![6. [10!] An LTI system has an impulse response hin] for which the z-transform is Homework#6, Ve216 Spring 2018 ue (a) [5] Plot the pole-zero pattern for H(z). (b) [5!] Using the fact that signals of the form 2 are eigenfunctions of LTI systems, determin the system output for all n if the input r[n] is](http://img.homeworklib.com/questions/905dc930-cb0a-11ea-93a5-dd2432e4caad.png?x-oss-process=image/resize,w_560)
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6. [10!] An LTI system has an impulse response hin] for which the z-transform is Homework#6,...
1. An LTI system has an impulse response h[n] for which thez transform is a. Plot...
1. An LTI system has an impulse response h[n] for which thez transform is a. Plot the pole-zero pattern for H(z). b. Using the fact that signals of the form z are eigenfunctions of LTI systems, determine the system output for all n if the input x [n] is given by 72 I3(2)
Problem 3 (30 points) An LTI system has an impulse response hin], whose z-transform equals 1-1...
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.
Please solve the following with full steps. 2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three no...
Please solve the following
with full steps.
2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
a=8 b=7 5. Consider a LTI system is stable, and the Z transform of its impulse...
a=8
b=7
5. Consider a LTI system is stable, and the Z transform of its impulse response is (2) = suppose the input signal x[n] is a unit step sequence. 1) Sketch the magnitude response (rough) for the system 2) find the output Y(z).
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: \(x(n)=\left(\frac{1}{4}\right)^{n} u(n)\)
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine:...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine: (i) The system function representation; (ii) the difference-equation representation (Note: this is just terminology that refers to expressing the input and output time-domain signals in the form of an equation. E.g., what we did when we went over the equations for block diagrams); (iii) The pole-zero plot, sketched by hand; and (iv) the output y(n) if the input is x(n) = (0.25)n u(n) [10...
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 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)...
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the imp...
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Deter...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
1. An LTI system has an impulse response h[n] for which thez transform is a. Plot the pole-zero pattern for H(z). b. Using the fact that signals of the form z are eigenfunctions of LTI systems, determine the system output for all n if the input x [n] is given by 72 I3(2)
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.
Please solve the following
with full steps.
2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
a=8
b=7
5. Consider a LTI system is stable, and the Z transform of its impulse response is (2) = suppose the input signal x[n] is a unit step sequence. 1) Sketch the magnitude response (rough) for the system 2) find the output Y(z).
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 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)...
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
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