Question 1 10 points Using the definition of the transform, determine the transforms for each of...
Term brua 2019 Instructor: Ahnet A 1. Determine the Laplace transform and the associated region of convergence and pole-zero plot for each of the following functions of time (b) r(t)te-24 elsewhere (d) a(t) (t)+u(t) 2. Determine the function of time, a(t), for each of the following Laplace transforms and their associated regions of convergenice: )부부, Rds) > 1 d)승부 R1(s) >-1 3. Consider an LTI systern with input r(t)-ε-lu(t) and impulse response h(t)-e-2u(t). (a) Determine the Laplace transforms of ar(t)...
3. (Oppenheim Willsky) Determine the z-transform for each of the following sequences. Sketch the pole-zero plot and indicate the region of convergence. Indicate whether or not the discrete-time Fourier transform of the sequence exists. (a) 8[n +5] (b) (-1)"u[n] (c) (-3)”u[-n – 2] (d) 27u[n] +(4)”u[n – 1]
Please answer all questions with math detail 3. (21 points) Laplace Transform (a) (15 points) Find the Laplace transforms of the following signals and determine their region of convergence sinwot)-iu i. f(t) -i, e-2(t-3 2<t otherwise (b) (6 points) The Laplace transform of a causal signal x(t) is given by X (s) = s2 , ROC: Re{s) > -1 Which of the following Fourier transforms can be obtained from X(s) without actu- ally determining the signal x(t)? In each case,...
8. Find the Fourier transform of the following signal. (5 points) x(0) 2 1 9. Determine whether or not the following signals are periodic, and if periodic, give their periods in seconds and frequency in hertz. a. X(t) = 12.8 Cos (320xt - . (3 points). b. x(n) = 11.6 Cos (3n). (3 points). 6. x(n) = 1.45 sinn). (3 points). 10. Determine whether or not the LTI systems with the following impulse responses are causal and stable. Note that...
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
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)
?3: (a). Find the Z-Transform of h(t)-1 (?[n] + fin-1] + ?[n-21 + fin-31) (b). Find the unit impulse response corresponding to the following system (c)Plot the region of convergence and the Z transform for ln"un], where uin- 0 elscwhere and a is
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
1. Laplace Transform. (10 pts) Find the Laplace Transform of the following signals and sketch the corresponding pole-zero plot for each signal. In the plot, indicate the regions of convergence (ROC). Write X(s) as a single fraction in the forin of (a) (2 pts) z(t) = e-Mu(t) + e-6tu(t). Show that X(s)-AD10 (b) (4 pts)-(t) = e4ta(-t) + e8ta(-t). (c) (4 pts) (t)-(t)-u(-t) . with ROC of Re(s) >-4. (s+4)(8+6)
BC:6.1 For the following signals, use the defini- tion to calculate the z-transform and find the region of convergence for each signal below. Does it matter whether you use the 1-sided or 2-sided definition for these signals? If this matters, calculate it using each definition c.) zefn] = (0.5)"-7uln-3] un +5