bandpower, why doesn't percentage power add up?

Question

CarrotCakeIsYum 2015-10-19

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https://ww2.mathworks.cn/matlabcentral/answers/249420-bandpower-why-doesn-t-percentage-power-add-up

评论： CarrotCakeIsYum 2016-10-26

I'm measuring the frequency people sway at whilst they balance. I need to calculate the percentage power of specific frequency bands. The input vector is sampled at 1000Hz, and has a length of 15000.

To do this I've been using the Matlab function 'bandpower', and have written the following function:

function output = balance_power_test(data)
%Calculates the power of frequencies in four frequency bands.
%Output is given as percentage of total power.
output = zeros(4,1);
ptot = bandpower(data,1000,[0 500]);
pwr_band1 = bandpower(data,1000,[0 50]);
pwr_band2 = bandpower(data,1000,[50 100]);
pwr_band3 = bandpower(data,1000,[100 200]);
pwr_band4 = bandpower(data,1000,[200 500]);
output(1) = 100*(pwr_band1/ptot);
output(2) = 100*(pwr_band2/ptot);
output(3) = 100*(pwr_band3/ptot);
output(4) = 100*(pwr_band4/ptot);
end

However I'm finding that the percentages of power don't add up to anywhere near 100%. E.g. testing the above:

rng('default')
t = 0:0.001:1-0.001;
x = cos(2*pi*100*t)+randn(size(t));
>> balance_power_test(x)
ans =
      0.0847
      0.0847
      0.0847
      0.3879

The percentage powers add up to 64.19%. What am I doing wrong!?

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Answer 1

Greg Dionne 2015-10-22

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在 MATLAB Online 中打开

Looks like you're double-counting frequencies.

Try this instead:

function output = balance_power_test(data)
%Calculates the power of frequencies in four frequency bands.
%Output is given as percentage of total power.
output = zeros(4,1);
ptot = bandpower(data,1000,[0 500]);
pwr_band1 = bandpower(data,1000,[0 50]);
pwr_band2 = bandpower(data,1000,[51 100]);
pwr_band3 = bandpower(data,1000,[101 200]);
pwr_band4 = bandpower(data,1000,[201 500]);
output(1) = 100*(pwr_band1/ptot);
output(2) = 100*(pwr_band2/ptot);
output(3) = 100*(pwr_band3/ptot);
output(4) = 100*(pwr_band4/ptot);
end