# bandpower

## Syntax

• p = bandpower(x) example
• p = bandpower(x,fs,freqrange) example
• p = bandpower(pxx,f,'psd') example
• p = bandpower(pxx,f,freqrange,'psd') example

## Description

example

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, specified as a two-element vector. You must input the sampling frequency, 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 string 'psd' indicates 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 string 'psd' indicates the input is a PSD estimate and not time series data.

## Examples

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### Comparison with Euclidean Norm

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 norm.

t = 0:0.001:1-0.001; x = cos(2*pi*100*t)+randn(size(t)); p = bandpower(x) l2norm = norm(x,2)^2/numel(x) 
p = 1.5264 l2norm = 1.5264 

### Percentage of Total Power in Frequency Interval

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.

t = 0:0.001:1-0.001; x = cos(2*pi*100*t)+randn(size(t)); pband = bandpower(x,1000,[50 100]); ptot = bandpower(x,1000,[0 500]); per_power = 100*(pband/ptot) 
per_power = 40.0243 

### Periodogram Input

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') avpow = norm(x,2)^2/numel(x) 
p = 1.5264 avpow = 1.5264 

### Percentage of Power in Frequency Band (Periodogram)

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,[50 100],'psd'); ptot = bandpower(Pxx,F,'psd'); per_power = 100*(pband/ptot) 
per_power = 42.0767 

### Average Power of a Multichannel Signal

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 norm.

p = bandpower(x) l2norm = dot(x,x)/length(x) 
p = 1.5264 1.5382 1.4717 l2norm = 1.5264 1.5382 1.4717 

## Input Arguments

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### x — Time series inputvector | matrix

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

### fs — Sampling frequency1 (default) | positive scalar

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

Data Types: double | single

### freqrange — Frequency range for band power computationtwo-element real-valued row or column vector

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 the following 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

### pxx — PSD estimatesreal-valued column vector with nonnegative elements

One- or two-sided PSD estimate, specified as a column vector with nonnegative elements.

Data Types: double | single

### f — Frequency vector for PSD estimatescolumn vector with real-valued elements

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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### p — Average band powernonnegative scalar

Average band power, returned as a nonnegative scalar.

Data Types: double | single