DSP Blockset

Burg Method

Compute a parametric spectral estimate using the Burg method

Library

Estimation / Power Spectrum Estimation

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

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. Nontunable.

Estimation order

The order of the AR model. This parameter is enabled when Inherit estimation order from input dimensions is not selected. Nontunable.

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. Nontunable.

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. Nontunable.

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 your data types 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

See Power Spectrum Estimation for related information.

Burg AR Estimator

Check Signal Attributes