File:Gate sequence discrete-time low-pass filter output (r=0.8).pdf

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Description
English: Output of discrete-time low-pass filter , with gate sequence as the input.
Italiano: Uscita del filtro passa-basso a tempo discreto , con la sequenza porta all'ingresso.
Date
Source Own work
Author Luca Ghio
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(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
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N=11;
n=[0:N-1];
x=ones(1,N);
r1=0.8;
r2=0.5;
r3=0.2;
h1=r1.^n;
h2=r2.^n;
h3=r3.^n;
figure
set (gca,'FontSize',14)
stem(n,x)
xlabel('n')
ylabel('x(n)')
axis([0 10 0 2])
grid on
figure
set (gca,'FontSize',14)
stem(n,h1)
xlabel('n')
ylabel('h_1(n)')
axis([0 10 0 1])
grid on
figure
set (gca,'FontSize',14)
stem(n,h2)
xlabel('n')
ylabel('h_2(n)')
axis([0 10 0 1])
grid on
figure
set (gca,'FontSize',14)
stem(n,h3)
xlabel('n')
ylabel('h_3(n)')
axis([0 10 0 1])
grid on

N=11;
n=[0:N-1];
x=ones(1,N);
r1=0.8;
r2=0.5;
r3=0.2;
k1=(1-r1)/(1-r1^N);
k2=(1-r2)/(1-r2^N);
k3=(1-r3)/(1-r3^N);
h1=k1*r1.^n;
h2=k2*r2.^n;
h3=k3*r3.^n;
%  figure
%  set (gca,'FontSize',14)
%  stem(n,x)
%  xlabel('n')
%  ylabel('x(n)')
%  axis([0 10 0 2])
%  grid on
%  figure
%  set (gca,'FontSize',14)
%  stem(n,h1)
%  xlabel('n')
%  ylabel('h_1(n)')
%  axis([0 10 0 1])
%  grid on
%  figure
%  set (gca,'FontSize',14)
%  stem(n,h2)
%  xlabel('n')
%  ylabel('h_2(n)')
%  axis([0 10 0 1])
%  grid on
%  figure
%  set (gca,'FontSize',14)
%  stem(n,h3)
%  xlabel('n')
%  ylabel('h_3(n)')
%  axis([0 10 0 1])
%  grid on

f=linspace(-0.5,0.5,1000);
H1=k1*(1-(r1*exp(-j*2*pi*f)).^N)./(1-r1*exp(-j*2*pi*f));
H2=k2*(1-(r2*exp(-j*2*pi*f)).^N)./(1-r2*exp(-j*2*pi*f));
H3=k3*(1-(r3*exp(-j*2*pi*f)).^N)./(1-r3*exp(-j*2*pi*f));
figure
set (gca,'FontSize',14)
plot(f,abs(H1))
hold on
plot(f,abs(H2),'r')
plot(f,abs(H3),'g')
xlabel('f')
ylabel('|H_i(e^{j\omega})|')
axis([-0.5 0.5 0 1.5])
grid on
legend('|H_1(e^{j\omega})|','|H_2(e^{j\omega})|', '|H_3(e^{j\omega})|')

N = 11;
X = (sin(pi*f*N) ./ sin(pi*f)) .* exp(-j*pi*f*(N-1));
figure
set (gca,'FontSize',14)
plot(f,abs(X))
xlabel('f')
ylabel('|X(e^{j\omega})|')
axis([-0.5 0.5 0 11])
grid on

Y1 = X .* H1;
Y2 = X .* H2;
Y3 = X .* H3;
figure
set (gca,'FontSize',14)
plot(f,abs(Y1))
hold on
plot(f,abs(Y2), 'r')
plot(f,abs(Y3), 'g')
xlabel('f')
ylabel('|Y_i(e^{j\omega})|')
axis([-0.5 0.5 0 11])
grid on
legend('|Y_1(e^{j\omega})|','|Y_2(e^{j\omega})|', '|Y_3(e^{j\omega})|')

N=11;
n=[0:N-1];
x=ones(1,N);
r1=0.8;
r2=0.5;
r3=0.2;
k1=(1-r1)/(1-r1^N);
k2=(1-r2)/(1-r2^N);
k3=(1-r3)/(1-r3^N);
h1=k1*r1.^n;
h2=k2*r2.^n;
h3=k3*r3.^n;
y1=conv(x,h1);
y2=conv(x,h2);
y3=conv(x,h3);
n=[0:length(y1)-1];
figure
set (gca,'FontSize',14)
stem(n,y1)
xlabel('n')
ylabel('y_1(n)')
axis([0 20 0 1.5])
grid on
figure
set (gca,'FontSize',14)
stem(n,y2)
xlabel('n')
ylabel('y_2(n)')
axis([0 20 0 1.5])
grid on
figure
set (gca,'FontSize',14)
stem(n,y3)
xlabel('n')
ylabel('y_3(n)')
axis([0 20 0 1.5])
grid on

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Date/TimeThumbnailDimensionsUserComment
current12:46, 23 September 2017Thumbnail for version as of 12:46, 23 September 20171,164 × 870 (5 KB)Luca Ghio (talk | contribs){{Information |Description= {{en|Output <math>y_1 \left( n \right)</math> of discrete-time low-pass filter <math>h_1 \left( n \right) = {0.8}^n \quad n = 0 , \ldots , N - 1</math>, with gate sequence <math>x \left( n \right) = u \left( n \right) - u \l...

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