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 LevinsonDurbin recursion.
The input must be a column vector or an unoriented vector. This input represents a frame of consecutive time samples from a singlechannel signal. The block outputs a column vector containing the estimate of the power spectral density of the signal at N_{fft} equally spaced frequency points. The frequency points are in the range [0,F_{s}), where F_{s} is the sampling frequency of the signal.
When you select the Inherit estimation order from input dimensions parameter, the order of the allpole 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 N_{fft} 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 N_{fft} as a power of 2. The block zeropads or wraps the input to N_{fft} 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 timedomain 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 YuleWalker 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 YuleWalker Method blocks.
Burg  Covariance  Modified Covariance  YuleWalker  

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 LD 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 YW 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 linesplitting  
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 linesplitting 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 positivedefinite, 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 poweroftwo FFT length using the FFT length parameter.
 FFT length
Enter the number of data points on which to perform the FFT, N_{fft}. When N_{fft} is larger than the input frame size, the block zeropads each frame as needed. When N_{fft} 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 timedomain 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 timedomain signal. This parameter becomes visible only when you clear the Inherit sample time from input check box.
Supported Data Types
Port  Supported Data Types 

Input 

Output 

References
[1] Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: PrenticeHall, 1988.
[2] Orfanidis, S. J. Introduction to Signal Processing. Englewood Cliffs, NJ: PrenticeHall, 1995.
[3] Orfanidis, S. J. Optimum Signal Processing: An Introduction. 2nd ed. New York, NY: Macmillan, 1985.
Extended Capabilities
See Also
Blocks
 Burg AR Estimator  Covariance Method  Modified Covariance Method  ShortTime FFT  YuleWalker Method