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Consider a continuous-time LTI system S with impulse response h(t) = 2(u(t + 1)-u(t 1)). Determine...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) -...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
2.6.1 Consider a causal continuous-time LTI system described by the differential equation u"(t) +...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
I. Assume that the system impulse response h(t) is defined by h(y-exp-2) u(o (a) Calculate the...
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
Exercise 2.5 response of the LTI system with impulse response h(t)-e cos(2t)u(t)
Exercise 2.5 response of the LTI system with impulse response h(t)-e cos(2t)u(t)
2.52 with cosine replaced with sine. 2.52. The step response s(t) of a continuous-time LTI system...
2.52 with cosine replaced with sine.
2.52. The step response s(t) of a continuous-time LTI system is given by s(t) = cos wat ju(t) Find the impulse response h(1) of the system. Ans. h(i)= 8(t) – woſsin wot]u(t)
Consider a continuous-time LTI system impulse response h(t) as given below. h(t) = 2/3 e^-tu(t)-1/3 e^2t...
Consider a continuous-time LTI system impulse response h(t) as given below. h(t) = 2/3 e^-tu(t)-1/3 e^2t u(-t) (a) Determine Laplace Transform H(s) of h(t). Determine and clearly sketch its ROC. (b) Is it possible to find the Fourier Transform H(j!) of h(t) by using Laplace Transform? If possible, determine H(j!). Why, or why not? Explain. (c) Is this system causal? Is this system stable? Explain your answers.
2.7.21 Match the impulse response h(t) of a continuous-time LTI system with the correct plot of...
2.7.21 Match the impulse response h(t) of a continuous-time LTI system with the correct plot of its frequency response H' (w)l. Explain how you obtain your answer IMPULSE RESPONSE 0.5 -0.5 0.5 2.5 3.5 4.5 0.5 0.6 0.4 0.8 w 0.6 O 0.4 0.2 0.8 0.4 S 0.2 0.8 u 0.6 0.4 S 0.2
Consider an LTI system with the impulse response h(t) = e- . Is the system casual?...
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
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...
Consider a LTI system with unit impulse response, h(t) = e-3tu(t). Using direct integration technique for...
Consider a LTI system with unit impulse response, h(t) = e-3tu(t). Using direct integration technique for finding convolution, find its zero-state response due to an input, x(t) = u(t) (which is called unit step response of the system). Also, from your answer above, write down its response due to an input of the form, x(t) = 2δ(t) – 4u(t). [Hint: Use principle of superposition] !!Please show/explain step, WILL RATE!!
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
2.6.1-2.6.62.6.1 Consider a causal contimuous-time LTI system described by the differential equation$$ y^{\prime \prime}(t)+y(t)=x(t) $$(a) Find the transfer function \(H(s)\), its \(R O C\), and its poles.(b) Find the impulse response \(h(t)\).(c) Classify the system as stable/unstable.(d) Find the step response of the system.2.6.2 Given the impulse response of a continuous-time LTI system, find the transfer function \(H(s),\) the \(\mathrm{ROC}\) of \(H(s)\), and the poles of the system. Also find the differential equation describing each system.(a) \(h(t)=\sin (3 t) u(t)\)(b)...
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
Exercise 2.5 response of the LTI system with impulse response h(t)-e cos(2t)u(t)
2.52 with cosine replaced with sine.
2.52. The step response s(t) of a continuous-time LTI system is given by s(t) = cos wat ju(t) Find the impulse response h(1) of the system. Ans. h(i)= 8(t) – woſsin wot]u(t)
2.7.21 Match the impulse response h(t) of a continuous-time LTI system with the correct plot of its frequency response H' (w)l. Explain how you obtain your answer IMPULSE RESPONSE 0.5 -0.5 0.5 2.5 3.5 4.5 0.5 0.6 0.4 0.8 w 0.6 O 0.4 0.2 0.8 0.4 S 0.2 0.8 u 0.6 0.4 S 0.2
Consider an LTI system with the impulse response h(t) = e- . Is the system casual? Explain. Find and plot the output s(t) given that the system input is x(t) = u(t). Note that s(t) in this case is commonly known as the step response of the system. If the input is x(t) = u(t)-u(t-T). Express the output y(t) as a function of s(t). Also, explicitly write the output y(t) as a function of t. a) b) c)
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...
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