bandpower, why doesn't percentage power add up?

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!?

Answer 1

[Greg Dionne]

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

[CarrotCakeIsYum]

Sorry to be very late... but thank you!