Question

: The Root Mean Square of a discrete-time signal is given by

We can easily calculate the RMS of signals in MATLAB using a combination of the sum, sqrt, and ^ commands. N represents the number of samples of the signal. Please note that the command .^ applied to a vector squares each element of the vector.

Write a script to calculate the RMS of the discrete-time signal x, defined as follows: n = a vector of number between -23 and 45 with increments of 0.1.

x = (n/2 + n³)./100

There is a function that calculates the rms in matlab (rms) compare the results of your formula with that of the native function.

Answer 1

n = [-23:0.1:45]   % creating a vector
x = (n/2 + n.^3)./100

% finding rms using conventional method
vs = sum(x.^2);
rms1 = sqrt(vs / (numel(x)+1))

% finding rms using matlab function
rms2 = rms(x)

As we can see that the inbuilt formula and conventional method only hold true until the decimal precision starts. Inbuilts formula gives the rms value slightly larger than the conventional method.