Estimate power spectrum or powerdensity spectrum
Estimation / Power Spectrum Estimation
dspspect3
The Spectrum Estimator block outputs the power spectrum or powerdensity spectrum of a real or complex input signal, using the Welch method of averaged modified periodograms and the filter bank approach.
When you choose the filter bank approach, the block uses an analysis filter bank to estimate the power spectrum. The filter bank approach produces a spectral estimate with a higher resolution, a more accurate noise floor, and more precise peaks than the Welch method, with low or no spectral leakage. They come at the expense of increased computation and slower tracking.
When you choose the Welch method, the block computes the averaged modified periodograms to compute the spectral estimate. The block buffers the input data into overlapping segments. Use the block parameters to set the length of the data segments, the amount of data overlap between consecutive segments, and other features of the power spectrum.
For more information on the Welch method and the filter bank method, see Algorithms.
Each column of the input signal is treated as a separate channel. If the input is a twodimensional signal, the first dimension represents the channel length (or frame size) and the second dimension represents the number of channels. If the input is a onedimensional signal, then it is interpreted as a single channel.
Specify the spectral estimation method.
Filter bank
(default) —
An analysis filter bank splits the broadband input signal into multiple
narrow subbands. The block computes the power in each narrow frequency
band, and the computed value is the spectral estimate over the respective
frequency band.
Welch
— The block
uses the Welch averaged modified periodograms method to compute the
power spectrum over the narrow subbands.
Specify the number of filter coefficients, or taps, for each frequency band. This value corresponds to the number of filter coefficients per polyphase branch. The total number of filter coefficients is equal to Number of taps per band times the FFT length.
This parameter applies when you set Method to Filter
bank
. The default is 12.
Type of spectrum to compute. You can set this parameter to:
Power
(default) —
Compute the power spectrum.
Power density
—
Compute the power spectral density.
This parameter is nontunable.
Frequency resolution method. You can set this parameter to:
Auto
(default) —
The Spectrum Estimator block computes the resolution bandwidth (RBW)
so that the frequency span fits 1024 RBW intervals.
Welch method — The window length, winLen, is calculated using . NENBW is the equivalent noise bandwidth of the window and Fs is the sample rate.
Filter bank method — The FFT length is the ceiling of the ratio of Sample rate (Hz) to the computed resolution bandwidth.
RBW
— Specify the
resolution bandwidth, which is used to determine the window length
(Welch method) or the FFT length (filter bank method). When the block
uses the Welch method, the behavior is equivalent to that of the Spectrum Analyzer block. The window length
is calculated using . NENBW is the
equivalent noise bandwidth of the window and Fs is
the sample rate. The FFT length is equal to the ceiling of the ratio
of Sample rate (Hz) to RBW (Hz).
Window length
—
Specify the window or segment length to use in the Welch algorithm.
This option appears when you set Method to Welch
.
Number of frequency bands
—
Specify the number of polyphase branches of the analysis filter bank.
This value corresponds to the FFT length that the filter bank uses.
This option appears when you set Method to Filter
bank
.
This parameter is nontunable.
Resolution bandwidth, specified as a positive scalar in Hz.
The default is 5
. This parameter applies when you
set Frequency resolution method to RBW
.
The ceiling of the ratio of the frequency span to RBW must be greater
than 2
.
This parameter is nontunable.
Source of the number of frequency bands. This parameter applies
when you set Method to Filter bank
and Frequency
resolution method to Number of frequency bands
.
You can set this parameter to:
Same as input frame length
(default)
— The FFT length is set to the frame size of the input.
Specify on dialog
—
The FFT length is the value you specify in Number of bands.
This parameter is nontunable.
Number of frequency bands, or the FFT length the filter bank
uses to compute the power spectral estimate, specified as a positive
scalar. The default is 1024
. This parameter applies
when you set Method to Filter bank
, Frequency
resolution method to Number of frequency bands
,
and Number of bands source to Specify
on dialog
. This parameter is nontunable.
Source of the window length value. This parameter applies when
you set Method to Welch
and Frequency
resolution method to Window length
.
You can set this parameter to:
Same as input frame length
(default)
— Window length is set to the frame size of the input. Specify
this option to obtain behavior equivalent to that of the Periodogram block.
Specify on dialog
—
Window length is the value you specify in the Window length parameter.
This parameter is nontunable.
Length of the window used to compute the spectrum estimate,
specified as a positive integer scalar greater than 2
.
The default is 1024
. This parameter applies when
you set Method to Welch
, Frequency
resolution method to Window length
,
and Window length source to Specify
on dialog
. This parameter is nontunable.
Source of the FFT length value. This parameter applies when
you set Method to Welch
and Frequency
resolution method to Window length
.
You can set this parameter to:
Auto
(default) —
The block sets the FFT length to the frame size of the input.
Property
— The block
sets the FFT length to the value you specify in FFT length.
This parameter is nontunable.
Length of the FFT used to compute the spectrum estimates, specified
as a positive integer scalar. This parameter applies when you set Method to Welch
, Frequency
resolution method to Window length
,
and FFT length source to Property
.
The default is 1024
. This parameter is nontunable.
When you select this check box, the block sample rate is computed as N/T_{s}, where N is the frame size of the input signal and T_{s} is the sample time of the input signal.
This check box applies when you do one of the following:
Set Method to Welch
and Frequency
resolution method to Window length
.
Set Method to Filter
bank
and Frequency resolution method to Number
of frequency bands
.
When you clear this check box, the block sample rate is the value you specify in Sample rate (Hz). By default, this check box is selected. This parameter is nontunable.
Sample rate of the input signal, specified as a positive scalar.
The default is 44100
. This parameter applies when
you do one of the following:
Set Frequency resolution method to Auto
or RBW
.
Set Method to Welch
, Frequency
resolution method to Window length
,
and clear the Inherit sample rate from input check
box.
Set Method to Filter
bank
, Frequency resolution method to Number
of frequency bands
, and clear the Inherit
sample rate from input check box.
This parameter is nontunable.
Window function the Welch algorithm uses, specified as one of Chebyshev
 Flat
Top
 Hamming
 Hann
 Kaiser
 Rectangular
.
This parameter appears when you set Method to Welch
.
The default is Hann
. This parameter is
nontunable.
Sidelobe attenuation of the window, specified as a real positive
scalar greater than or equal to 45
, in dB. The
default is 60
. This parameter appears when you
set Method to Welch
and Window
function to Chebyshev
or Kaiser
.
This parameter is nontunable.
Number of spectral averages, specified as a positive integer
scalar. The default is 1
. The spectrum estimator
computes the current power spectrum estimate by averaging the last N power
spectrum estimates, where N is the number of spectral
averages defined in Number of spectral averages.
This parameter is nontunable.
Percentage of overlap between successive data windows, specified
as a scalar from 0
and 100
.
The default value is 0
. To enable this parameter,
on the Main Tab, set Method to Welch
.
This parameter is nontunable.
Load used as a reference to compute the power values, specified
as a real positive scalar expressed in ohms. The default value is 1
.
This parameter is nontunable.
Frequency range of the spectrum estimator. You can set this parameter to:
Onesided
— The
spectrum estimator computes the onesided spectrum of a real input
signal. When the FFT length, NFFT
, is even, the
spectrum estimate has length (NFFT
/2
) + 1
and is computed
over the frequency range [0 SampleRate/2]
. SampleRate
is
the sample rate of the input signal. When NFFT
is
odd, the spectrum estimate has length (NFFT
+ 1)/2
and is computed
over the frequency range [0 SampleRate/2
).
Twosided
— The
spectrum estimator computes the twosided spectrum of a complex or
real input signal. The length of the spectrum estimate is equal to
the FFT length. The spectrum estimate is computed over the frequency
range [0 SampleRate
), where SampleRate
is
the sample rate of the input signal.
Centered
(default) —
The spectrum estimator computes the centered twosided spectrum of
a complex or real input signal. The length of the spectrum estimate
is equal to the FFT length. The spectrum estimate is computed over
the frequency range (SampleRate/2 SampleRate/2
]
when the FFT length is even and (SampleRate/2 SampleRate/2)
when
the FFT length is odd.
This parameter is nontunable.
Units used to measure power. You can set this parameter to:
'Watts'
(default) — The
spectrum estimator measures power in watts.
'dBw'
— The spectrum estimator
measures power in decibelwatts.
'dBm'
— The spectrum estimator
measures power in decibelmilliwatts.
This parameter is nontunable.
When you select this check box, the block computes the maxhold spectrum of the input signal by keeping, at each frequency bin, the maximum value of all the power spectrum estimates. By default, this check box is not selected. This parameter is nontunable.
When you select this check box, the block computes the minhold spectrum of the input signal by keeping, at each frequency bin, the minimum value of all the power spectrum estimates. By default, this check box is not selected. This parameter is nontunable.
When you select this check box, the block outputs the frequency vector. By default, this check box is not selected. This parameter is nontunable.
When you select this check box, the block computes the effective resolution bandwidth. By default, this check box is not selected. This parameter is nontunable.
Type of simulation to run. You can set this parameter to:
Code generation
(default)
— Simulate model using generated C code. The first time you
run a simulation, Simulink^{®} generates C code for the block. The
C code is reused for subsequent simulations, as long as the model
does not change. This option requires additional startup time but
provides faster simulation speed than Interpreted
execution
.
Interpreted execution
—
Simulate model using the MATLAB^{®} interpreter. This option
shortens startup time but has slower simulation speed than Code
generation
.
Estimate the Power Spectral Density (PSD) of a chirp signal using the Spectrum Estimator block. Compare the PSD data with a Bluetooth^{®} spectral mask and determine if the PSD data complies with the mask.
To view the complete model, enter ex_psd_spectralmask
in
the MATLAB command prompt.
Input Signal
The input to the Spectrum Estimator block is a chirp signal
embedded in Gaussian noise with zero mean and a variance of 0.01
.
The chirp signal is amplified with a gain factor in the range [0
1
].
Spectral Mask
The Spectral mask is created using the MATLAB Function block. The mask is based on the Bluetooth standard described in [5].
Live Processing
The Spectrum Estimator block estimates the PSD of the chirp.
In this example, the PSD data is compared with the spectral mask.
The Display block shows a 1
or 0
,
depending on whether the spectral data is within the mask or not.
During simulation, you can change the power in the input signal by
moving the slider in the Slider Gain block. Simultaneously,
you can view this change in the Array Plot block.
Port  Supported Data Types 

Input 

Output 

[1] Hayes, Monson H. Statistical Digital Signal Processing and Modeling. Hoboken, NJ: John Wiley & Sons, 1996.
[2] Kay, Steven M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice Hall, 1999.
[3] Stoica, Petre, and Randolph L. Moses. Spectral Analysis of Signals. Englewood Cliffs, NJ: Prentice Hall, 2005.
[4] Welch, P. D. “The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms.” IEEE Transactions on Audio and Electroacoustics. Vol. 15, No. 2, June 1967, pp. 70–73.
[5] Bluetooth Specification Version 4.2. Bluetooth SIG. December 2014, p. 217. Specification of the Bluetooth System