Thread Subject: HOW TO USE LOW PASS FILTER

Hi!
I am trying to demonstrate here a toy problem on how to use low pass filter, My goal is to reconstruct the spectrum in figure (b) by applying low pass filter like box car .......this is one of the basics of signal processing....but i am not aware how to do it in matlab .....i started the code but i am not able to finish it...i am wondering if some can help me out in this

1. I want to get figure b by applying simple box car on figure f, also my box car in figure h is errorfull i dont know how to construct it in matlab...i want to multiply figure f with box car in figure h and want to get figure b back.........

Looking forwad for your guidance

Thannks

%Showing the Uniform sampling reconstruction
close all;
clear all;
N=64;
Fs=80; %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);
imp_train_f(1)=[0];
imp_train_f(6)=[16];
imp_train_f(60)=[16];
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