Question

consider the signal using matlab

Problem 2: Consider a signal: x[n] 3cos(n7/3) + 2sin(nt/4)+ cos(n7/5) Using Matlab, (1) Plot this signal in time domain. Can you identify the various frequencies in this signal? Use n 0:1:1000 (2) Plot this signal in frequency domain using the "fft" command. Identify the individual frequencies in the plot. (3) Calculate the frequencies of these signals. In the frequency plot, 1000 2

Answer 1

MATLAB CODE

clc
clear all;
n=0:1:1000; %Time vector of 1 sec
x=3*cos(pi*n./3)+5*cos(n*pi./4)+cos(n*pi./5);
Fs=250000;% Sampling frequency
nfft=1024; % length of fft
X=fft(x,nfft); %fft calculation
X=X(1:nfft/2);
mx=abs(X); % magnitude response
f=(0:nfft/2-1)*Fs/nfft; % frequency vector
figure(1)
stem(x); %signal plot
xlim([0 1000]); % X axis limit
title('Given Signal')
xlabel('n')
ylabel('Amplitude')
figure(2)
plot(f,mx,'r')
title('Spectrum of sine wave')
xlabel('Frequency')
ylabel('Amplitude')

PLOTS

ै2 G G है 8 G- G G G- G- G G G G G- G Amplitude

Spectrum of sine wave 3000 2500 2000 1500 1000 500 6 8 10 12 14 Frequency x 10 Amplitude