3- If v(t) and w(t) are finite only for t 0(i.e. v(t) 0 and w(t) 0 for t
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1- Let's consider an LTI system with an impulse response of where Wo a) Find H(s) and the associa...
Consider the following waveform f(t) which is a one cycle of a sinusoid for 0 seconds...
Consider the following waveform f(t) which is a one cycle of a sinusoid for 0 seconds while zero elsewhere (Aperiodic Signal) 2- t π in fo) 0 -10 a) Represent f(t) mathematically. b) Determine the Laplace transform using the integral expression c) Repeat that using the properties of the Laplace transform
Consider the LTI system with input ??(??) = ?? ?????(??) and the impulse response ?(??) =...
Consider the LTI system with input ??(??) = ?? ?????(??) and the
impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine
??(??) and ??(??) and the ROCs B. (3 points) Using the
convolutional property of the Laplace transform, determine ??(??),
the Laplace transform of the output, ??(??) C. (3 points) From the
answer of part B, find ??(??)
9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
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...
1) Given the unit impulse response of a LTI system, find its transfer function H(s)-B(s)/A(s) in...
1) Given the unit impulse response of a LTI system, find its transfer function H(s)-B(s)/A(s) in canonical form and ROC using the definition of Laplace transform and state the stability and causality with a specific reason: e. he(t)-600e-90t[u(t)-u(t-2)] f. h(t)-ha(0.2t) and show that hr(s)-(1/0.2)H.(s/0.2) g. A practical Butterworth filter, he(t)- 10198e3214tsin(3214tju(t) (Tip: sin()(el h. hn(t)-600te-30tu(t) Tip: integral by parts J udv = uv-J val) e-/2i))
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine...
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine the frequency response of the system. b) Find the magnitude response and the phase response, given a = 1/2. No plots. c) Consider a LTI system whose impulse response h1[n] is a time-shifted version of h[n], i.e., h1[n] = h[n − n0]. Compute the frequency response H1(e^(jΩ)), and represent H1(e^(jΩ)) in terms of H(e^(jΩ)).
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...
need asap 1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as...
need asap
1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as following h(t) 6u(t) where u(t) is unit step function. The output(Y (s)) is expressed as the product of input (R(s)) and transfer function Y(s) = R(s)H(s) The Laplace transform is defined as LTI system R(H) Y (s) Figure 1: LTI system in s-plane (a) (5 points) Find the tranisfer function(H(s)) of the LITI system. (b) (5 points) Find the Laplace transform of the input(r(t)....
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a...
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a Laplace transform which is given by 5+1 H(3) and that the input to this system is x(t) = ell! $+ 25 +2 a) Determine the Laplace transform of the output y(t), along with its associated region of convergence. (12 pts) b) Determine the output y(t). (8 pts)
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)
Consider the following waveform f(t) which is a one cycle of a sinusoid for 0 seconds while zero elsewhere (Aperiodic Signal) 2- t π in fo) 0 -10 a) Represent f(t) mathematically. b) Determine the Laplace transform using the integral expression c) Repeat that using the properties of the Laplace transform
Consider the LTI system with input ??(??) = ?? ?????(??) and the
impulse response ?(??) = ?? ?2????(??). A. (3 points) Determine
??(??) and ??(??) and the ROCs B. (3 points) Using the
convolutional property of the Laplace transform, determine ??(??),
the Laplace transform of the output, ??(??) C. (3 points) From the
answer of part B, find ??(??)
9 points) Consider the LTI system with input x(t)eu(t) and the impulse response h(t)-e-2u(t) A. 3 points) Determine X(s) and H(s)...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
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...
1) Given the unit impulse response of a LTI system, find its transfer function H(s)-B(s)/A(s) in canonical form and ROC using the definition of Laplace transform and state the stability and causality with a specific reason: e. he(t)-600e-90t[u(t)-u(t-2)] f. h(t)-ha(0.2t) and show that hr(s)-(1/0.2)H.(s/0.2) g. A practical Butterworth filter, he(t)- 10198e3214tsin(3214tju(t) (Tip: sin()(el h. hn(t)-600te-30tu(t) Tip: integral by parts J udv = uv-J val) e-/2i))
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...
need asap
1, (20 points) Suppose we have a İTİ system with impulse response(h(t) described as following h(t) 6u(t) where u(t) is unit step function. The output(Y (s)) is expressed as the product of input (R(s)) and transfer function Y(s) = R(s)H(s) The Laplace transform is defined as LTI system R(H) Y (s) Figure 1: LTI system in s-plane (a) (5 points) Find the tranisfer function(H(s)) of the LITI system. (b) (5 points) Find the Laplace transform of the input(r(t)....
Problem 6 (20 pts) Suppose that the impulse response of a causal LTI system has a Laplace transform which is given by 5+1 H(3) and that the input to this system is x(t) = ell! $+ 25 +2 a) Determine the Laplace transform of the output y(t), along with its associated region of convergence. (12 pts) b) Determine the output y(t). (8 pts)
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)
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