a)
Y(s) /X(s) = 1/(s+1)
s*y(s) + Y(s) = X(s)
converting into digital form
y(n+1)-y(n) +y(n)
5. Given the following transfer function, Y(s)_ 1 X(S) s +1 a) Using Euler's forward method,...
Styles Paragraph 6. Given the difference equation y(n)-x(n-1)-0.75y(n-1)-0.125(n-2) a. Use MATLAB function filterl) and filticl) to calculate the system response y(n)for n 0, 1, 2, 3, 4 with the input of x(n (0.5) u(n)and initial conditions x(-1)--1, y(-2) -2, and y(-1)-1 b. Use MATLAB function filter!) to calculate the system response y(n) for n-0, 1, 2, 3,4 with the input of x(n) (0.5)"u(n)and zero initial conditions x(-1)-0, (-2)-0, and y(-1)-0 Design a 5-tap FIR low pass filter with a cutoff...
a system is given by the following transfer function Y(s)/u(s) = 1/(s^2-16) a)find the output in time domain Y(t) if the input u(t) is a unit step. (Hint the transfer function of the unit step function is 1/s) b)what is Y(t) as t goes to infinity
(40) 3. Make an approximation of the transfer function (s+10) G(s)-Y(s)/U(s) =__ (s+25) using Euler's approximation. Find the actual solution and the approximate solution for a sampling interval T-0.1 sec for t=0, 0.1, 0.2. u(t) = 10tfort O and u(t) =0 fort 30
3. Euler's Method (a) Use Euler's Method with step size At = 1 to approximate values of y(2),3(3), 3(1) for the function y(t) that is a solution to the initial value problem y = 12 - y(1) = 3 (b) Use Euler's Method with step size At = 1/2 to approximate y(6) for the function y(t) that is a solution to the initial value problem y = 4y (3) (c) Use Euler's Method with step size At = 1 to...
7. A causal LTI system has a transfer function given by H (z) = -1 (1 4 The input to the system is x[n] = (0.5)"u[n] + u[-n-1] ) Find the impulse response of the system b) Determine the difference equation that describes the system. c) Find the output y[n]. d) Is the system stable?
Q2: Solve the following differential equation using modified Euler's method y' = sin(k. x + y) - et To find y(1.0)? if we have y(0) = 4 and h = 0.1
1. Consider the following differential equation. ag = ty, y(0)=1. dt (a) Use Euler's Method with At = .1 to approximate y(1). (b) Use Euler's Method with At = .05 to approximate y(1). (c) Find the exact solution to the problem. Use this solution to compare the error for the different values of At. What does this say about the method? Note: On the course page there are notes describing an implementation of Euler's method on a spread sheet.
Please show Matlab code and Simulink screenshots 2. Differential Equation (5 points) Using (i) Euler's method and (ii) modified Euler's method, both with step size h-0.01, to construct an approximate solution from t-0 to t-2 for xt 2 , 42 with initial condition x(0)-1. Compare both results by plotting them in the same figure. 3. Simulink (5 points) Solve the above differential equation using simplink. Present the model and result. 2. Differential Equation (5 points) Using (i) Euler's method and...
4. (20 points) An ideal analog integrator is described by the system function: H(s) 1) Design a discrete-time "integrator" using the bilinear transformation with Ts 2 sec. t is the difference equation relating xin) to yin) thint: divide top and bottom of H(Z) by ) 3) Determine the unit sample (impulse) response of the digital fite. 4) Assuming a sampling frequency of 0.5 Hz, use the impulse invariance method to find an approximation for Hz). Hint: Inverse Laplace Transform of...