QUESTION 17 The sequence x[n]=cos os(n)i -n is input into the difference equation y[n] + y[n...
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
QUESTION 1 The output of the LSI system y[n] = 0.5(x[n]- x[n - 1]) to the input x[n] = 1 is: Oy[n] = cos(it) Oy[n] = 1 Oy[n] = 0 y[n] = Tt QUESTION 2 The output of an LSI system with frequency response Halw)= wejsinw, [W] < it to the input x[n] = 10 cos cos (Th 1 + 45 45°) is Oy[n] = 0 y[n] = 5jt sin 2 πη 4 O 1 πη y[n] = 10 cosi...
For a system with the difference equation: y[n] = -2y[n-1] + x[n] + 2x[n-2], find a.The impulse response b.The step response
Please be neat and show all work. thank you.
Given the difference equation, y(n) -y(n-2)-x(n);n 2 y(-1) 1, y(-2)0, and the input x(n) a) yh (n), p (n) and hence y (n) b) yzi (n), ½,( ) 1. 0, and the initial conditions as u(n), determine n) and hence v n
Given the difference equation, y(n) -y(n-2)-x(n);n 2 y(-1) 1, y(-2)0, and the input x(n) a) yh (n), p (n) and hence y (n) b) yzi (n), ½,( ) 1....
A discrete-time system has a difference equation given by y(n) = y(n-1) - 2y(n-2) + x(n) + 2x(n-1) + x(n-2). (a) Find h(n) using iteration. (b) Find the system's z-transfer function H(z). (c) Assume x(n) = δ(n) - 2δ(n-1) + 3δ(n-2). Find y(3) using any method you like. (d) Is this system a FIR or IRR system? How can you tell?
2. We have a system with the following difference equation: y nTx [nx n]2 cos () x n - ]xn 2 _ (a) Find the frequency response of the system for wo. = (b) If we want to tune the system so that the response to a an all zero signal, how should we set &o? Show that the response to the following signal is zero for all n with a properly selected wn value: given sinusoid with frequency û\...
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...
3.21. Given a filter described by the difference equation y[n] = 2x[n] + 3x[n - 1] + 2x[n - 2] where x[n] is the input signal and y[n] is the output signal. (a) Find and plot h[n] the impulse response of the filter. (b) find and plot H(Ω).
(a) Determine the difference equation relating the input (x[n]) and outpt (y[n]) for an LTI system whose impulse response is given by: h(n) = (1/4){δ(n) + δ(n - 1) (b) Find and plot the amplitude and phase response of the above LTI system. Indicate what kind of filter this system represents.
Question 1 The difference equation of a causal filter is: y[n] = x[n] – 2x[n – 1] + 3x[n – 5] The filter is an IR filter. True False