Sampling and reconstruction of signal > Matlab

Sampling and reconstruction of a signal > Matlab

Digital Signal Processing

%Showing the Uniform sampling reconstruction

close all;

clear all;

N=64;

Fs=100; %Sampling frequency

Ts=1/Fs; %Sampling time

t=Ts*[-N/2:N/2-1]

fo=2;%Fundamental frequency

f1=4;%Fundamental frequency

s=2*sin(2*pi*fo*t)+2*sin(2*pi*f1*t);

subplot(5,2,1)

plot(t,s)

xlabel('t(Seconds)','fontsize',10)

ylabel('Amplitude','fontsize',10)

axis([-0.33 0.31 -3.6 3.6])

text(-0.37,4.2,'(a)')

box on

grid on

% Plotting the Frequency spectra

f=1/Ts/N/2*[-N:2:N-1];

s_f=fft(s);

subplot(5,2,2)

plot(f,fftshift(abs(s_f/max(s_f))))

xlabel('f (Hertz)','fontsize',10)

ylabel('Amplitude','fontsize',10)

axis([ -40 40 0 1])

text(-45,1.25,'(b)')

box on

grid on

%Creating train of impulses

x_range=[0:1:63];

imp_train=zeros(1,64);

select=find(rem(x_range,4)==0);

imp_train(select)= ones(size(select));

subplot(5,2,3)

bar(t,imp_train)

xlabel('t(Seconds)','fontsize',10)

ylabel('Amplitude','fontsize',10)

axis([-0.33 0.31 -3.6 3.6])

text(-0.38,4.0,'(c)')

box on

grid on

%Creating frequeny spectra of the spikes

imp_train_f=fft(imp_train);

subplot(5,2,4)

bar(f,fftshift(abs(imp_train_f/max(imp_train_f))))

xlabel('f (Hertz)','fontsize',10)

ylabel('Amplitude','fontsize',10)

text(-64,1.25,'(d)')

axis([ -44 40 0 1])

box on

grid on

%Multiplying spikes with signal in time domain

imp_train_s=imp_train.*s;

subplot(5,2,5)

hold on

bar(t,imp_train_s)

plot(t,s,'--r')

hold off

xlabel('t(Seconds)','fontsize',10)

ylabel('Amplitude','fontsize',10)

axis([-0.33 0.31 -3.6 3.6])

text(-0.39,4.5,'(e)')

box on

grid on

%Convolving the Frequency spectra of the spike and frequency spectra of signal

Conv_imp_s_f=conv(s_f(:),imp_train_f(:))

length_output=length(s_f)+length(imp_train_f)-1;

k=linspace(-2*N/2,2*N/2,length_output);

subplot(5,2,6)

plot(k,abs(Conv_imp_s_f/max(Conv_imp_s_f)))

xlabel('f (Hertz)','fontsize',10)

ylabel('Amplitude','fontsize',10)

text(-72,1.25,'(f)')

axis([-65 65 0 1.0])

box on

grid on

%Constructing a sinc function

%Constructing a Box car function

x_range=[0:1:63]

rec= zeros(1,64);

select =find(x_range>26 & x_range<38);

rec(select) = ones(size(select));

subplot(5,2,8)

plot(f,rec,'r-')

xlabel('f (Hertz)','fontsize',10)

ylabel('Amplitude','fontsize',10)

axis([ -40 40 0 1])

%axis([-25 25 0 1])

text(-28,1.25,'(h)')

box on

grid on

%Constructing a sinc function

subplot(5,2,7)

sinc = real(fftshift(ifft(fftshift(rec))));

plot([-32:31], sinc, 'r')

xlabel('t(Seconds)','fontsize',10)

ylabel('Amplitude','fontsize',10)

axis([-38 38 -0.4 0.4])

text(-45,.5,'(g)')

box on

grid on

Output: