Sketch the Fourier transforms of the following functions assuming |w1|> [w2| a. f(t) = [cos(wit) + i sin(@¡t)] - [cos(@zt) + i sin(@2t)] b. f(t) = [cos(wot)]e¬t/T2

Q: (a) Find the Fourier transform of the function g: RR defined by Ste-kt, for t > 0, g(t) = otherwise.…

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

Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

A: If Fourier transform of f(x) is F(p), then we have to prove that the Fourier transform of f(x)…

Q: Q8 Find the Fourier transforms of: sin* - pn Sx< pn f(x) otherwise

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Q: f(t) = 2 2 (3 cos 6t-5 sin 6t)

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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.…

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Q: Find Laplace transform of b) f(t) = te'cos(t) %3D

A: Given:  (1) f(t)=tetcost

Q: Find the Fourier transform of (a) f (x) = sin (x²), (b) f (x) = cos (x2)

A: 4. Given that,fx=sinx2andfx=cosx2The Fourier transform of the above functions isdetermined as shown…

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

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Q: The Laplace transform of the 4e cos2t – et sin2tis Select one: 4s+2 O a. F(s) s2+2s+5 2s+2 O b. F(s)…

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Q: ) Compute the Fourier transform of the function. (a) f(x) = h(x + 1) – 2h(x) + h(x - 1), where 1, if…

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

A: As per the question we have to first find the expression for the signal x(t), and then we have to…

Q: EVALUATE THE LAPLACE TRANSFORM OF THE GIVEN FUNCTION USING APPROPRIATE THEOREMS. 1. f(t) = et+1 cos…

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Q: 3. Find the Fourier Transform of a t < 2 a а f(t) = 1 %3D -- 2 < t Whose graph is shown below V t. V

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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: 13. Let the function f (x) be 2n-periodic and suppose it is represented by the Fourier series: f (x)…

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Q: Consider a function f(t) with a finite discontinuity at t = 0. Given that its Fourier transform is…

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Q: Find the Fourier transform of the following: f) f(x) = k(x), where k,k', ...,km) are all absolutely…

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Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: Compute the Fourier transform of the following signal: x(t) = e-31e|sin(2t)u(t)

A: The Fourier transform of the function x(t) is represented as X(w), it is defined as ∫-∞∞e-iwtx(t)dt,…

Q: Give the Laplace transform of 3x f(x): 0 <x and x < 3 -4 3 3x 3 2 + 2 -3s 4 F(s) = + e 3 -3s 15 3 10…

A: Option C is correct.

Q: 2) Find the (complex) Fourier transform of 1-2, if r| S1, F(z) 0. if |피> 1, I COS I- Sin z and hence…

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Q: Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal x(t) with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find the Fourier transform of -et +2 cos(t). (a) -27 8(w+ 1) (b) 2n 8(w + 1) (c) -27 8(w- 1) (d) 2n…

A: To solve this problem we use the following the results and formula:

Q: Find the Fourier Transform of Hence Prove that f(x): cos(sx) + Ssin(sx) 1+s² -ds = x 0 OEIN 0 2 Tex…

A: Introduction: Through Fourier transformation, a real-time function can be converted into a complex…

Q: Q2- Find the Fourier Transform for f (t) =A cos o,t, where o, = 2n fo %3D

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Q: Obtain the z-transform of the following: x(n)=na" sin(an)u(n)

A: Let us start solving the problem step by step.... We need to find the z-transform of x(n)

Q: Find Laplace transform of R) =-t+1#0st<1 OA 1 es OB 1 1 es OC. 1 1 OD Non of the above. OE 1 1 e-s…

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Q: Find the Fourier transform of f (x) defined bv f x) = , a 10, > a and hence evaluate sin pa cos dp…

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Q: Give the Laplace transform of 5 0Sx and x <I f(x) = -7 sin (2x) 2 +e 2 4 +4 b) O Fe)-+" ( 5 F(s) 7 5…

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Q: a) Find the finite Fourier cosine Transform of f (x) = x² in 0 < x < 4.

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Q: 7. Find the Fourier sine and cosine transforms of the following functions defined on [0, ∞). x =…

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Q: Find the Fourier Transform of Sa? – x², for |æ| a f(x) = and hence deduce that (sin s- s coss -) ds…

A: Fourier transform of gx=1 for x&lt;a0 for x&gt;a is ∫-aa1.e-isxdx. Calculate it:…

Q: (a) Find the Fourier Transform of the function: f(t) = e, for t>0 and a > 0.

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Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: Find the Laplace transform of the following 7- e-t sin² t 8- £f"(t) = tan-¹(¹), f(0)=2, f'(0)=-1…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: If F(s) is the complex Fourier transform of the function f (x), then prove that F{f (x – a)} = e-ias…

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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: Find the Fourier transform of the function : S (t) = e-x2 %3D

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Q: 1. Consider the function [x-1, f(x) = 0, (1.1) Find the Fourier transform of f(x). if 0 ≤ x ≤ 1,…

A: For part 1.1, we are given the function f(x)=x-1,           if  0≤x≤10,                  elsewhere…

Q: a Find the Fourier transform of the signal x(7) = 2 cos(m)[(1+3)-(1-3)], using the Fourier integral.

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Q: Find the Fourier transform of f (x) defined by |x| a f (x) = sin? ax ta and hence prove that x2 2

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Q: Find the Fourier Transform F(w) = {e-at t≥0 t≤0

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Q: 1. Find the Fourier transform of the function h(t) 4 -+ 2e-nt2 - ei4nt

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

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Q: y(t) = t2 sin(t-2) -x(2t) 1(t-2)

A: To calculate the Fourier transform of y(t), we shall calculate the Fourier transform of x(t). Since…

Q: If f(x) has the Fourier transform F(p), then f(x) cos ax has the Fourier transform [F(p-a) + F(p +…

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Q: 8. Find the Laplace transform of the function g(t) = e"[4t + 5 cos(3t) + 6 sin(3t)] %3D

A: Given below the detailed solution

Q: will rate if correct.

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Q: ind the Laplace Transform of the following periodic functions (-) -1 3) f()=e', (0<t< 2n) Ans. F(s)…

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