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# pburg() - Signal Processing

### Syntax

### Example

### Output / Return Value

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### Reference

pxx = pburg(x,order) returns the power spectral density (PSD) estimate, pxx, of a discrete-time signal, x, found using Burg's method. When x is a vector, it is treated as a single channel. When x is a matrix, the PSD is computed independently for each column and stored in the corresponding column of pxx. pxx is the distribution of power per unit frequency. The frequency is expressed in units of rad/sample. order is the order of the autoregressive (AR) model used to produce the PSD estimate. examplepxx = pburg(x,order,nfft) uses nfft points in the discrete Fourier transform (DFT). For real x, pxx has length (nfft/2+1) if nfft is even, and (nfft+1)/2 if nfft is odd. For complex–valued x, pxx always has length nfft. pburg uses a default DFT length of 256. [pxx,w] = pburg(___) returns the vector of normalized angular frequencies, w, at which the PSD is estimated. w has units of rad/sample. For real-valued signals, w spans the interval [0,π] when nfft is even and [0,π) when nfft is odd. For complex-valued signals, w always spans the interval [0,2π). example[pxx,f] = pburg(___,fs) returns a frequency vector, f, in cycles per unit time. The sampling frequency, fs, is the number of samples per unit time. If the unit of time is seconds, then f is in cycles/second (Hz). For real-valued signals, f spans the interval [0,fs/2] when nfft is even and [0,fs/2) when nfft is odd. For complex-valued signals, f spans the interval [0,fs). [pxx,w] = pburg(x,order,w) returns the two-sided AR PSD estimates at the normalized frequencies specified in the vector, w. The vector, w, must contain at least two elements. [pxx,f] = pburg(x,order,f,fs) returns the two-sided AR PSD estimates at the frequencies specified in the vector, f. The vector, f, must contain at least two elements. The frequencies in f are in cycles per unit time. The sampling frequency, fs, is the number of samples per unit time. If the unit of time is seconds, then f is in cycles/second (Hz). [___] = pburg(x,order,___,freqrange) returns the AR PSD estimate over the frequency range specified by freqrange. Valid options for freqrange are: 'onesided', 'twosided', or 'centered'. [___,pxxc] = pburg(___,'ConfidenceLevel',probability) returns the probability × 100% confidence intervals for the PSD estimate in pxxc. examplepburg(___) with no output arguments plots the AR PSD estimate in dB per unit frequency in the current figure window.

pxx = pburg(x,order)pxx = pburg(x,order,nfft) example[pxx,w] = pburg(___)[pxx,f] = pburg(___,fs) example[pxx,w] = pburg(x,order,w)[pxx,f] = pburg(x,order,f,fs)[___] = pburg(x,order,___,freqrange)[___,pxxc] = pburg(___,'ConfidenceLevel',probability)pburg(___) example

Burg PSD Estimate of an AR(4) ProcessOpen This Example Create a realization of an AR(4) wide-sense stationary random process. Estimate the PSD using Burg's method. Compare the PSD estimate based on a single realization to the true PSD of the random process. Create an AR(4) system function. Obtain the frequency response and plot the PSD of the system.A = [1 -2.7607 3.8106 -2.6535 0.9238]; [H,F] = freqz(1,A,[],1); plot(F,20*log10(abs(H))) xlabel('Frequency (Hz)') ylabel('PSD (dB/Hz)') Create a realization of the AR(4) random process. Set the random number generator to the default settings for reproducible results. The realization is 1000 samples in length. Assume a sampling frequency of 1 Hz. Use pburg to estimate the PSD for a 4th-order process. Compare the PSD estimate with the true PSD.rng default x = randn(1000,1); y = filter(1,A,x); [Pxx,F] = pburg(y,4,1024,1); hold on plot(F,10*log10(Pxx)) legend('True Power Spectral Density','pburg PSD Estimate') Reflection Coefficients for Model Order DeterminationOpen This Example Create a realization of an AR(4) process. Use arburg to determine the reflection coefficients. Use the reflection coefficients to determine an appropriate AR model order for the process. Obtain an estimate of the process PSD. Create a realization of an AR(4) process 1000 samples in length. Use arburg with the order set to 12 to return the reflection coefficients. Plot the reflection coefficients to determine an appropriate model order.A = [1 -2.7607 3.8106 -2.6535 0.9238]; rng default x = filter(1,A,randn(1000,1)); [a,e,k] = arburg(x,12); stem(k,'filled') title('Reflection Coefficients') xlabel('Model Order') The reflection coefficients decay to zero after order 4. This indicates an AR(4) model is most appropriate.Obtain a PSD estimate of the random process using Burg's method. Use 1000 points in the DFT. Plot the PSD estimate.pburg(x,4,length(x)) Burg PSD Estimate of a Multichannel SignalOpen This Example Create a multichannel signal consisting of three sinusoids in additive white Gaussian noise. The sinusoids' frequencies are 100 Hz, 200 Hz, and 300 Hz. The sampling frequency is 1 kHz, and the signal has a duration of 1 s. Fs = 1000; t = 0:1/Fs:1-1/Fs; f = [100;200;300]; x = cos(2*pi*f*t)'+randn(length(t),3); Estimate the PSD of the signal using Burg's method with a 12th-order autoregressive model. Use the default DFT length. Plot the estimate.morder = 12; pburg(x,morder,[],Fs)