Periodogram

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

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Libraries:
DSP System Toolbox / Estimation / Power Spectrum Estimation

Description

The Periodogram block estimates the power spectral density (PSD) or mean-square spectrum (MSS) of the input. The block uses the periodogram method and Welch's averaged, modified periodogram method. The block averages the squared magnitude of the FFT function computed over windowed sections of the input. It then normalizes the spectral average by the square of the sum of the window samples. For more information, see Periodogram and Welch's Method.

Examples

Compute Periodogram of Signal

Using the Periodogram block, compute the periodogram of signal.

• Open Model

Ports

Input

Port_1 — Input signal

vector | matrix

Input signal, specified as a vector or a matrix.

The block treats M-by-N matrix input as M sequential time samples from N independent channels.

Data Types: single | double
Complex Number Support: Yes

Output

Port_1 — Output signal

vector | matrix

Output signal, returned as a vector or a matrix.

Each column of the output matrix contains the estimate of the power spectral density of the corresponding input column 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.

The block computes a separate estimate for each of the N independent channels and generates an N_fft-by-N matrix output.

Data Types: single | double

Parameters

Measurement — Measurement type

Power spectral density (default) | Mean-square spectrum

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

Tunable: No

Window — Window type

Hamming (default) | Bartlett | Blackman | Boxcar | Chebyshev | Hann | Hanning | Kaiser | Triang

Select the type of window to apply.

For details, see the Window Function block reference page.

Tunable: Yes

Beta — Beta

5 (default) | scalar

Enter the β parameter for the Kaiser window. Increasing Beta widens the mainlobe and decreases the amplitude of the sidelobes in the displayed frequency magnitude response.

For more details, see the Window Function block reference page.

Tunable: Yes

Dependencies

This parameter becomes visible if, for the Window parameter, you chose Kaiser.

Window sampling — Window sampling

Symmetric (default) | Periodic

From the list, choose Symmetric or Periodic.

See the Window Function block reference page for more details.

Tunable: Yes

Dependencies

This parameter becomes visible only if you set the Window parameter to one of Blackman, Hamming, Hann, or Hanning.

FFT implementation — FFT implementation

Auto (default) | Radix-2 | FFTW

Set this parameter to FFTW to support an arbitrary length input signal. The block restricts generated code with an 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 by using 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 enable the block choose the FFT implementation. For non-power-of-two transform lengths, the block restricts generated code to MATLAB host computers.

Tunable: No

Stopband attenuation in dB — Stopband attenuation in dB

50 (default) | scalar

Enter the level, in decibels (dB), of stopband attenuation, R_s, for the Chebyshev window.

Tunable: Yes

Dependencies

This parameter becomes visible if, for the Window parameter, you choose Chebyshev.

Inherit FFT length from input dimensions — Inherit FFT length

off (default) | on

When you select this check box, the block uses the input frame size as the number of data points, N_fft, on which to perform the FFT. To specify the number of points on which to perform the FFT, clear the Inherit FFT length from input dimensions check box. You can then specify a power of two FFT length by using the FFT length parameter.

Tunable: No

FFT length — Number of data points

256 (default) | scalar

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 zero-pads each frame as needed. When N_fft is smaller than the input frame size, the block wraps each frame as needed.

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

Tunable: No

Dependencies

This parameter becomes visible only when you clear the Inherit FFT length from input dimensions check box.

Number of spectral averages — Number of spectral averages

4 (default) | scalar

Specify the number of spectral 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.

Tunable: No

Inherit sample time from input — Inherit sample time from input

on (default) | off

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 by using the Sample time of original time series parameter.

Dependencies

This parameter becomes visible only if you set the Measurement parameter to Power spectral density.

Sample time of original time series — Sample time of original time series

1 (default) | scalar

Specify the sample time of the original time-domain signal.

Tunable: No

Dependencies

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

Block Characteristics

Data Types	double | single
Multidimensional Signals	No
Variable-Size Signals	No

References

[1] FFTW ( https://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.

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

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

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Usage notes and limitations:

• Generated code relies on the memcpy or memset function (string.h) under certain conditions.

• When the following conditions apply, the executable generated from this block relies on prebuilt dynamic library files (.dll files) included with MATLAB:

  • FFT implementation is set to FFTW.

  • Inherit FFT length from input dimensions is cleared and FFT length is set to a value that is not a power of two.

  Use the packNGo function to package the code generated from this block and all the relevant files in a compressed zip file. Using this zip file, you can relocate, unpack, and rebuild your project in another development environment where MATLAB is not installed. For more details, see How To Run a Generated Executable Outside MATLAB.

• When the FFT length is a power of two, you can generate standalone C and C++ code from this block.

Version History

Introduced before R2006a