSpectrumEstimator System object, cse, with each specified property name set to the specified value. Unspecified properties have default values.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

FFTLengthSource — Source of FFT length value

'Auto' (default) | 'Property'

Specify the source of the FFT length value as either 'Auto' or 'Property'. If you set this property to 'Auto', the cross-spectrum estimator sets the FFT length to the input frame size. If you set this property to 'Property', then specify the number of FFT points using the FFTLength property.

FFTLength — FFT Length

128 (default) | positive integer

Specify the length of the FFT that the cross-spectrum estimator uses to compute cross-spectral estimates as a positive, integer scalar.

Dependencies

This property applies when you set the FFTLengthSource property to 'Property'.

Data Types: double

Window — Window function

'Hann' (default) | 'Rectangular' | 'Chebyshev' | 'Flat Top' | 'Hamming' | 'Kaiser'

Specify a window function for the cross-spectrum estimator as one of 'Rectangular', 'Chebyshev', 'Flat Top', 'Hamming', 'Hann', or 'Kaiser'.

SidelobeAttenuation — Side lobe attenuation of window

60 (default) | positive scalar

Specify the side lobe attenuation of the window as a real, positive scalar, in decibels (dB).

Dependencies

This property applies when you set the Window property to 'Chebyshev' or 'Kaiser'.

Data Types: double

FrequencyRange — Frequency range of the cross-spectrum estimate

'Twosided' (default) | 'onesided' | 'centered'

Specify the frequency range of the cross-spectrum estimator as one of 'twosided', 'onesided', or 'centered'.

If you set the FrequencyRange to 'onesided', the cross-spectrum estimator computes the one-sided spectrum of real input signals, x and y. If the FFT length, NFFT, is even, the length of the cross-spectral estimate is NFFT/2+1 and is computed over the interval [0, SampleRate/2]. If NFFT is odd, the length of the cross-spectrum estimate is equal to (NFFT+1)/2, and the interval is [0, SampleRate/2].

If you set the FrequencyRange to 'twosided', the cross-spectrum estimator computes the two-sided spectrum of complex or real input signals, x and y. The length of the cross-spectrum estimate is equal to NFFT. This value is computed over [0, SampleRate].

If you set the FrequencyRange to 'centered', the cross-spectrum estimator computes the centered two-sided spectrum of complex or real input signals, x and y. The length of the cross-spectrum estimate is equal to NFFT, and the estimate is computed between [-SampleRate/2, SampleRate/2] and (-SampleRate/2, SampleRate/2) for even and odd lengths, respectively.

AveragingMethod — Averaging method

'Running' (default) | 'Exponential'

Specify the averaging method as 'Running' or 'Exponential'. In the running averaging method, the object computes an equally weighted average of a specified number of spectrum estimates defined by the SpectralAverages property. In the exponential method, the object computes the average over samples weighted by an exponentially decaying forgetting factor.

SpectralAverages — Number of spectral averages

8 (default) | positive integer

Specify the number of spectral averages as a positive, integer scalar. The object computes the current cross-spectral estimate by averaging the last N estimates. N is the number of spectral averages defined in the SpectralAverages property.

Dependencies

This property applies when you set AveragingMethod to 'Running'.

Data Types: double

ForgettingFactor — Forgetting factor

0.9 (default) | scalar in the range (0,1]

Specify the exponential weighting forgetting factor as a scalar value greater than zero and smaller than or equal to one.

Tunable: Yes

Dependencies

This property applies when you set AveragingMethod to 'Exponential'.

Data Types: single | double

SampleRate — Sample rate of input

1 (default) | positive scalar

Specify the sample rate of the input, in hertz, as a finite numeric scalar. The sample rate is the rate at which the signal is sampled in time.

Data Types: single | double

Usage

Syntax

pxy = cse(x,y)

Description

pxy = cse(x,y) computes the cross power spectrum density, pxy, of the input signals, x and y.

Input Arguments

x — First data input

vector | matrix

First data input, specified as a vector or a matrix. The inputs, x and y must have the same size and data type.

Data Types: single | double
Complex Number Support: Yes

y — Second data input

vector | matrix

Second data input, specified as a vector or a matrix. The inputs, x and y must have the same size and data type.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

pxy — Cross-power spectrum density output

vector | matrix

Cross-power spectrum density output, returned as a vector or a matrix. The output has the same size and data type as the input signals.

Data Types: single | double
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to dsp.CrossSpectrumEstimator

getFrequencyVector	Vector of frequencies at which estimation is done
getRBW	Resolution bandwidth of spectrum

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Compute Cross-Power Spectrum of Two Noisy Sine Waves

Generate two sine waves.

sin1 = dsp.SineWave('Frequency',200, 'SampleRate', 1000);
sin1.SamplesPerFrame = 1000;
sin2 = dsp.SineWave('Frequency',100, 'SampleRate', 1000);
sin2.SamplesPerFrame =  1000;

Use the dsp.CrossSpectrumEstimator System object™ to compute the cross-spectrum of the signals. Also, use the dsp.ArrayPlot object to display the spectra.

cse = dsp.CrossSpectrumEstimator('SampleRate', sin1.SampleRate,...
    'FrequencyRange','centered');
aplot = dsp.ArrayPlot('PlotType','Line','XOffset',-500,'YLimits',...
    [-150 -60],'YLabel','Power Spectrum Density (Watts/Hz)',...
    'XLabel','Frequency (Hz)',...
    'Title','Cross Power Spectrum of Two Signals');

Add random noise to the sine waves. Stream in the data, and plot the cross-power spectrum of the two signals.

for ii = 1:10
x = sin1() + 0.05*randn(1000,1);
y = sin2() + 0.05*randn(1000,1);
Pxy = cse(x, y);
aplot(20*log10(abs(Pxy)));
end

Algorithms

Welch's Method of Averaged Modified Periodograms

Give two signal inputs x and y:

1. Multiply the inputs by the window and scale the result by the window power.

2. Compute FFT of the signals X and Y, and multiply X with conj(Y) using Z = X.*conj(Y).

3. Compute the current cross-power spectrum estimate by taking the moving average of the last N number of Zs and scaling the answer by the sample rate.

For more information on the algorithms, see the Averaging Method section in Spectrum Analyzer.

References

[1] Hayes, Monson H. Statistical Digital Signal Processing and Modeling. Hoboken, NJ: John Wiley & Sons, 1996.

[2] Kay, Steven M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice Hall, 1999.

[3] Stoica, Petre, and Randolph L. Moses. Spectral Analysis of Signals. Englewood Cliffs, NJ: Prentice Hall, 2005.

[4] Welch, P. D. ''The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short Modified Periodograms.'' IEEE Transactions on Audio and Electroacoustics. Vol. 15, No. 2, June 1967, pp. 70–73.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• System Objects in MATLAB Code Generation (MATLAB Coder)

Version History

Introduced in R2013b