Step response:
clc;close all;clear all;
h=(-0.9).^[0:49];
u=ones(1,50)
s=conv(u,h)
subplot(311)
stem([0:49],u)
xlabel('n');ylabel('u(n)');title('step input')
subplot(312)
stem([0:49],h)
xlabel('n');ylabel('h(n)');title('Impulse response h(n)')
subplot(313)
stem([0:49],s(1:50))
xlabel('n');ylabel('s(n)');title('Step response s(n)')
Difference equation:
clc;close all;clear all;
a=[1 -1.143 0.4128]
b=[0.0675 0.1349 0.675]
%Zero input response
yi=[1 2]
x=zeros(1,50)
zi=filtic(b,a,yi)
y=filter(b,a,x,zi)
subplot(311)
stem([0:49],y(1:50))
xlabel('n');ylabel('y(n)');title('Zero input response')
%Zero state response
n=0:1:99
x=cos(pi*n/6)
y=filter(b,a,x)
subplot(312)
stem([0:99],y(1:100))
xlabel('n');ylabel('y(n)');title('Zero state response')
%Step response
x=ones(1,100)
y=filter(b,a,x)
subplot(313)
stem([0:99],y(1:100))
xlabel('n');ylabel('s(n)');title('Step response')
State variable description:
clc;close all;clear all;
A=[-0.5572 -0/7814 ;0.7814 0];
B=[1 -1;0 2];
C=[1.9691 6.4493];
D=0;
sys=ss(A,B,C,D,0.1)
figure;
step(sys)
figure;
impulse(sys)
figure;
x0 = [1 ; 0];
initial(sys,x0)
figure;
%Response to sinusoidal input
f=0.25
[u,t] = gensig('sin',1/f,10,0.1);
lsim(sys,[u,u],t)
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
(42)1+ (z-0.5)z-0.9)(z-0.8) 3. The transfer function of a system is H(z) = a) Compute an analytical expression for the response y[n] if x[n] = u[n]. . Use Matlab to calculate the coefficients b) Simulate the response using Matlab (stem plot). Generate 50 points. (enter transfer function into Matlab and apply step input) (42)1+ (z-0.5)z-0.9)(z-0.8) 3. The transfer function of a system is H(z) = a) Compute an analytical expression for the response y[n] if x[n] = u[n]. . Use Matlab...
The unit impulse response and the input to an LTI system are given by: h(t) u(t) - u(t - 4) x(t) e2[u(t)-u(t - 4)] x(t) 1 y(t) h(t) 1. Determine the output signal, i.e.y(t), you may use any method. 2. Is this system memoryless? Why? 3. Is this system causal? Why? 4. Is this system BIBO stable? Why?
Problem 2: Find the impulse response h(n) of a causal LTI system if the input x(n) and the output y(n) are given as follows 72 42)un-1) y(n)-G)na(n) xnun)
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...
4. The impulse response of a system is given by h[n]=(0.3)"u[n]. If the input to the system is x[r]=(-0.6)" u [n], giving an output of y[n]=[n]*x[n]: a. (5 pts) Find the spectrum of the output, Y(e/2/). b. (10 pts) Use partial fraction decomposition to rewrite Y (e/2*) as a sum of two terms then take the inverse DTFT to find the output, y[n]
2. A system is described by the following difference equation n]1.5y[n0.56y[n -2]+x{n-0.2x{n-] a) Find the transfer function of the system b) Let xn]un]. Compute an analytical expression for the response y[n]. Use Matlab to calculate the coefficients c) Simulate and plot the response using Matlab.(stem plot) Generate 50 points. (Matlab: x ones(1,50)); 2. A system is described by the following difference equation n]1.5y[n0.56y[n -2]+x{n-0.2x{n-] a) Find the transfer function of the system b) Let xn]un]. Compute an analytical expression for...
1. An LTI digital system with impulse response h[n] = 2(1/4)"u[n] produces an output y[n] = (-3)"u[n]. Determine the corresponding input x[n] using Z-transform. (30 points)
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine the frequency response of the system. b) Find the magnitude response and the phase response, given a = 1/2. No plots. c) Consider a LTI system whose impulse response h1[n] is a time-shifted version of h[n], i.e., h1[n] = h[n − n0]. Compute the frequency response H1(e^(jΩ)), and represent H1(e^(jΩ)) in terms of H(e^(jΩ)).