Question

Modify the windowfft.m program used in the previous experiment, so x is the product of two sinusoids x1 and x2. Let the modulating signal, x1, have a frequency of 1k Hz with amplitude of 1. Let the carrier signal, x2, have a frequency of 20k Hz with amplitude of 1. The Matlab code would look as follows % this is referred to as the modulating or message signal xl - sin(2*pi*f0*t) x2- sin(2 pi 20 O): % this is referred to as the carrier signal x-x1.x2 Recall that when you multiply sin4 sinB [cos(A-B) - cos(4+B)/2 two sinusoids you obtain the following Determine the resulting signal x: x =in(2πfο* in(2π(20f,))- Now that you expressed x as a sum of sinusoids you know the highest frequency component of x What is the highest frequency component of x?, What is the minimum sampling rate for x ?

Answer 1

sin (2 2000ot) レ=sin t+pit 20*fo *t); > (CO1A -)CA+ B))/2_ Sin A sin B sin ( 20001TE). * sin (400o0TFt) A + 4-oooo Tt -Cos20ooTt Cos 2000TTE -4 2. (-3s000 TE) cos(4-2000TE) 2. franetrion cosine an Cos0 since even 1 Cos42000Tt) 38000Tt) CDS2T K)E) 21KHと Minumum Sampling double the highert breanenuy omponect ate iu Nyquist >^ate i-e., minumum 2X21KH : 42-KH Minimum Samplany