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bandpower

Band power

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Syntax

p = bandpower(x)
p = bandpower(x,fs,freqrange)
p = bandpower(pxx,f,"psd")
p = bandpower(pxx,f,freqrange,"psd")

Description

p = bandpower(x) returns the average power in the input signal x. If x is a matrix, then bandpower computes the average power in each column independently.

example

p = bandpower(x,fs,freqrange) returns the average power in the frequency range freqrange. You must input the sample rate fs to return the power in a specified frequency range. bandpower uses a modified periodogram to determine the average power in freqrange.

example

p = bandpower(pxx,f,"psd") returns the average power computed by integrating the power spectral density (PSD) estimate pxx. The integral is approximated by the rectangle method. The input f is a vector of frequencies corresponding to the PSD estimates in pxx. The "psd" option indicates that the input is a PSD estimate and not time series data.

example

p = bandpower(pxx,f,freqrange,"psd") returns the average power contained in the frequency interval freqrange. If the frequencies in freqrange do not match values in f, the closest values are used. The average power is computed by integrating the power spectral density (PSD) estimate pxx. The integral is approximated by the rectangle method. The "psd" option indicates the input is a PSD estimate and not time series data.

example

Examples

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Open Live Script

Create a signal consisting of a 100 Hz sine wave in additive N(0,1) white Gaussian noise. The sampling frequency is 1 kHz. Determine the average power and compare it against the ℓ2 norm.

t = 0:0.001:1-0.001;
x = cos(2*pi*100*t)+randn(size(t));

p = bandpower(x)
p = 
1.5264

l2norm = norm(x,2)^2/numel(x)
l2norm = 
1.5264
Open Live Script

Determine the percentage of the total power in a specified frequency interval.

Create a signal consisting of a 100 Hz sine wave in additive N(0,1) white Gaussian noise. The sampling frequency is 1 kHz. Determine the percentage of the total power in the frequency interval between 50 Hz and 150 Hz. Reset the random number generator for reproducible results.

rng('default')

t = 0:0.001:1-0.001;
x = cos(2*pi*100*t)+randn(size(t));

pband = bandpower(x,1000,[50 150]);
ptot = bandpower(x,1000,[0 500]);
per_power = 100*(pband/ptot)
per_power = 
51.9591
Open Live Script

Determine the average power by first computing a PSD estimate using the periodogram. Input the PSD estimate to bandpower.

Create a signal consisting of a 100 Hz sine wave in additive N(0,1) white Gaussian noise. The sampling frequency is 1 kHz. Obtain the periodogram and use the 'psd' flag to compute the average power using the PSD estimate. Compare the result against the average power computed in the time domain.

t = 0:0.001:1-0.001;
Fs = 1000;
x = cos(2*pi*100*t)+randn(size(t));

[Pxx,F] = periodogram(x,rectwin(length(x)),length(x),Fs);
p = bandpower(Pxx,F,'psd')
p = 
1.5264

avpow = norm(x,2)^2/numel(x)
avpow = 
1.5264
Open Live Script

Determine the percentage of the total power in a specified frequency interval using the periodogram as the input.

Create a signal consisting of a 100 Hz sine wave in additive N(0,1) white Gaussian noise. The sampling frequency is 1 kHz. Obtain the periodogram and corresponding frequency vector. Using the PSD estimate, determine the percentage of the total power in the frequency interval between 50 Hz and 150 Hz.

Fs = 1000;
t = 0:1/Fs:1-0.001;
x = cos(2*pi*100*t)+randn(size(t));

[Pxx,F] = periodogram(x,rectwin(length(x)),length(x),Fs);
pBand = bandpower(Pxx,F,[50 150],'psd');
pTot = bandpower(Pxx,F,'psd');
per_power = 100*(pBand/pTot)
per_power = 
49.1798
Open Live Script

Create a multichannel signal consisting of three sinusoids in additive N(0,1) 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);

Determine the average power of the signal and compare it to the ℓ2 norm.

p = bandpower(x)
p = 1×3

    1.5264    1.5382    1.4717


l2norm = dot(x,x)/length(x)
l2norm = 1×3

    1.5264    1.5382    1.4717

Input Arguments

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Input time series data, specified as a row or column vector or as a matrix. If x is a matrix, then its columns are treated as independent channels.

Example: cos(pi/4*(0:159))'+randn(160,1) is a single-channel column-vector signal.

Example: cos(pi./[4;2]*(0:159))'+randn(160,2) is a two-channel noisy sinusoid.

Data Types: double | single
Complex Number Support: Yes

Sampling frequency for the input time series data, specified as a positive scalar.

Data Types: double | single

Frequency range for the band power computation, specified as a two-element real-valued row or column vector. If the input signal x contains N samples, freqrange must be within these intervals:

  • [0, fs/2] if x is real-valued and N is even

  • [0, (N – 1)fs/(2N)] if x is real-valued and N is odd

  • [–(N – 2)fs/(2N), fs/2] if x is complex-valued and N is even

  • [–(N – 1)fs/(2N), (N – 1)fs/(2N)] if x is complex-valued and N is odd

Data Types: double | single

One- or two-sided PSD estimates, specified as a real-valued column vector or matrix with nonnegative elements.

The power spectral density must be expressed in linear units, not decibels. Use db2pow to convert decibel values to power values.

Example: [pxx,f] = periodogram(cos(pi./[4;2]*(0:159))'+randn(160,2)) specifies the periodogram PSD estimate of a noisy two-channel sinusoid sampled at 2π Hz and the frequencies at which it is computed.

Data Types: double | single

Frequency vector, specified as a column vector. The frequency vector f contains the frequencies corresponding to the PSD estimates in pxx.

Data Types: double | single

Output Arguments

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Average band power, returned as a nonnegative scalar.

Data Types: double | single

References

[1] Hayes, Monson H. Statistical Digital Signal Processing and Modeling. New York: John Wiley & Sons, 1996.

[2] Stoica, Petre, and Randolph Moses. Spectral Analysis of Signals. Upper Saddle River, NJ: Prentice Hall, 2005.

Extended Capabilities

Version History

Introduced in R2013a

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See Also

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