Question

Frequency Analysis Quiz Q1. You have been asked to generate a single signal by summing three different sine waves of equal length (say 5 seconds). The resulting signal is sampled at a rate of 250 Hz. The frequencies of the sinusoidal components are 25 Hz, 40 Hz and 95 Hz. The amplitudes of the signals are 2.0,3.0 and 5.0 units respectively. You have been asked to plot the signal against time. Write the text for a simple m- script that can achieve this:

Answer 1

%matlab

fs=250;%sampling rate
f=[25 40 95];%frequency components
w=2.*pi.*f;
A=[2 3 5];%amplitudes
t=0:1/fs:100/fs;
x=zeros(size(t));
for k=1:3
x=x+A(k).*cos(w(k).*t);
end
stem(t,x);
xlabel('t(seconds)');
ylabel('x(t)');

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(1)x / // // 11 O 0.05 0.1 0.15 0.3 0.35 0.4 02 0.25 t(seconds)

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с cus (и чо) + '3 " 240 , 76 cod 20105) no- - +5 cos (21 95t) When sompted at od rate the resulting signal 7+: & quo S(tant) 1 To: Yes dis = 250 Hy govern Now the spectum is given by [19:x<f-hof) Nappal: 84-28) + Sifters) (54f-w) e o duro)] +5 84-95) +8H+95) kard Now 2 i folded speckim Xs (f): 2ds { xf-est LO

Magnitude na. (6250) =( st . 35 12 T 25 an 40 95 ISJ 210 225 250 275 290 345 of t