Question

Given continuous analog signal x_a(t)= e^-100|t|. Write a MATLAB program to display its frequency spectra using FFT.

(Hints: To obtain the sampling signals x(n) = x_a(nT_s) , the sampling interval T_scan be less than 0.0025 sec)

Answer 1

close all;
fs = 8000;
f = 400; %Hz

t = 0:0025fs:1-1/fs;
signal = sin(2*pi*f*t);

plot(t, signal);
title('Time-Domain signal');

fftSignal = fft(signal);

fftSignal = fftshift(fftSignal);

f = fs/2*linspace(-1,1,fs);

figure;
plot(f, abs(fftSignal));
title('magnitude FFT of sine');
xlabel('Frequency (Hz)');
ylabel('magnitude');

noise = 2*randn(size(signal));
figure, plot(t,noise), title('Time-Domain Noise');
fftNoise = fft(noise);
fftNoise = fftshift(fftNoise);
figure, plot(f,abs(fftNoise)), title('Magnitude FFT of noise');
xlabel('Frequency (Hz)');
ylabel('magnitude');

noisySignal = signal + noise;
figure, plot(t,noisySignal), title('Time-Domain Noisy Signal');
fftNoisySignal = fft(noisySignal);
fftNoisySignal = fftshift(fftNoisySignal);
figure, plot(f,abs(fftNoisySignal)), title('Magnitude FFT of noisy signal');
xlabel('Frequency (Hz)');
ylabel('magnitude');