Question

Some signals can be conveniently written as a product of a slowly-varying amplitude function and a rapidly-varying sinusoid or sum of sinusoids. Let a signal have amplitude function a(t) = 3(t^0.5)(10^(−t)) and sum of sinusiods c(t) = 0.5 sin(2 π 300 t) + 0.5 sin(2 π 450 t). Multiply these to obtain the total signal, y(t) = a(t) c(t). Let the time interval be from 0 to 5 seconds and the sample rate be 8000 samples per second. Plot a(t) vs. t over the entire time interval. Plot c(t) vs. t but show only about a 0.03 second interval on the time axis so the waveform is clearly visible. Use the "sound" function to play the sound and describe what you hear. MATLAB CODE NEEDED!!!!!!!!!!!!!!!!!

Some signals can be conveniently written as a product of a slowly-varying amplitude function and a rapidly-varying sinusoid or sum of sinusoids. Let a signal have amplitude function a()- 3(t 0.5)(10^( t)) and sum of sinusiods c(t) = 0.5 sin(2 π 300 t) + 0.5 sin(2 π 450 t). Multiply these to obtain the total signal, y(t) = a(t) C(t) Let the time interval be from 0 to 5 seconds and the sample rate be 8000 samples per second. Plot a(t) vs. t over the entire time interval. Plot ct) vs.t but show only about a 0.03 second interval on the time axis so the waveform is clearly visible Use the "sound" function to play the sound and describe what you hear.

Answer 1

clear all
close all
%initialzing time vector from 0 to 5 sec with 8000 samples per second
t=0:1/8000:5;
%defining a(t)
a=3*sqrt(t).*10.^(-t);
%defining c(t)
c=0.5*sin(2*pi*300*t)+0.5*sin(2*pi*450*t);
%obtaining y(t)=a(t)*c(t)
y=a.*c;
%plotting a(t) vs. t for full time 0 to 5 seconds
figure(1)
plot(t,a,'LineWidth',1.5);
xlabel('Time (sec)')
ylabel('a(t)')
legend({'a(t)=3t^{0.5}10^{-t}'},'Box','off')
%plotting c(t) vs. t for first 0.03 seconds
figure(2)
plot(t(t<=0.03),c(t<=0.03),'LineWidth',1.5)
xlabel('Time (sec)')
ylabel('c(t)')
legend({'c(t)=0.5sin(2\pi300t)+0.5sin(2\pi450t)'},'Box','off')
%using the sound function to play y(t)
sound(y)

0.9 a(t)-3t0 10 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.5 1 15 2 25 3 3.5 4 45 5 Time (sec)

c(t) 0.5sin(2 +300t)+0.5sin(2T450t) 0.8 0.6 0.4 0.2 -0.2 -0.4 -0.6 -0.8 -1 0.005 0.01 0.015 Time (sec) 0.02 0.025 0.03