Periodogram

Power spectral density or mean-square spectrum estimate using periodogram method

Library

Estimation / Power Spectrum Estimation

dspspect3

Description

The Periodogram block estimates the power spectral density (PSD) or mean-square spectrum (MSS) of the input. It does so by using the periodogram method and Welch's averaged, modified periodogram method. The block averages the squared magnitude of the FFT computed over windowed sections of the input. It then normalizes the spectral average by the square of the sum of the window samples. See Periodogram and Welch's Method in the Signal Processing Toolbox™ documentation for more information.

The block treats M-by-N frame-based matrix input and M-by-N sample-based matrix input as M sequential time samples from N independent channels. The block computes a separate estimate for each of the N independent channels and generates an Nfft-by-N matrix output.

Each column of the output matrix contains the estimate of the power spectral density of the corresponding input column at Nfft equally spaced frequency points. The frequency points are in the range [0,Fs), where Fs is the sampling frequency of the signal. The block always outputs sample-based data.

Dialog Box

Measurement

Specify the type of measurement for the block to perform: Power spectral density or Mean-square spectrum. Tunable.

Window

Select the type of window to apply. See the Window Function block reference page for more details. Tunable.

Stopband attenuation in dB

Enter the level, in decibels (dB), of stopband attenuation, Rs, for the Chebyshev window. This parameter becomes visible if, for the Window parameter, you choose Chebyshev. Tunable.

Beta

Enter the β parameter for the Kaiser window. This parameter becomes visible if, for the Window parameter, you chose Kaiser. Increasing Beta widens the mainlobe and decreases the amplitude of the sidelobes in the displayed frequency magnitude response. Tunable. See the Window Function block reference page for more details.

Window sampling

From the list, choose Symmetric or Periodic. See the Window Function block reference page for more details.Tunable.

FFT implementation

Set this parameter to FFTW [1], [2] to support an arbitrary length input signal. The block restricts generated code with FFTW implementation to MATLAB® host computers.

Set this parameter to Radix-2 for bit-reversed processing, fixed or floating-point data, or for portable C-code generation using the Simulink® Coder™. The first dimension M, of the input matrix must be a power of two. To work with other input sizes, use the Pad block to pad or truncate these dimensions to powers of two, or if possible choose the FFTW implementation.

Set this parameter to Auto to let the block choose the FFT implementation. For non-power-of-two transform lengths, the block restricts generated code to MATLAB host computers.

Inherit FFT length from input dimensions

When you select this check box, the block uses the input frame size as the number of data points, Nfft, on which to perform the FFT. 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 power of two FFT length using the FFT length parameter.

FFT length

Enter the number of data points on which to perform the FFT, Nfft. When Nfft is larger than the input frame size, the block zero-pads each frame as needed. When Nfft 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.

When you set the FFT implementation parameter to Radix-2, this value must be a power of two.

Number of spectral averages

Specify the number of spectra to average. When you set this value to 1, the block computes the periodogram of the input. When you set this value greater 1, the block implements Welch's Method to compute a modified periodogram of the input.

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 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 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 time-domain signal. This parameter becomes visible only when you clear the Inherit sample time from input check box.

Example

The dspstfftdspstfft example provides an illustration of using the Periodogram and Matrix Viewer blocks to create a spectrogram. The dspsacompdspsacomp example compares the Periodogram block with several other spectral estimation methods.

References

Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1989.

Orfanidis, S. J. Introduction to Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1995.

Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.

References

[1] FFTW (http://www.fftw.org)

[2] Frigo, M. and S. G. Johnson, "FFTW: An Adaptive Software Architecture for the FFT,"Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Vol. 3, 1998, pp. 1381-1384.

Supported Data Types

PortSupported Data Types

Input

  • Double-precision floating point

  • Single-precision floating point

Output

  • Double-precision floating point

  • Single-precision floating point

See Also

Burg MethodDSP System Toolbox
Inverse Short-Time FFTDSP System Toolbox
Magnitude FFTDSP System Toolbox
Short-Time FFTDSP System Toolbox
Spectrum AnalyzerDSP System Toolbox
Window FunctionDSP System Toolbox
Yule-Walker MethodDSP System Toolbox

See Spectral Analysis for related information.

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