Question

6) Consider the below wave form when a-1 Hz (2n rad/sec) and b-0.9a F(t) sin(at)+sin(bt) I. Calculate the beat frequency. II. Plot the beat frequency II. What is the optimum sampling rate? IV. Calculate the time interval between samples at the optimum sampling rate

Please help, the plotting can be done in excel or matlab

Answer 1

Given

I. $F(t)=sin(at)+sin(bt)$

The beat frequency is $\Delta f=\frac{b\sim a}{2 \pi } ( Hz)$ $=\frac{1-0.9}{2 \pi } ( Hz)=0.016(Hz)$

II. %%% MATLAB CODE

close all;
clear all;
clc;
a=1;
b=0.9*a;
t=0:01:250
y = sin(a*t)+sin(b*t);
plot(t, y);
xlabel('times');
ylabel( ' resultant wave');
%%%%%%%END

resultant wave 9
III) Optimum Sampling rate is twice the beat frequency. i.e $f_s=2 \Delta f=0.032(Hz)$

IV) Intervals between the samples at optimum sampling rate is $T_s=\frac{1}{2 \Delta f}=\frac{1}{0.032}=31.25(s)$