# Documentation

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# Burg Method

Power spectral density estimate using Burg method

## Library

Estimation / Power Spectrum Estimation

`dspspect3`

## Description

The Burg Method block estimates the power spectral density (PSD) of the input frame using the Burg method. This method fits an autoregressive (AR) model to the signal by minimizing (least squares) the forward and backward prediction errors. Such minimization occurs with the AR parameters constrained to satisfy the Levinson-Durbin recursion.

The input must be a column vector or an unoriented vector. This input represents a frame of consecutive time samples from a single-channel signal. The block outputs a column vector containing the estimate of the power spectral density of the signal at Nfft equally spaced frequency points. The frequency points are in the range [0,Fs), where Fs is the sampling frequency of the signal.

When you select the Inherit estimation order from input dimensions parameter, the order of the all-pole model is one less than the input frame size. Otherwise, the Estimation order parameter specifies the order. The block computes the spectrum from the FFT of the estimated AR model parameters.

Selecting the Inherit FFT length from estimation order parameter specifies that Nfft is one greater than the estimation order. Clearing the Inherit FFT length from estimation order check box, allows you to use the FFT length parameter to specify Nfft as a power of 2. The block zero-pads or wraps the input to Nfft before computing the FFT. The output is always sample based.

When you select the Inherit sample time from input check box, the block computes the frequency data from the sample period of the input signal. For the block to produce valid output, the following conditions must hold:

• The input to the block is the original signal, with no samples added or deleted (by insertion of zeros, for example).

• The sample period of the time-domain signal in the simulation equals the sample period of the original time series.

If these conditions do not hold, clear the Inherit sample time from input check box. You can then specify a sample time using the Sample time of original time series parameter.

The Burg Method and Yule-Walker Method blocks return similar results for large frame sizes. The following table compares the features of the Burg Method block to the Covariance Method, Modified Covariance Method, and Yule-Walker Method blocks.

BurgCovarianceModified CovarianceYule-Walker

Characteristics

Does not apply window to data

Does not apply window to data

Does not apply window to data

Applies window to data

Minimizes the forward and backward prediction errors in the least squares sense, with the AR coefficients constrained to satisfy the L-D recursion

Minimizes the forward prediction error in the least squares sense

Minimizes the forward and backward prediction errors in the least squares sense

Minimizes the forward prediction error in the least squares sense (also called autocorrelation method)

High resolution for short data records

Better resolution than Y-W for short data records (more accurate estimates)

High resolution for short data records

Performs as well as other methods for large data records

Always produces a stable model

Able to extract frequencies from data consisting of p or more pure sinusoids

Able to extract frequencies from data consisting of p or more pure sinusoids

Always produces a stable model

Does not suffer spectral line-splitting

Peak locations highly dependent on initial phase

May produce unstable models

May produce unstable models

Performs relatively poorly for short data records

May suffer spectral line-splitting for sinusoids in noise, or when order is very large

Frequency bias for estimates of sinusoids in noise

Peak locations slightly dependent on initial phase

Frequency bias for estimates of sinusoids in noise

Frequency bias for estimates of sinusoids in noise

Minor frequency bias for estimates of sinusoids in noise

Conditions for Nonsingularity

Order must be less than or equal to half the input frame size

Order must be less than or equal to 2/3 the input frame size

Because of the biased estimate, the autocorrelation matrix is guaranteed to be positive-definite, hence nonsingular

## Parameters

Inherit estimation order from input dimensions

Selecting this check box sets the estimation order to one less than the length of the input vector.

Estimation order

The order of the AR model. This parameter becomes visible only when you clear the Inherit estimation order from input dimensions check box.

Inherit FFT length from estimation order

When selected, the FFT length is one greater than the estimation order. To specify the number of points on which to perform the FFT, clear the Inherit FFT length from estimation order check box. You can then specify a power-of-two FFT length using the FFT length parameter.

FFT length

Enter the number of data points on which to perform the FFT, Nfft. When Nfft is larger than the input frame size, the block zero-pads each frame as needed. When Nfft is smaller than the input frame size, the block wraps each frame as needed. This parameter becomes visible only when you clear the Inherit FFT length from input dimensions check box.

Inherit sample time from input

If you select the Inherit sample time from input check box, the block computes the frequency data from the sample period of the input signal. For the block to produce valid output, the following conditions must hold:

• The input to the block is the original signal, with no samples added or deleted (by insertion of zeros, for example).

• The sample period of the time-domain signal in the simulation equals the sample period of the original time series.

If these conditions do not hold, clear the Inherit sample time from input check box. You can then specify a sample time using the Sample time of original time series parameter.

Sample time of original time series

Specify the sample time of the original time-domain signal. This parameter becomes visible only when you clear the Inherit sample time from input check box.

## Supported Data Types

PortSupported Data Types

Input

• Double-precision floating point

• Single-precision floating point

Output

• Double-precision floating point

• Single-precision floating point

## References

[1] Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.

[2] Orfanidis, S. J. Introduction to Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1995.

[3] Orfanidis, S. J. Optimum Signal Processing: An Introduction. 2nd ed. New York, NY: Macmillan, 1985.