Signal Processing Toolbox 
Spectral Estimation Method
The various methods of spectrum estimation available in the Signal Processing Toolbox are categorized as follows:
Nonparametric methods are those in which the PSD is estimated directly from the signal itself. The simplest such method is the periodogram. An improved version of the periodogram is Welch's method [8]. A more modern nonparametric technique is the multitaper method (MTM).
Parametric methods are those in which the PSD is estimated from a signal that is assumed to be output of a linear system driven by white noise. Examples are the YuleWalker autoregressive (AR) method and the Burg method. These methods estimate the PSD by first estimating the parameters (coefficients) of the linear system that hypothetically "generates" the signal. They tend to produce better results than classical nonparametric methods when the data length of the available signal is relatively short.
Subspace methods, also known as highresolution methods or superresolution methods, generate frequency component estimates for a signal based on an eigenanalysis or eigendecomposition of the correlation matrix. Examples are the multiple signal classification (MUSIC) method or the eigenvector (EV) method. These methods are best suited for line spectra  that is, spectra of sinusoidal signals  and are effective in the detection of sinusoids buried in noise, especially when the signal to noise ratios are low.
All three categories of methods are listed in the table below with the corresponding toolbox function and spectrum object names. More information about each function is on the corresponding function reference page. See Parametric Modeling for details about lpc
and other parametric estimation functions.
Method 
Description 
Functions 
Periodogram 
Power spectral density estimate 

Welch 
Averaged periodograms of overlapped, windowed signal sections 
spectrum.welch , pwelch , cpsd , tfestimate , mscohere 
Multitaper) 
Spectral estimate from combination of multiple orthogonal windows (or "tapers") 

YuleWalker AR 
Autoregressive (AR) spectral estimate of a timeseries from its estimated autocorrelation function 

Burg 
Autoregressive (AR) spectral estimation of a timeseries by minimization of linear prediction errors 

Covariance 
Autoregressive (AR) spectral estimation of a timeseries by minimization of the forward prediction errors 

Modified Covariance 
Autoregressive (AR) spectral estimation of a timeseries by minimization of the forward and backward prediction errors 

MUSIC 
Multiple signal classification 

Eigenvector 
Pseudospectrum estimate 

Nonparametric Methods
The following sections discuss the periodogram, modified periodogram, Welch, and multitaper methods of nonparametric estimation, along with the related CPSD function, transfer function estimate, and coherence function.
Periodogram
One way of estimating the power spectrum of a process is to simply find the discretetime Fourier transform of the samples of the process (usually done on a grid with an FFT) and take the magnitude squared of the result. This estimate is called the periodogram.
The periodogram estimate of the PSD of a lengthL signal x_{L}[n] is
The actual computation of X_{L}(f) can be performed only at a finite number of frequency points, N, and usually employs the FFT. In practice, most implementations of the periodogram method compute the Npoint PSD estimate
It is wise to choose N > L so that N is the next power of two larger than L. To evaluate X_{L}[f_{k}], we simply pad x_{L}[n] with zeros to length N. If L > N, we must wrap x_{L}[n] moduloN prior to computing X_{L}[f_{k}].
As an example, consider the following 1001element signal xn
, which consists of two sinusoids plus noise:
randn('state',0); fs = 1000; % Sampling frequency t = (0:fs)/fs; % One second worth of samples A = [1 2]; % Sinusoid amplitudes (row vector) f = [150;140]; % Sinusoid frequencies (column vector) xn = A*sin(2*pi*f*t) + 0.1*randn(size(t));
Note
The three last lines illustrate a convenient and general way to express the sum of sinusoids. Together they are equivalent to xn = sin(2*pi*150*t) + 2*sin(2*pi*140*t) + 0.1*randn(size(t));

The periodogram estimate of the PSD can be computed by creating a periodogram object
and a plot of the estimate can be displayed with the psd
method:
The average power can be computed by approximating the integral with the following sum:
You can also compute the average power from the onesided PSD estimate:
Spectral Analysis  Performance of the Periodogram 
© 19942005 The MathWorks, Inc.