SINAIS EXPONENCIAIS REAIS

Prévia do material em texto

Universidade Federal Rural do Semi-Árido – UFERSA 
Disciplina: Análise de Sinais e Sistemas 
Professor: Isaac Barros Tavares da Silva 
Aluno: Paulo Henrique dos Reis Caldeira 
 
GRAFICOS 
 
SINAIS EXPONENCIAIS REAIS 
 
 
 
 
 
 
1 a. 𝑥(𝑡) = 𝐶𝑒𝑎𝑡 
 
clear all; 
clc; 
t=[0:500]; 
a=0.01; 
c=1; 
x=c*exp(a*t); 
plot(t,x); 
 
b. 𝑥(𝑡) = 𝐶𝑒−𝑎𝑡 
 
clear all; 
clc; 
t=[0:500]; 
a=-0.01; 
c=1; 
x=c*exp(a*t); 
plot(t,x); 
 
 
SINAIS COMPLEXOS PERIÓDICOS 
 
 
 
 
 
 
SINAIS COMPLEXOS GERAIS (𝑟 < 0) 
 
 
2 a. 𝑥(𝑡) = 𝐶𝑒𝑗2𝜋𝑡 
clear all; 
clc; 
t=[0:300]; 
w0=0.063; 
x=cos(w0*t)+j*sin(w0*t); 
plot(t,x); 
 
 
b. 𝑥(𝑡) = 𝐶𝑒𝑗4𝜋𝑡 
clear all; 
clc; 
t=[0:300]; 
w0=0.063; 
x=cos(w0*t)+j*sin(w0*t); 
plot(t,x); 
 
 3.a. 𝑥(𝑡) = 𝑒4𝑡 
clear all; 
clc; 
t=[750:900]; 
c=0.05; 
r=4; 
w0=0.04; 
x=exp(w0*t); 
plot(t,x); 
 
 
 
 
 
 
 
 
4. 𝑥(𝑡) = 𝑒4𝑡cos (8π𝑡) 
 
clear all; 
clc; 
t=[750:1000]; 
x=exp(0.04*t).*cos(0.08*pi*t); 
y=exp(0.04*t); 
plot(t,x,'r',t,y,'g'); 
 
 
 
 
b. 𝑥(𝑡) = cos (2π ∗ 4𝑡) 
 
clear all; 
clc; 
t=[0:900]; 
c=0.05; 
r=4; 
w0=0.042; 
x=cos(w0*t); 
plot(t,x); 
 
 
 
 
 
 
 
 
 
5. a. 𝑥(𝑡) = 𝑒−4𝑡 
clear all; 
clc; 
t=[0:150]; 
c=0.05; 
r=4; 
w0=-0.04; 
x=exp(w0*t); 
plot(t,x); 
 
b. 𝑥(𝑡) = cos (2π ∗ 4𝑡) 
clear all; 
clc; 
t=[0:150]; 
c=0.05; 
r=4; 
w0=0.25; 
x=cos(w0*t); 
plot(t,x); 
 
6. 𝑥(𝑡) = 𝑒−4𝑡cos (8π𝑡) 
clear all; 
clc; 
t=[0:150]; 
x=exp(-0.04*t).*cos(-0.08*pi*t); 
y=exp(-0.04*t); 
plot(t,x,'r',t,y,'g'); 
 
 
 
SINAIS EXPONENCIAIS REAIS 
 
 
 
7. 𝑥[𝑛] = 𝑎𝑛 
(𝑎 > 1) 
clear all; 
clc; 
n=[0:50]; 
a=1.072; 
x=a.^n; 
stem(n,x); 
 
 
 
 
 
 
 
 
 
9. 𝑥[𝑛] = 𝑎𝑛 
(−1 > 𝑎 > 0) 
clear all; 
clc; 
n=[0:50]; 
a=0.9; 
x=a.^n; 
stem(n,x); 
 
10. 𝑥[𝑛] = 𝑎𝑛 
(𝑎 < −1) 
clear all; 
clc; 
n=[0:50]; 
a=0.9; 
x=a.^n; 
stem(n,x); 
 
8. 𝑥[𝑛] = 𝑎𝑛 
(0 > 𝑎 > 1) 
clear all; 
clc; 
n=[0:50]; 
a=0.9; 
x=a.^n; 
stem(n,x); 
 
SINAIS EXPONENCIAIS COMPLEXOS GERAIS (𝑎 > 1) 
 
 
12. 𝑥[𝑛] = |𝑎|𝑛𝑒𝑗(𝑛𝜔0+𝜃) 
(𝑎 < 1) 
clear all; 
clc; 
n=[0:100]; 
w0=0.4; 
teta=-pi/2; 
a=0.96; 
x=abs(a).^n.*exp(j*(w0*n+teta)); 
stem(n,x,'r'); 
hold on 
y=abs(a).^n; 
stem(n,y); 
 
 
11. 𝑥[𝑛] = 𝑒𝑗(𝑛𝜔0+𝜃) 
(𝑎 = 1) 
clear all; 
clc; 
n=[0:50]; 
w0=0.2; 
teta=-pi/2; 
x=exp(j*(w0*n+teta)); 
stem(n,x); 
 
13. 𝑥[𝑛] = |𝑎|𝑛𝑒𝑗(𝑛𝜔0+𝜃) 
(𝑎 > 1) 
clear all; 
clc; 
n=[0:100]; 
w0=0.4; 
teta=-pi/2; 
a=1.03; 
x=abs(a).^n.*exp(j*(w0*n+teta)); 
stem(n,x); 
hold on 
y=abs(a).^n; 
stem(n,y) 
 
 
 
PERIODICIDADE DE EPONENCIAIS 
 
 
4. 𝑥[𝑛] = 𝑒𝑗0𝑛 
(𝜔0 = 0 𝑟𝑎𝑑/𝑠) 
clear all; 
clc; 
n=[0:2:100]; 
x=[0:2]; 
w0=0; 
x=exp(j*(w0*n)); 
stem(n,x); 
 
 
 
 
 
 
 
 
16. 𝑥[𝑛] = 𝑒𝑗𝑛𝜋 
(𝜔0 = 𝜋 𝑟𝑎𝑑/𝑠) 
clear all; 
clc; 
n=[0:35]; 
x=[0:2]; 
w0=pi; 
x=exp(j*(w0*n)); 
stem(n,x); 
 
15. 𝑥[𝑛] = 𝑒𝑗𝑛𝜋/4 
(𝜔0 =
𝜋
4
 𝑟𝑎𝑑/𝑠) 
clear all; 
clc; 
n=[0:35]; 
x=[0:2]; 
w0=pi/4; 
x=exp(j*(w0*n)); 
stem(n,x); 
 
 
 
 
 
 
 
 
 
17. 𝑥[𝑛] = 𝑒𝑗𝑛7𝜋/4 
(𝜔0 =
7𝜋
4
 𝑟𝑎𝑑/𝑠) 
clear all; 
clc; 
n=[0:35]; 
x=[0:2]; 
w0=pi; 
x=exp(j*(w0*n)); 
stem(n,x); 
 
18. 𝑥[𝑛] = 𝑒𝑗𝑛2𝜋 
(𝜔0 = 2𝜋 𝑟𝑎𝑑/𝑠) 
clear all; 
clc; 
n=[0:35]; 
x=[0:2]; 
w0=2*pi; 
x=exp(j*(w0*n)); 
stem(n,x); 
 
 
 
 
 
 
 
 
19. 
𝑥[𝑛] = 𝑒
𝑗(𝑛2𝜋)
12 
𝑥(𝑡) = 𝑒
𝑗(2𝜋𝑡)
12 
clear all; 
clc; 
n=[0:35]; 
x=[0:2]; 
w0=2*pi/12; 
x=exp(j*(w0*n)); 
stem(n,x); 
hold on 
t=[0:35]; 
x=exp(j*(w0*t)); 
plot(t,x); 
 
20. 
𝑥[𝑛] = 𝑒
𝑗(𝑛8𝜋)
31 
𝑥(𝑡) = 𝑒
𝑗(8𝜋𝑡)
31 
clear all; 
clc; 
n=[0:35]; 
x=[0:2]; 
w0=8*pi/31; 
x=exp(j*(w0*n)); 
stem(n,x); 
hold on 
t=[0:35]; 
x=exp(j*(w0*t)); 
plot(t,x); 
 
 
 
 
IMPULSO UNITÁRIO 
 
22. 𝑢[𝑛] = {
0, 𝑛 ≠ 0
1, 𝑛 = 0
 
clear all; 
clc; 
delta=[zeros(1,10),1,zeros(1,10)] 
t=-1:0.1:1 
stem(t,delta) 
 
 
 
21. 
𝑥[𝑛] = 𝑒
𝑗(𝑛)
6 
𝑥(𝑡) = 𝑒
𝑗(𝑡)
6 
clear all; 
clc; 
n=[0:35]; 
x=[0:2]; 
w0=1/6; 
x=exp(j*(w0*n)); 
stem(n,x); 
hold on 
t=[0:35]; 
x=exp(j*(w0*t)); 
plot(t,x); 
 
DEGRAL UNITÁRIO 
 
 
23. . 𝑢[𝑛] = {
0, 𝑛 < 0
1, 𝑛 ≥ 0
 
 
 
clear all; 
clc; 
u=zeros(1,100) 
u=[u,ones(1,1001)]; 
t=-1:0.01:10; 
stem(t,u), axis([-0.1 0.1 -0.2 1.2]);