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1. Suppose that for the LTi system depicred in the following Sgure al the impulse response...
Suppose that for the LTI system depicted in the following figure (a), the impulse response and th...
Suppose that for the LTI system depicted in the following figure (a), the impulse response and the transfer function are given by h(t) = e-tu(t) H(S) = s+1 1 H 100 The input signal x(t) is the square wave of Figure (b), where t is in seconds. Since the fundamental period is To = 2π, the fundamental frequency is ao-2π/L = 1 rad/s and kaa-k. 3t (a) Use the Table provided to find the exponential Fourier series of the signal...
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x)...
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) a) find the Fourier transform of x(t) b) find the Fourier transform of h(t) c) Is this LTI system BIBO stable? Prove d) find the output y(t) of the LTI system
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x)...
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) find the Fourier transform of h(t). Is this LTI system BIBO stable? Find output y(t)
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has...
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients o...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If...
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
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...
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...
A continuous-time LTI system has unit impulse response h(t). The Laplace transform of h(t), also called...
A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called the “transfer function” of
the LTI system, is
.
For each of the following cases, determine the region of
convergence (ROC) for H(s) and the corresponding h(t), and
determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
8...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
For the LTI system described by the following impulse response:
For the LTI system described by the following impulse response: \(h(n)=n\left(\frac{1}{3}\right)^{n} u(n)+\left(-\frac{1}{4}\right)^{n} u(n)\)Determine the following:1) The system function representation,2) The Difference equation representation3) The pole-zero plot4) the output \(y(n)\) if the input \(x(n)\) is: \(x(n)=\left(\frac{1}{4}\right)^{n} u(n)\)
Suppose that for the LTI system depicted in the following figure (a), the impulse response and the transfer function are given by h(t) = e-tu(t) H(S) = s+1 1 H 100 The input signal x(t) is the square wave of Figure (b), where t is in seconds. Since the fundamental period is To = 2π, the fundamental frequency is ao-2π/L = 1 rad/s and kaa-k. 3t (a) Use the Table provided to find the exponential Fourier series of the signal...
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
5. (12 points) Consider a continuous-time LTI system whose frequency response is sin(w) H(ju) 4w If the input to this system is a periodic signal 0, -4<t<-1 x(t)=1, -1st<1 0, 1st<4 with period T= 8 (a) (2 points) sketch r(t) for -4ts4 (b) (5 points) determine the Fourier series coefficients at of x(t), (c) (5 points) determine the Fourier series coefficients be of the corresponding system output y(t)
5. (12 points) Consider a continuous-time LTI system whose frequency response is...
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...
A continuous-time LTI system has unit impulse response h(t). The
Laplace transform of h(t), also called the “transfer function” of
the LTI system, is
.
For each of the following cases, determine the region of
convergence (ROC) for H(s) and the corresponding h(t), and
determine whether the Fourier transform of h(t) exists.
(a) The LTI system is causal but not stable.
(b) The LTI system is stable but not causal.
(c) The LTI system is neither stable nor causal
8...
Given a zero-state LTI system whose impulse response h(t) = u(t) u(t-2), if the input of the system is r(t), find the system equation which relates the input to the output y(t) 4. (20 points) If a causal signal's s-domain representation is given as X (s) = (s+ 2)(s2 +2s + 5) (a) find all the poles and zero of the function. 2 1 52243 orr
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