Question

Write a MATLAB code for the question below.

There is an initial signal containing 60 Hz sinusoid of amplitude 0.8 and a 150 Hz sinusoid of amplitude 1.2 corrupted by a noise - using the randn command - (zero-mean white noise with variance of 4). Plot the noisy signal in the time domain. After that compute the Fourier transform -using the fft command of the noisy signal, compute the two-sided spectrum. Define the frequency domain f and plot the single-sided amplitude spectrum, and clearly explain the graph. (Sampling frequency=1000, Sampling period=1/Sampling frequency, Length of the initial signal= 1000, Time vector = (0:Length of the initial signal-1)*Sampling period)

Answer 1

fs=1000;
n=1000;
t=0:1/fs:(n-1)/fs;
f1=60;
f2=150;
v = 4; % variance
sigma = sqrt(v); % standard deviation
mu = 0; % mean
y = sigma .* randn(1, n) + mu;
figure(2)
plot(t,y)
x=0.8*sin(2*pi*f1*t)+1.2*sin(2*pi*f2*t);
z=x+y;
zfft=fft(z,n);
z_mag=2*fftshift(abs(zfft))/n;
df=-fs/2:1:fs/2;
figure(3)
plot(df(fs/2:fs),z_mag(fs/2:fs));
xlim([0 fs/2])