Burg Method

Power spectral density estimate using Burg method

Libraries:
DSP System Toolbox / 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. The block minimizes the errors by constraining the AR parameters to satisfy the Levinson-Durbin recursion.

The block computes the spectrum from the FFT of the estimated AR model parameters.

Ports

Input

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Input — Input
column vector | unoriented vector

Specify the input as a column vector or an unoriented vector. This input represents a frame of consecutive time samples from a single-channel signal.

Data Types: single | double

Output

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Output — Power spectral density estimate
column vector

Power spectral density estimate of the signal at N_fft equally spaced frequency points, returned as a column vector. The frequency points are in the range [0,F_s), where F_s is the sampling rate of the signal.

Data Types: single | double

Parameters

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Inherit estimation order from input dimensions — Inherit estimation order from input dimensions
`off` (default) | `on`

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

Estimation order — Order of AR model
`6` (default) | nonnegative integer

Specify the estimation order of the AR model as a nonnegative integer.

Dependencies

To enable this parameter, clear the Inherit estimation order from input dimensions parameter.

Inherit FFT length from estimation order — Inherit FFT length from estimation order
`off` (default) | `on`

When you select this parameter, the FFT length N_fft 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 parameter. You can then specify the FFT length as a power of 2 using the FFT length parameter. The block zero-pads or wraps the input to N_fft before computing the FFT.

FFT length — FFT length
`256` (default) | positive integer greater than or equal to 2

Enter the number of data points N_fft on which to perform the FFT as a positive integer greater than or equal to 2. When N_fft is larger than the input frame size, the block zero-pads each frame as needed. When N_fft is smaller than the input frame size, the block wraps each frame as needed.

Dependencies

To enable this parameter, clear the Inherit FFT length from input dimensions parameter.

Inherit sample time from input — Inherit sample time from input
`on` (default) | `off`

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

The input to the block is an 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 parameter. You can then specify a sample time using the Sample time of original time series parameter.

Sample time of original time series — Sample time of original time-domain signal
`1` (default) | positive scalar

Specify the sample time of the original time-domain signal as a positive scalar.

Dependencies

To enable this parameter, clear the Inherit sample time from input parameter.

Block Characteristics

Data Types	`double` \| `single`
Multidimensional Signals	`No`
Variable-Size Signals	`No`

More About

expand all

Compare Power Spectral Density Estimation Methods

The Burg Method and Yule-Walker Method blocks return similar results for large frame sizes.

This table compares the features of the Burg Method block to the Covariance Method, Modified Covariance Method, and the 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
Characteristics	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 Yule-Walker 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
	Always produces a stable model		Does not suffer spectral line-splitting	Always produces a stable model
Disadvantages	Peak locations highly dependent on initial phase	Can produce unstable models	Can produce unstable models	Performs relatively poorly for short data records
	Can 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	Frequency bias for estimates of sinusoids in noise	Minor frequency bias for estimates of sinusoids in noise	Frequency bias for estimates of sinusoids in noise
Conditions for Nonsingularity		Order must be less than or equal to 1/2 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

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.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Usage notes and limitations:

When the FFT length is not a power of 2, the executable generated from this block relies on prebuilt dynamic library files (.dll files) included with MATLAB^®. Use the packNGo function to package the code generated from this block and all the relevant files in a compressed zip file. Using this zip file, you can relocate, unpack, and rebuild your project in another development environment where MATLAB is not installed. For more details, see How To Run a Generated Executable Outside MATLAB.
When the FFT length is a power of 2, you can generate standalone C and C++ code from this block.

Version History

Introduced before R2006a

Burg Method

Description

Ports

Input

Input — Input
column vector | unoriented vector

Output

Output — Power spectral density estimate
column vector

Parameters

Inherit estimation order from input dimensions — Inherit estimation order from input dimensions
`off` (default) | `on`

Estimation order — Order of AR model
`6` (default) | nonnegative integer

Dependencies

Inherit FFT length from estimation order — Inherit FFT length from estimation order
`off` (default) | `on`

FFT length — FFT length
`256` (default) | positive integer greater than or equal to 2

Dependencies

Inherit sample time from input — Inherit sample time from input
`on` (default) | `off`

Sample time of original time series — Sample time of original time-domain signal
`1` (default) | positive scalar

Dependencies

Block Characteristics

More About

Compare Power Spectral Density Estimation Methods

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

Topics

Burg Method

Description

Ports

Input

Input — Input column vector | unoriented vector

Output

Output — Power spectral density estimate column vector

Parameters

Inherit estimation order from input dimensions — Inherit estimation order from input dimensions off (default) | on

Estimation order — Order of AR model 6 (default) | nonnegative integer

Dependencies

Inherit FFT length from estimation order — Inherit FFT length from estimation order off (default) | on

FFT length — FFT length 256 (default) | positive integer greater than or equal to 2

Dependencies

Inherit sample time from input — Inherit sample time from input on (default) | off

Sample time of original time series — Sample time of original time-domain signal 1 (default) | positive scalar

Dependencies

Block Characteristics

More About

Compare Power Spectral Density Estimation Methods

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

Topics

Input — Input
column vector | unoriented vector

Output — Power spectral density estimate
column vector

Inherit estimation order from input dimensions — Inherit estimation order from input dimensions
`off` (default) | `on`

Estimation order — Order of AR model
`6` (default) | nonnegative integer

Inherit FFT length from estimation order — Inherit FFT length from estimation order
`off` (default) | `on`

FFT length — FFT length
`256` (default) | positive integer greater than or equal to 2

Inherit sample time from input — Inherit sample time from input
`on` (default) | `off`

Sample time of original time series — Sample time of original time-domain signal
`1` (default) | positive scalar

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.