The impulse sesponse o an LTIC System ca) Findl the ero stok spos of this systm...
4: An LTIC system is specified by the impulse response h() 3sin(rt) shown in Fig. 2. Find the zero state sponse for the input a) xt)-2ut) b)x) 8(-1) h(t) 3sin(t) 1/2 1 Fig. 2
7. Find the zero-state response of the input signal r(t) = ej2t for the LTIC system with the unit impulse response h(t) = e-tu(t).
I. Assume that the system impulse response h(t) is defined by h(y-exp-2) u(o (a) Calculate the Hin using the definition of Fourier Integral (Solve the integral) (b) Based on the results of part (a) you calculated, what do you think this system is? IGive reasoning for your answer!] (2) (e) For the signal x(-4Cos od +4 Sin'od, find All Complex (exponential) Fourier Series Coefficients Ca [Use formula sheet for Cos and Sine for exponential
Consider an impulse response h(t) = 5e-Stu(t) and if the system is causal, what is the unit step response s(t)? [Hint: for a causal system, hít – 1) = 0 for 1> 5(1 +e+St)uce) O re-** - 1) (t) O(1-* Xu(t) (1+e-su(t)
III.(6 pts.) A system is defined the following pole zero plot, where H(0)-10. a) Find the step response of the system.< Note: step response, not impulse response. b) (+3) Find the output, y(). when the input is x()-8(0)-e) H(O) 10 -1 -2
III.(6 pts.) A system is defined the following pole zero plot, where H(0)-10. a) Find the step response of the system.
Consider a linear time-invariant system with impulse response hin (-1, n o 2, n 1 h[n]--1, n=2 0, otherwise (a) Determine the system frequency response H(e"). Then compute the magnitude and (b) Does the system have a linear phase? Briefly explain your answer. (2 marks) (c) Compute the system output yin] for all values of n if the input r[n] has the form of: phase of H(e (6 marks) 1,n=1 2, n 2 n3, n 3 4, n-4 0, otherwise...
1. Consider the system described by: *(t) - 6 m (0) + veu(t): y(t) = 01 (1) 60 = {1, 1421 a) Find the state transition matrix and the impulse response matrix of the system. b) Determine whether the system is (i) completely state controllable, (ii) differentially control- lable, (iii) instantaneously controllable, (iv) stabilizable at time to = 0. c) Repeat part (b) for to = 1. d) Determine whether the system is (i) observable, (ii) differentially observable, (iii) instanta-...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
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Consider the system characterized by the characteristic polynomial D2+4D+4. (0) Find the zero-input response go(t) of the system, such that vol(o) 0 and o(0) -1. Impulse Response and Zero-State Response 4 Consider the system characterized by the following diferential equation where z() represents the iaut and y(t) the output (D2 +4D+4) y(t) Da(t) (i) Determine the impulse response h(t) of the system. (i) Compute the convolution h r(t) for r(t) eu(t). Hint:...
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