Generate a signal wave: y_signal= 1 + 0.1* cos(2*pi*f_1*t) and calculate its spe

Question

Generate a signal wave: y_signal= 1 + 0.1* cos(2*pi*f_1*t) and calculate its spectrum using fft (suppose f_1 = 100.02 MHz) Generate a reference wave y_reference = 1 + cos (2*pi*f_2*t) and calculate its spectrum using fft (suppose f_2 = 100.00 MHz) Mathematically multiply them (y_mix= y_signal* y_reference) and calculate its spectrum using fft See how many frequency components you can see from the spectrum of the mixed signal and compare them with your theoretical results (using the equations shown before) Design a bandpass filter to only pass through the signal with a frequency of frf2 and show how your filtered data look like.

Explanation / Answer

% [1]

f1 = 100.02;

t = -pi : pi/4:pi;

Ysignal = 1 + 0.1*cos(2*pi*f1*t);

subplot(2,2,1)

title('Magnitude f1')

plot(Ysignal)

fft(Ysignal)

%[2]

f2 = 100.00;

t = -pi : pi/4:pi;

Yreference = 1 + cos(2*pi*f1*t);

subplot(2,2,2)

title('Magnitude f2')

plot(Yreference)

fft(Yreference)

%[3]

Ymix = Ysignal.*Yreference;

subplot(2,2,3)

title('Magnitude Mix')

plot(Ymix)

[4] 4 Frequency coponents

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