QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles...
Problem 3 (30 points) An LTI system has an impulse response hin], whose z-transform equals 1-1 1. List all the poles and zeros of H(2). Sketch the pole-zero plot.. 2. If this system is causal, provide the ROC of H(2) and the expression of hin. case, is this system also stable? 3. If the ROC of H(z) does not exist, provide and the expression of hn.
Question 2: Poles and zeros, and how they affect the transient response modes This question tests your understanding of the effects of nearby poles and ze- ros to the response mode of a specified pole (or conjugate pair). You should also understand what a pole-zero-gain plot is and how it is specified by, and specifies a transfer function A unit impulse function is applied to the system described by the transfer function G(8) = K (8+) (s + 1)(8 +2)...
Answer the following questions for a causal digital filter with the following system function H(z) 23-2+0.64z-0.64 1-1. (0.5 point) Locate the poles and zeros of H(z) on the z-plane. (sol) 1-2. (1.5 point) Sketch the magnitude spectrum, H(e i), of the filter. Find the exact values of lH(eml. IH(efr/2)I, and IH(e") , (sol) 1-3. (1 point) Relocate only one pole so that 9 s Hle)s 10 (sol) 1-4 (1 point) Take the inverse Z-transform on H(z) to find the impulse...
Poles and Zeros For the transfer function given: 0.85 8-44.64 G(s) = 긁+0.83 12.00 Part A-Poles Find the system pole 8 Submit Part B-Poles Find the system pole s2 Submit Part C-Zeros Find the system zero Submit Part D-Type of Response Based on the locations af the poles and zeros, what will be the response to a unit step inpue? O Harmonic Oscillations (Marginally stable) Oscillatory motion with exponential decay tending to zero (stable O Critically damped exponential decay (stable)...
Find the system transfer function of a causal LSI system whose impulse response is given by h[n]=(−0.55)n−1 sin[3.7 (n−2)] u [n−2].
(a) A system has the impulse response, h[n], and is excited with the input signal, xIn], as shown below. Using either a mathematical or a graphical convolution technique, determine the output of the system, y[n] (that is, evaluate y[n] h[nl'xIn], where" denotes convolution). 17 marks xIn INPUT FIR filter 0.5 0.25 OUTPUT 0 1 345 6 7 .. 0.5 0123 4567 (b) An IIR filter is shown below: ylnl One sample delay (z) 0.4 i) Derive the difference equation describing...
1.Using the transformed-Z unilateral determine and [n] for n20 for 7t With y [-1] 1 2. it wants to design a system, linear and invariant in the time with the property that for the entry unun 1 The corresponding output is 2) un) determine the transfer function H (z) and the response to the impulse H [n] of the would fulfill the response condition system that Graph the map of poles and zeros in the complex plane. . Find the...
Please show all the steps clearly.
Find the system transfer function of a causal LSI system whose impulse response is given by 2. 0.5)"l sin[0.5(n- 2)]u[n - 2] and express the result in positive powers of z. 72-1 h[n] = Hint: The transfer function is just the z-transform of impulse response. However, we must first convert the power of -0.5 from (n - 1) to (n - 2) by suitable algebraic manipulation
Find the system transfer function of a causal...
Problem 1: The impulse response ht) for a particular LTI system is shown below hit) Be5e (4 cos(3t)+ 6 sin(3t) e. u(t) 1. Plot the impulse response for h(t) directly from the above equation by creating a time vector 2. Use the residue function to determine the transfer function H(s). Determine the locations of the poles and zeros of H(s) with the roots function, and plot them in the s-plane (x for poles, o for zeros). Use the freas function...
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...