The Laplace transform F(s) of the signal f (t) is given by: F(s) = | f(t)e¯stdt %3D (a) Using this formula, find the Laplace transform of the function f (t) = t²u(t). Show details of the integration by part. %3D (b) Using the above formula find the Laplace transform of f(t) = 8(t) + e¯3{u(t – 2). %3D 1. (c) If the Laplace transform of elwot is find the Laplace transform of the Cosine s-jao function f (t) = cos(5t).

9. Find the Laplace transform of the waveform shown below a) b) Answer: a) F(s) =[1- e-s - e-3s - e-1$] b) F(s) = [e¬s + e-25 + e-3$ + e-4s - 4e-5s1 %3D

Part (a) only

Determine the Laplace transform of the following function using the definition and/or L.T. properties. Ifusing LT properties, indicate which property you are using. For all functions, assume f(t)=0, t<0

Please answer all questions for like this Please all subpart is compulsory please

Find the inverse z-transform for each of the following functions: 4z a. X(z) = 2+ %3D Z-1 Z-0.5 5z 2z b. X(z) %3D (z - 1)2 (z - 0.5)?

1. Find the Laplace transform of the following functions: a. t b. 8(t) c. e-at d. 2t + sin(wt) meraya gpool beeots sitt to animarh to 20uten ed e. sin(2t-10) nalfonat f. e-at cos (wt) a nismoh g. F(s) is Laplace transform of f(t), what's the Laplace of transform of f(2t)? h. F(s) is Laplace transform of f(t), what's the Laplace of transform of f(t)? dt i. F(s) is Laplace transform of f(t), what's the Laplace of transform of f f(t)dt?

Q1// Determine z-transform and the ROC of the following sequence X(n) = n-1 {(e)-0.5n 8(n – 1) * (0.2)" u(n – 1)}

please do both parts

The inverse z-transform of F(z) is: Select one: O a. f(k)= O b. f(k)= O c. f(k)= O d. f(k)= x (5)* x cos(0.92k +1.57) x(-5) x cos(0.92k-1.57) x (5)* x cos(0.92k-1.57) x (5)* x cos(1.57k - 0.92) F(2) = 25-62+25