| Signal Processing Blockset™ | |
Estimation / Power Spectrum Estimation
dspspect3
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 Nfft equally spaced frequency points in the range [0,Fs), where Fs is the signal's sample frequency.
When you select the Inherit estimation order from input dimensions parameter, 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 you select the Inherit FFT length from estimation order parameter, Nfft is specified by the frame size of the input, which must be a power of 2. When you do not select Inherit FFT length from estimation order, Nfft is specified as a power of 2 by the FFT length parameter, and the block zero pads or wraps the input to Nfft 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 |
The dspsacomp demo compares the Burg method with several other spectral estimation methods.
When selected, sets the estimation order to one less than the length of the input vector.
The order of the AR model. This parameter is enabled when you do not select Inherit estimation order from input dimensions.
When selected, uses the input frame size as the number of data points, Nfft, on which to perform the FFT.
Enter the number of data points on which to perform the FFT, Nfft. When Nfft is larger than the input frame size, each frame is zero-padded as needed. When Nfft is smaller than the input frame size, each frame is wrapped as needed. This parameter is enabled when you clear the Inherit FFT length from input dimensions check box.
Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.
Orfanidis, S. J. Introduction to Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1995.
Orfanidis, S. J. Optimum Signal Processing: An Introduction. 2nd ed. New York, NY: Macmillan, 1985.
| Port | Supported Data Types |
|---|---|
Input |
|
Output |
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| Burg AR Estimator | Signal Processing Blockset |
| Covariance Method | Signal Processing Blockset |
| Modified Covariance Method | Signal Processing Blockset |
| Short-Time FFT | Signal Processing Blockset |
| Yule-Walker Method | Signal Processing Blockset |
| pburg | Signal Processing Toolbox |
See Power Spectrum Estimation for related information.
| Burg AR Estimator | Check Signal Attributes | |
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