Consider an LTI system whose input x[n] and output y[n] are related by the difference equation...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
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...
sin((n-16)/4) (n-16) Consider an LTI discrete-time system that has impulse respo 6)/4) if n #16 if otherwise a) Determine the magnitude H(12) and the phase response ZH(12) for –< 1 < . Enter 12 as “O” and enter the piecewise function |H(12) using the heaviside function. |H(12) = ZH(12) = b) Determine the output of the system, y[n], if the input is given by x[n] = S[n – 9] + cos( 72 ). Enter your answer in terms of h[n]....
sin(r(n-18/6) r(n-18) n#18 if Consider an LTI discrete-time system that has impulse response h[n] = if otherwise a) Determine the magnitude lH(Q)I and the phase response LH(Q) for-r < Ω < π. Enter Ω as "O" and enter the piecewise function H(S2) using the heaviside function. IH(Q)| = LH(S2) = b) Determine the output of the system, y[n], if the input is given by x[n] = δ[n-71+ cos(쮜. Enter your answer in terms of h[n]. y[n] = In your answers,...
Question 6 1 pts An LTI system has impulse response h[n] = (-1)”[n+1] Is the system causal? Is it stable? (a) It is both causal and stable. (b) It is causal, but not stable. (e) It is stable, but not causal. (d) It is neither stable, nor causal (e) The system is stable, but the information provided is insufficient to determine causality (f) The system is elusal, but the information provided is insufficient to determine stability (g) Neither causality nor...
Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution determine yin, 1f XIn = 1 un.(6 marks Consider a causal LTI system whose input xn] and output y[n] are related by the differenoe equation yn In--n] a. Find the impulse response of the system (without using any transform). (5 marks) b. Using convolution...
a causal discrete time LTI system is implemented using the difference equation y(n)-0.5y(n-1)=x(n)+x(n-1) where x(n) is the input signal and y(n) the output signal. Find and sketch the impulse response of the system
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
LTI Systems-Stability Consider an LTI system with system function: s-1 H (s) = If the system is non-causal and un-stable, determine the time domain impulse response
4. (5 pts) Consider a discrete-time LTI system T that generates an output y[n] according to a2 y[n] bx[n] – ay[n – 1] - *[n – 2] where a, b are non-negative real constants. (a) (2 pts) Find the poles of the z-transform of the impulse response h[n] of T. (b) (3 pts) Let H(ejl be the frequency response of T. Find a, b so that the system is causal and stable, |H(1)| = |H(ejº)] = 0.04, and |H(-1)] =...