The ROC for the causal discrete LTI system where H (2) = H(3)= (1+} = ')(1-13-)...
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
Problem 2 Consider a continuous-time LTI system whose frequency response is given by 2 sin(40 (a) Find the impulse response, h(t) of the system (b) Determine the outputy() =x(t)*h(t) of the system given an input x(f)--1, ț < 8 4 otherwise 0,
1-2-1 A discrete-time causal LTI system has the function of transference H(z) = The response to the inital impulse is: 7 h[n)= 3(-4)"-2-1+1 --[n] 5 a h[n)- 4-1-2-n+1 -La[n] 3 5(3-)-2-1+1 h[n]= -[n] 3 h[n)- 5(-4)-" +2-6 - + 1 --[n] 3 h[n)- 5(-4)-"-2-n+1 u[n] 3
2. Circle the causal BIBO stable ROC below. a) 1.1<\리<1.2 b) Izk1/201zP1/2 d) 0.5<Izl<0.9 e) none above 3. A linear time-invariant IIR system is always BIBO stable a) True b) False 4. If a fiter has z-transform H(z)05, then the fiter s ;z>0.5, then the filter is zz-0.5z a) Nonlinear b)FIR )R d) two-sided e) none above 5. The discrete-time frequency o in rad/ sample of the sinusoid hin] below is d) T2 e) none above hIn] -1
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
Laplace Transform 5. Given a causal LTI system with pole-zero cancellation such as H(s)= S+1 what is the region of convergence and why. (5+1)(3+2) i. ROC = undefined ii. ROC = Re(s) > 0 iii. ROC = Re(s) >-2 iv. ROC = Re(s) >-1
A discrete time LTI filter at rest is given by its system function H(z), 1+z-1 H2) = 1-0 8-1 R.O.C [z] > 0.8 (Hint: Use the z-transform and Partial Fraction Expansion to fill in the blanks.) The steady state unit-step response of the above filter is: Yuss [n] = — u[n]
please show detailed work/proof 3. The input and output of a causal LTI system satisfy the following difference equation (d.e.) y[n] = ayln-1] + x[n]-a"x[n-N], N > 0 a. Determine the impulse response h[n]. Hint: solve it iteratively starting from n=0, 1, , n=N+1; x[n] = δ[n] then think what is y[n] ? b. Sketch the impulse response h[n] c. Is this an FIR or an IIR system? d. For what values of the parameter a is the system stable?
р Question 3 Consider the transfer function, H(s), of a non-causal LTI system H(S) = s+2 (8+3)(82 +8+5) (82–8+5) 1. Determine ROC for H(s) = = = xx, E P T
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.