atividade prática Sinais e Sistemas

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CENTRO UNIVERSITÁRIO INTERNACIONAL UNINTER 
ESCOLA SUPERIOR POLITÉCNICA 
BACHARELADO EM ENGENHARIA ELÉTRICA 
 
 
 
 
 
 
 
ATIVIDADE PRÁTICA: SINAIS E SISTEMAS 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
2022 
 
1 
 
1 ATIVIDADE 1 – TEMPO CONTÍNUO 
RU= xxxxxxx 
• 𝑎1 = 𝑅𝑈3 3 , se 𝑎1 = 0 adotar 𝑎1 = 1 
• 𝑏1 = 𝑅𝑈4 2 , se 𝑏1 = 0 adotar 𝑏1 = 2 
• 𝑐1 = 𝑅𝑈7 15 , se 𝑐1 = 0 adotar 𝑐1 = 1 7 
• 𝑑1 = 𝑅𝑈6 20 , se 𝑑1 = 0 adotar 𝑑1 = 1 6 
• 𝑒1 = 𝑅𝑈4 10 , se 𝑒1 = 0 adotar 𝑒1 = 0,4 
𝑎1 = 3 
𝑏1 = 2 
 𝑐1 = 0.533 
𝑑1 = 0.35 
 𝑒1 = 0.4 
 
Gerar um vetor 𝑡 de zero a 2𝜋 com intervalo de 0,01. 
Gerar as seguintes funções: 
a. (0,5p) 𝑥(𝑡) = 𝑠𝑒𝑛 (𝑎1𝜋𝑡 + 𝑏1𝜋). 
b. (0,5p) 𝑦(𝑡) = 𝑐𝑜𝑠 (𝑐1𝜋𝑡 − 𝑑1𝜋). 
c. (0,5p) 𝑣(𝑡) = 𝑒 ^𝑒1𝑡 . 
d. (0,5p) 𝑤(𝑡) = 𝑒 ^−𝑒1𝑡. 
Função de t--> t=0:0.1:2*%pi 
t = 
column 1 to 12 
0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. 1.1 
column 13 to 23 
1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2. 2.1 2.2 
column 24 to 34 
2.3 2.4 2.5 2.6 2.7 2.8 2.9 3. 3.1 3.2 3.3 
column 35 to 45 
3.4 3.5 3.6 3.7 3.8 3.9 4. 4.1 4.2 4.3 4.4 
column 46 to 56 
4.5 4.6 4.7 4.8 4.9 5. 5.1 5.2 5.3 5.4 5.5 
column 57 to 63 
5.6 5.7 5.8 5.9 6. 6.1 6.2 
 
2 
 
a. 𝑥(𝑡) = 𝑠𝑒𝑛 (𝑎1𝜋𝑡 + 𝑏1𝜋). 
--> x=sin(a1*%pi*(t)+b1*%pi) 
 x = 
 column 1 to 6 
 -2.449D-16 0.809017 0.9510565 0.309017 -0.5877853 -1. 
 column 7 to 12 
 -0.5877853 0.309017 0.9510565 0.809017 6.123D-16 -0.809017 
 column 13 to 18 
 -0.9510565 -0.309017 0.5877853 1. 0.5877853 -0.309017 
 column 19 to 24 
 -0.9510565 -0.809017 -9.797D-16 0.809017 0.9510565 0.309017 
 column 25 to 30 
 -0.5877853 -1. -0.5877853 0.309017 0.9510565 0.809017 
 column 31 to 36 
 4.900D-15 -0.809017 -0.9510565 -0.309017 0.5877853 1. 
 column 37 to 42 
 0.5877853 -0.309017 -0.9510565 -0.809017 -1.715D-15 0.809017 
 column 43 to 48 
 0.9510565 0.309017 -0.5877853 -1. -0.5877853 0.309017 
 column 49 to 54 
 0.9510565 0.809017 5.635D-15 -0.809017 -0.9510565 -0.309017 
 column 55 to 60 
 0.5877853 1. 0.5877853 -0.309017 -0.9510565 -0.809017 
 column 61 to 63 
 -2.449D-15 0.809017 0.9510565 
 
b. 𝑦(𝑡) = 𝑐𝑜𝑠 (𝑐1𝜋𝑡 − 𝑑1𝜋). 
--> y= cos(c1*%pi*(t)-d1*%pi) 
 y = 
 
 column 1 to 5 
 0.4539905 0.5962249 0.7217602 0.8270806 0.9092361 
 column 6 to 10 
 0.9659258 0.995562 0.9973145 0.9711343 0.9177546 
 column 11 to 15 
 0.8386706 0.7360971 0.6129071 0.4725508 0.3189593 
 
3 
 
 column 16 to 20 
 0.1564345 -0.0104718 -0.1770847 -0.3387379 -0.4909038 
 column 21 to 25 
 -0.6293204 -0.7501111 -0.8498927 -0.9258706 -0.9759168 
 column 26 to 30 
 -0.9986295 -0.9933728 -0.9602937 -0.9003188 -0.8151278 
 column 31 to 35 
 -0.7071068 -0.5792812 -0.4352311 -0.2789911 -0.1149372 
 column 36 to 41 
 0.052336 0.2181432 0.3778408 0.5269558 0.6613119 0.777146 
 column 42 to 46 
 0.8712138 0.9408808 0.9841956 0.9999452 0.9876883 
 column 47 to 52 
 0.9477684 0.8813035 0.790155 0.676876 0.544639 0.3971479 
 column 53 to 57 
 0.2385335 0.0732382 -0.0941083 -0.258819 -0.4162808 
 column 58 to 62 
 -0.5620834 -0.6921432 -0.8028175 -0.8910065 -0.9542403 
 column 63 
 -0.9907478 
 
c. 𝑣(𝑡) = 𝑒 ^𝑒1𝑡 . 
v= %e*exp(e1*t) 
v column 1 to 5 
 2.7182818 2.829217 2.9446796 3.0648542 3.1899333 
 column 6 to 11 
 3.3201169 3.4556135 3.5966397 3.7434214 3.8961933 4.0552 
 column 12 to 16 
 4.2206958 4.3929457 4.5722252 4.7588212 4.9530324 
 column 17 to 21 
 5.1551695 5.365556 5.5845285 5.8124374 6.0496475 
 column 22 to 26 
 6.2965383 6.5535049 6.8209585 7.0993271 7.3890561 
 column 27 to 31 
 7.6906092 8.0044689 8.3311375 8.6711377 9.0250135 
 column 32 to 36 
 9.3933313 9.7766804 10.175674 10.590951 11.023176 
 column 37 to 41 
 11.473041 11.941264 12.428597 12.935817 13.463738 
 column 42 to 46 
 
4 
 
 14.013204 14.585093 15.180322 15.799843 16.444647 
 column 47 to 51 
 17.115766 17.814273 18.541287 19.297972 20.085537 
 column 52 to 57 
 20.905243 21.758402 22.64638 23.570596 24.53253 25.533722 
 column 58 to 63 
 26.575773 27.660351 28.789191 29.9641 31.186958 32.459722 
 
d. 𝑤(𝑡) = 𝑒 ^−𝑒1𝑡. 
--> w= %e*exp(-e1*t) 
 w column 1 to 5 
 2.7182818 2.6116965 2.5092904 2.4108997 2.316367 
 column 6 to 10 
 2.2255409 2.1382762 2.0544332 1.9738777 1.8964809 
 column 11 to 15 
 1.8221188 1.7506725 1.6820276 1.6160744 1.5527072 
 column 16 to 20 
 1.4918247 1.4333294 1.3771278 1.3231298 1.2712492 
 column 21 to 26 
 1.2214028 1.1735109 1.1274969 1.0832871 1.0408108 1. 
 column 27 to 31 
 0.9607894 0.9231163 0.8869204 0.8521438 0.8187308 
 column 32 to 37 
 0.7866279 0.7557837 0.726149 0.6976763 0.67032 0.6440364 
 column 38 to 42 
 0.6187834 0.5945205 0.5712091 0.5488116 0.5272924 
 column 43 to 48 
 0.506617 0.4867523 0.4676664 0.449329 0.4317105 0.4147829 
 column 49 to 53 
 0.398519 0.3828929 0.3678794 0.3534547 0.3395955 
 column 54 to 58 
 0.3262798 0.3134862 0.3011942 0.2893842 0.2780373 
 column 59 to 63 
 0.2671353 0.2566608 0.246597 0.2369278 0.2276377 
 
5 
 
 
RU1 = x;RU2 = x;RU3= x;RU4=x;RU5=x;RU6=x;RU7=x; 
a1=RU3/3;b1=RU4/2;c1=RU7/15;d1=RU6/20;e1=RU4/10; 
a2=RU3;b2=RU4/10; 
clc// limpa console 
clf// limpa grafico 
 
//n 
t=0:0.1:2*%pi; 
 
x=sin(a1*%pi*(t)+b1*%pi) 
y= cos(c1*%pi*(t)-d1*%pi) 
v= %e*exp(e1*t) 
w= %e*exp(-e1*t) 
 
subplot (221) 
plot (t,x) 
title ('x(n)') 
xlabel ('tempo') 
ylabel ('amplitude') 
 
subplot (222) 
plot (t,y) 
title ('y(n)') 
xlabel ('tempo') 
ylabel ('amplitude') 
 
subplot (223) 
plot (t,v) 
title ('v(n)') 
xlabel ('tempo') 
ylabel ('amplitude') 
 
subplot (224) 
plot (t,w) 
title ('w(n)') 
xlabel ('tempo') 
ylabel ('amplitude') 
 
 
 
 
2. Gerar e plotar no mesmo gráfico os seguintes sinais: 
 
6 
 
 
a. 𝑥1 (𝑡) = 𝑅𝑈1𝑐𝑜𝑠(𝑡) 
b. 𝑥2 (𝑡) = 𝑅𝑈2 3 𝑠𝑒𝑛(3𝑡) 
c. 𝑥3 (𝑡) = 𝑅𝑈3 5 𝑐𝑜𝑠(5𝑡) 
d. 𝑥4 (𝑡) = 𝑅𝑈4 7 𝑠𝑒𝑛(7𝑡) 
e. 𝑥5 (𝑡) = 𝑅𝑈5 9 𝑐𝑜𝑠(9𝑡) 
f. 𝑥6 (𝑡) = 𝑅𝑈6 11 𝑠𝑒𝑛(11𝑡) 
g. 𝑥7 (𝑡) = 𝑅𝑈7 13 𝑐𝑜𝑠(13𝑡) 
h. 𝑦(𝑡) = 𝑥1 (𝑡) + 𝑥2 (𝑡) + 𝑥3 (𝑡) + 𝑥4 (𝑡) + 𝑥5 (𝑡) + 𝑥6 (𝑡)+𝑥7 (𝑡) 
 
x1= 3*cos(t) 
x2= 2/3*sin(3*t) 
x3= 9/5*cos(5*t) 
x4= 4/7*sin(7*t) 
x5 = 5/9*cos(9*t) 
x6 = 7/11*sin(11*t) 
x7=8/13*cos(13*t) 
y=x1+x2+x3+x4+x5+x6+x7 
plot(t,x1,t,x2,t,x3,t,x4,t,x5,t,x6,t,x7,t,y) 
legend('x1','x2','x3','x4','x5','x6','x7','y') 
title('função senoides') 
xlabel('Tempo') 
ylabel('Amplitude') 
 
 
7 
 
2 ATIVIDADE 2 
Gerar um vetor 𝑛 de -10 a 10 com intervalo igual a 1. 
Criar a função impulso unitário. Criar a função degrau unitário. 
• 𝑎2 = 𝑅𝑈3, se 𝑎2 = 0 adotar 𝑎2 = 3 • 𝑏 
2 = 𝑅𝑈4/10, se 𝑏2 = 0 adotar 𝑏2 = 0,4 • 
Os parâmetros 𝑐1 e 𝑑1 são os mesmos da Atividade 1 
 
Gerar as seguintes funções: 
a. (0,5p) 𝑥[𝑛] = [(−𝑅𝑈3) 𝑅𝑈3 𝑅𝑈1 𝑅𝑈2 𝑅𝑈5 (−𝑅𝑈7) ] 
b. (1p) 𝑦[𝑛] = (3𝑒 −𝑐1𝑛 𝑐𝑜𝑠(𝑐1𝜋𝑛 − 𝑑1𝜋))𝑢[𝑛 + 𝑅𝑈1] 
c. (1,5p) 𝑧[𝑛] = 0,5. 2 −𝑏2𝑛𝑥[−𝑛 − 𝑅𝑈4] + 𝑥[𝑛 + 𝑅𝑈2] −4 ≤ 𝑛 < 𝑅𝑈1 
 
Calcular: 𝑜[𝑛] = 𝑥[𝑛] + 𝑦[𝑛]. 𝑧[𝑛] 𝑝[𝑛] = 𝑥[𝑛]. (𝑦[𝑛] − 𝑧[𝑛]) 𝑞[𝑛] = 𝑥[𝑛] + 𝑦[𝑛] + 𝑧[𝑛] 3. 
 
Plotar todos os gráficos (𝑥[𝑛], 𝑦[𝑛],𝑧[𝑛]. 𝑜[𝑛], 𝑝[𝑛] e 𝑞[𝑛]) como sinal discreto na mesma 
figura usando o comando subplot. Colocar os nomes nos eixos e o título de cada figura como 
no exemplo a seguir. Será tirada nota se a imagem não cumprir com o solicitado. Usar o co-
mando plot2d3 para melhor visualização. 
 
function [y]=impulso(x) 
 y=zeros(1,length(x)); 
 y(find (x==0))=1; 
endfunction // função impulso 
 
function [y]=degrau(x) 
 y=zeros(1,length(x)); 
 y(find(x>=0))=1; 
endfunction // função degrau 
 
 
 
RU1 = x;RU2 = x;RU3= x;RU4=x;RU5=x;RU6=x;RU7=x; 
a1=RU3/3;b1=RU4/2;c1=RU7/15;d1=RU6/20;e1=RU4/10; 
a2=RU3;b2=RU4/10; 
 
clc// limpa console 
clf// limpa grafico 
f= gcf();//manipulador grafico 
 
//n 
n=-10:1:10; 
 
//a 
a=-RU3*impulso(n+4)+RU3*impulso(n+3)+RU1*impulso(n+2)+RU2*impulso(n+1)+RU5*impulso(n)-RU7*im-
pulso(n-1); 
 
 
8 
 
//b 
u1= degrau(n+RU1); 
b= (3*%e^(-c1*n).*cos(c1*%pi*n - d1*%pi)).*u1 
 
//c 
u2=degrau(n+4)-degrau(n-RU1); 
 
x1=cshift(a,[0,RU4]); 
x2=cshift(a,[0,-RU2]); 
for i=-10:1:10 
c(i+11)= (0.5*2^-b2*i.*x1(-i+11)+x2(-i+11))*u2(i+11) 
end 
 
o=(a+b).*c' 
p=a.*(b-c') 
q=a+b+c' 
 
//GRAFICOS 
 
subplot (321) 
plot2d3 (n,a,style=1) 
f.children.children(1).children.thickness=2; 
title ('a(n)') 
xlabel ('n') 
ylabel ('amplitude') 
 
subplot (322) 
plot2d3 (n,b,style=2) 
f.children.children(1).children.thickness=2; 
title ('b(n)') 
xlabel ('n') 
ylabel ('amplitude') 
 
subplot (323) 
plot2d3 (n,c,style=1) 
f.children.children(1).children.thickness=2; 
title ('c(n)') 
xlabel ('n') 
ylabel ('amplitude') 
 
subplot (324) 
plot2d3 (n,o,style=2) 
f.children.children(1).children.thickness=2; 
title ('o(n)') 
xlabel ('n') 
ylabel ('amplitude') 
 
subplot (325) 
plot2d3 (n,p,style=2) 
f.children.children(1).children.thickness=2; 
title ('p(n)') 
xlabel ('n') 
ylabel ('amplitude') 
 
subplot (326) 
plot2d3 (n,q,style=2) 
f.children.children(1).children.thickness=2; 
title ('q(n)') 
xlabel ('n') 
ylabel ('amplitude') 
 
 
9 
 
 
 
3 REFERÊNCIAS BIBLIOGRÁFICAS 
Website da Uninter. Disciplina de sinais e sistemas. AULA12. Orientações. 2022 
https://univirtus.uninter.com/ava/web/#/ava/roteiro-de-estudo, acesso em 12/11/2022. 
https://univirtus.uninter.com/ava/web/#/ava/roteiro-de-estudo