You are given a infinite sinusoidal function x(t) = 100cos (1000t) Express this

Question

You are given a infinite sinusoidal function x(t) = 100cos (1000t) Express this function in matlab and plot. Use matlab's FFT function and plot the absolute value of FFT coefficients in Matlab. You should see two pikes can you speculate the locations of these two pikes. Change the frequency of x(t) and plot new function and plot the absolute value of FFT coefficients in Matlab. (this is the spectrum of the signal x(t)) What happened to two pikes? Why? Add one more sinoisidal function to x(t) and observe how the pikes change in the spectrum plot. clear all; t = -100:1:100; x = 100 * cos(1000*t); plot(x); xf = fft(x); figure plot(abs(xf));

Explanation / Answer

4 ) Amplitude of pikes has changed and distance between pikes also changes

5) Four pikes appear. We can see the added frequencies with the smaller weight.

clear all;
close all;
clc;
t = 0:1:100;
x = 100*cos(1000*t);
plot(t,x)
xf = fft(x);
figure
plot(abs(xf))
x1 = 100*cos(200*t);
figure
plot(t,x1)
xf1 = fft(x1);
figure
plot(abs(xf1))
x2 = x + 200*cos(5000*t);
figure
plot(t,x1)
xf2 = fft(x2);
figure
plot(abs(xf2))

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