(a) Show that the Fourier transform of the function ga(x) := f(ax), where a > 0 is a constant, is Flg.(e) = f (:). a

Q: e-2t cos 3t cOS

A: The given question is related to Laplace Transform. The solution is explained below.

Q: What is the initial value of f(t) if its Laplace transform is

A:

Q: 40. Find the inverse Fourier transform off (p) = e¯ ™ Y.

A:

Q: 4. Using the "final value theorem" predict the final value in time for signal having the following…

A: The Final value theorem states that, limt→∞x(t) =lims→0 s X(s)  We have, limt→∞ f(t) = lims→0s F(s)…

Q: 1 The Fourier transform of [e 2 x(t + )] is jt 1 jn( f- X(f)e#ft X(f – e"(s-±) 4 t A. O . A.…

A:

Q: (b) Find the Fourier transform of the function given below 1– x? if |x|1 and hence find the value of…

A: Calculate Fourier transform: Fω=∫-∞∞fxe-iωxdx         =∫-111-x2cosωx-isinωxdx…

Q: 3s-1 L-1 Is²-6s+16)

A: Given:     L-13s-1s2-6s+16

Q: 14. Find the inverse Laplace transform of 2s+1 a) F(s) : s2+25

A:

Q: 1. Find the Fourier transform of this rectangular pulse X (w) and show that sin πωτ X(w) = A² 2.…

A:

Q: 2. Find the Laplace transform of the ff. a. t cos 3t b. e

A:

Q: (A) Find Laplace transform of the function : f(t)=1 sin(2t+) cos(21-7)

A:

Q: Find the Laplace transform of e-4t cos6t.

A:

Q: . Find Fourier cosine transform of - and deduce that 2. bx e 1 e V2m log р ға cos px dx

A:

Q: e the inverse Laplace transform of

A: The given function is ss2+2s+2  to find the inverse Laplace Transform proceed as follows rewrite the…

Q: to find the inverse Laplace transform of the given function. 18.F(s)=2n+1n!sn+1

A:

Q: Example 3.2 Find the Laplace Transform of the following functions: (a) (b) 1 e at

A: The detailed solution is as follows below:

Q: (a) Consider a continuous-time signal g(t) with its Fourier Transform as below: (2 sin(w) G(jw) =…

A: Given equation is, Gjω=1-e-jω22sinωω+e-jω3 We have a recttT⇒2AsinωT2ω Let, A=1, T=2 then…

Q: Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in…

A: The Fourier transform of the function is represented as , it is defined as , where . Since the…

Q: 5. Find the inverse Laplace transform of the function as +b H(s) = (s – a)² + B²' -

A:

Q: Find the Exponential Fourier coefficient Cn for signal f(x) = x Defined on interval [-1 ,1]

A: Complex form of Fourier series is defined as follows: fx=∑n=-∞∞cne-inx2πL where,…

Q: What is the laplace transform of the periodic function shown in the picture.

A: Solution

Q: 1 Determine the inverse Laplace transform of (s–2)(s-3)

A:

Q: Question 2 Find the inverse Laplace transform of -4s H(s) = - e

A: The solution is given as

Q: Find the LaPlace transform for the periodic function. 1. 2 3 4. 3.

A: Consider the given figure. Given that function is periodic function. We have to find the Laplace…

Q: 1. Show that the function 2t et cos (et“) is not of exponential order, however its Laplace transform

A:

Q: 14. Find the inverse Laplace transform of 2s+1 a) F(s) s²+25

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Solve the Laplace transform of (1+e-t)2

A:

Q: (d) Show that the Fourier transform of a Gaussian is a Gaussian, and hence show that eik dk 2πδ(x).

A: The Dirac delta function is one of the most significant functions in mathematics. It is widely used…

Q: of the function. 4. Find the Fourier transform of of 1/(1+t²).

A:

Q: 3. Find the Inverse Laplace transform of : 5s-2 a) s2 (s+2)(s-1)

A:

Q: 1. Find the inverse Laplace transform of the function 2/ s (s + 1) with the help of convolution.

A: 2-2e^(-t)

Q: 4) Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in…

A: Given:

Q: FInd the Laplace transform of cos t cos 2t cos 3t

A:

Q: Determine the laplace transform e-6t + cos 6t

A: Determine the laplace transform e-6t +cos6t

Q: 1: Find the inverse Laplace transform of the function: -2s3+12s2-8s- 4 F(s) = (s-2)2(s+ 1)s

A:

Q: 3. Find the inverse Laplace transform of: 2s2 + 3s - 5 F(s) = s(s + 1)(s – 2)

A:

Q: 1. Compute the Fourier transform of the following signal: x(t) = e-3|t| sin(2t)u(t)

A: Hint: The convolution theorem of Fourier transform states that, the Fourier transform of the…

Q: Solve the Laplace transform of e-2t cos/3t – t²e-2t

A:

Q: Find the inverse laplace transform of e-2s

A:

Q: 5 The inverse Laplace transform of the function sin(2t) (A) 1 – 2 sinh(2t) (B) t- 2 sin(2t) (C) t- 2…

A:

Q: ve an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in Figure…

A:

Q: 1 (5+3)(s+7) Laplace Inverse Transform of.

A:

Q: +5s, The inverse Laplace transform of is 1 1 5 5 f(t) = S sin 5t - sin

A: It is required to find inverse Laplace transform of L-11s3+5s. That is, L-11s3+5s=L-11ss2+5 Here…

Q: Find the Laplace transform of the periodic function whose graph is shown. 2 3 4 5

A:

Q: 3) There is a function F (s), which is a 'folded or repeated root state". Make the inverse laplace…

A:

Q: 1 (iv) If f(t) = e2ºH(t), its Fourier transform is F(@) = -2+iw

A: In this question we have to find whether it is true or false.

Q: Example 22.3. Find the Fourier transform of: f (x) = %3D 0 x|> 1 Hence evaluate C COS x - sin x -…

A: Fourier transform, of even function

Q: (b) Using Laplace transform, evaluate te -2t Cos 2t dt 0.

A: