Determine the response of the following system to an input x[n] = u[n] with initial conditions...
Solve y[n+2]−5 6y[n+1]+1 6y[n]=5x[n+1]−x[n] if the initial conditions are y[−1]=2, y[−2]=0, and the input x[n]=u[n]. Separate the response into zero-input and zero-state responses.
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
(20 pts.) Determine the response of the system described by the difference equation 7. 1 1 y(n) yn 1)n2)x(n) n for input signal x(n) = (;) u(n) under the following initial conditions y(-1) 1, y-2) 0.5
1. Given the impulse response, h[n duration 50 samples. (-0.9)"u[n, find the step response for a step input of h-(0.9)-10:491 -ones (1,50) s- conv(u,h) 2. Plot h and u using stem function for 50 samples only stem(10:491, s(1:50) 1. Given a system described by the following difference equation: yIn] 1143yn 1 0.4128y[n -2 0.0675x[n0.1349xn 0.675x[n-2] Determine the output y in response to zero input and the initial conditionsy-11 and yl-2] 2 for 50 samples using the following commands: a -,-1.143,...
Let a DT system described by the following difference equation: y[n]-5/6y[n-1]-1/6y[n-2]=1/6x[n-1] Find the zero input and zero state responses of this system for n≥0 assuming that the input s x[n]=2^nu[n] and the initial conditions y[-1]=1 and y[-2]=2.
5- For the following system: x( Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F, C2-1F. Identify the natural and forced response of the system a) Find the zero input response. b) Unit impulse response. c) zero state response. d) The total response. e Identify the natural and forced response of the system.
5- For the following system: x(
Input: x(t)s u(t) Output: y() With the initial condition y(0) 1, y(O)-0, RI-1, R2-12, CI-2F,...
3.5. The response of a linear and time-invariant system to the input signal x[n]= 6[n] is given by Sys {on]}= { 2,1, -1} n=0 Determine the response of the system to the following input signals: n] = 8[n]+6[n - 1 r[n] 6[n]26n - 1][n - 2] [n] un]- un - 5] xn] = а. b. C. 1 (u[n]- u[n - 5]) d.
If the input to the system described by the difference equation y(n+1) (1/2)x(n+) -x(n) is a) Does it matter what are the initial conditions for nc0 in order to find y(n) for n20? Explain your b) x(n) -u(n) answer. (3 points). Determine the transfer function H(z) and the Frequency Response (H(est) (10 points). Find the amplitude lH(epT)I and the phase He*') as a function of co. Evaluate both for normalized frequency ω T=z/4. ( 10 points) c) Find the steady...
for a discrete system, answer the following
5- Find the total response for: y(n 2) +13y(n +1) + 22y(n)-x(n + 1) + 5x(n) x(n)- (0.2)nu(n) With the initial condition y(-1) - 0 and y(-2) 3 Identify the natural and forced response of the system. 6- Find the total response for: y(n 2) + 3y(n + 1) + 2y(n)- x(n + 2) +3x(n +1) + 3x(n) With the initial condition y(-1) -1 and y(-2) 2 Identify the natural and forced response...
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]