Burg Method (DSP Blockset)

Compute a parametric spectral estimate using the Burg method.

Library

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 while constraining the AR parameters to satisfy the Levinson-Durbin recursion.

The input is a sample-based vector (row, column, or 1-D) or frame-based vector (column only) representing a frame of consecutive time samples from a single-channel signal. The block's output (a column vector) is the estimate of the signal's power spectral density at N_fft equally spaced frequency points in the range [0,F_s), where F_s is the signal's sample frequency.

When Inherit estimation order from input dimensions is selected, the order of the all-pole model is one less that the input frame size. Otherwise, the order is the value specified by the Estimation order parameter. The spectrum is computed from the FFT of the estimated AR model parameters.

When Inherit FFT length from estimation order is selected, N_fft is specified by the frame size of the input, which must be a power of 2. When Inherit FFT length from estimation order is not selected, N_fft is specified as a power of 2 by the FFT length parameter, and the block zero pads or truncates the input to N_fft before computing the FFT. The output is always sample-based.

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.

Burg
Covariance
Modified Covariance
Yule-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")

Advantages
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

Disadvantages
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 positive-definite, hence nonsingular

	Burg	Covariance	Modified Covariance	Yule-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")
Advantages	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
Disadvantages	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 positive-definite, hence nonsingular

Examples

The dspsacomp demo compares the Burg method with several other spectral estimation methods.

Dialog Box

Inherit estimation order from input dimensions: When selected, sets the estimation order to one less than the length of the input vector. Tunable.
Estimation order: The order of the AR model. This parameter is enabled when Inherit estimation order from input dimensions is not selected.
Inherit FFT length from estimation order: When selected, uses the input frame size as the number of data points, N_fft, on which to perform the FFT. Tunable.
FFT length: The number of data points, N_fft, on which to perform the FFT. If N_fft exceeds the input frame size, the frame is zero-padded as needed. This parameter is enabled when Inherit FFT length from input dimensions is not selected.

References

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

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

Supported Data Types

Double-precision floating point
Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Burg AR Estimator
DSP Blockset

Covariance Method
DSP Blockset

Modified Covariance Method
DSP Blockset

Short-Time FFT
DSP Blockset

Yule-Walker Method
DSP Blockset

pburg
Signal Processing Toolbox

Burg AR Estimator	DSP Blockset
Covariance Method	DSP Blockset
Modified Covariance Method	DSP Blockset
Short-Time FFT	DSP Blockset
Yule-Walker Method	DSP Blockset
`pburg`	Signal Processing Toolbox

See Power Spectrum Estimation for related information. Also see a list of all blocks in the Power Spectrum Estimation library.

Burg AR Estimator Check Signal Attributes