Calculate the sum of two RMS values and theoretical RMS.

Question

Michael 2023-2-17

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https://ww2.mathworks.cn/matlabcentral/answers/1914510-calculate-the-sum-of-two-rms-values-and-theoretical-rms

回答： Rik 2023-2-17

2.19 Verify Equation 2.28 using simulated data. Generate two 1000-point random waveforms using randn. Make one waveform twice the amplitude of the other. Calculate the RMS of each, then add the two together and determine the RMS of this sum. Compare the RMS of the sum with the theoretical value determined by taking the square root of the sum of the two individual RMS values squared as predicted by Equation 2.28. Am I calculating xyRMS and tRMS correctly?

Code:

clear all;
close all;
clc;
N = 1000;
x = randn(1, N);
y = 2*randn(1, N);
z = x + y;
xRMS = sqrt(sum(x.^2));        % Evaluate the RMS value of x
yRMS = sqrt(sum(y.^2));        % Evaluate the RMS value of y
xyRMS = xRMS + yRMS;                % Calculate the sum of RMS?
tRMS = sqrt(sum(x.^2)+sum(y.^2));   % Calculate the theoretical sum of RMS?
disp('RMS value of the two sums of RMS values:');
disp(xyRMS);
disp('Theoretical RMS value of the mean of two RMS sums combined:');
disp(tRMS);

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Answer 1

Rik 2023-2-17

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With vectors of the same size you shouldn't notice a difference, but you are calculating a root sum square, not a root mean square. Simply replace sum by mean and what you wrote looks fine.