Power Computation of a Digital Stream

kaz - February 26, 2012 Coded in Matlab

This snippet implements the very basic concepts of power computation of a given digital stream. It looks at total power, ac power and dc power. It also compares the results with the statistical parameters of variance and its square root (standard of deviation or std).

The example stream given is complex but the same rules apply to real vector by setting the imaginary element to zero.

clear all;

%example vector having ac & dc power
x = complex(randn(1,2048)+.2,randn(1,2048)-.1);

%total power, three equivalent methods
pwr1_total = mean(abs(x).^2);                %mean of squared values
pwr2_total = mean(real(x).^2 + imag(x).^2);
pwr3_total = mean(x .* conj(x));

%total expressed as rms
rms_total = sqrt(pwr1_total);

%dc power
pwr1_dc = mean(real(x))^2 + mean(imag(x))^2; %square of mean of values

%ac power
pwr1_ac = pwr1_total - pwr1_dc;              %mean of squares - square of mean

%relation of ac power to statistical variance 
pwr2_ac = var(x);              %approximately

%ac expressed as rms
rms1_ac = sqrt(pwr1_ac);

%ac relation to standard of deviation, std = sqrt(var)
rms2_ac = std(x);              %approximately

%dc relation to variance
pwr2_dc = pwr1_total - var(x); %approximately

fprintf('power(total),          : %1.5f, %1.5f, %1.5f\r',pwr1_total,pwr2_total,pwr3_total);
fprintf('rms(total)             : %1.5f\r',rms_total);
fprintf('power(ac),  variance   : %1.5f, %1.5f\r',pwr1_ac,pwr2_ac);
fprintf('rms(ac),    std        : %1.5f, %1.5f\r',rms1_ac,rms2_ac);
fprintf('power(dc), (total-var) : %1.5f, %1.5f\r',pwr1_dc,pwr2_dc);