Find the Fourier transform of each of the following signals and sketch the magnitude and phase as a function of frequency, including both positive and negative frequencies. (you should not use the property table, you will need to show the proof) a) x(t) = e2'u(t) b) y(t) = e(3-J4)u(t)

Q: Find the Inverse Fourier transform of e) e 2 cw-4Jj 4- C4-wJj

A: Given: In this question, the given details are Here, the given expression is, e2(ω-4)j4-(4-ω)j To…

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: Evaluate fa tan() da 1 글 [(22 + 2a) tan-1 ()-피+C o b을[(22+ 2a) tan-1 () + z] +C 2a) tan-1 ()- 피 +C…

A: Solve the above integration.

Q: sin X 1/ガースゴ+スコービsinx

A: Given differential equation is  y" -3y' +2y=e^x sinx

Q: Evaluate (3x + cos 4x) dx

A:

Q: Evaluate cos³ (72) sin(7x)dr / COS³ + C

A:

Q: evaluate

A: Given integral is evaluated as follows.

Q: Could you explain to me how to find the inverse Fourier transform of the function __ (w+4)² 32 a.…

A:

Q: State the sum and difference formulas for the cosine. cos (x + y) = cos (x) cos (y) - sin (y) sin(x)…

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Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

A:

Q: Sint dt ds く ーb ヒニb

A:

Q: Find The Fourier Transform for the signal Given y-Cosht

A: Given: Signal, y=coshtTo find: Fourier transform of the given signal.

Q: Homework: Find the Fourier transform of the signal given below y(t) = Y(w) = ? -12 2 0 >t

A:

Q: Describe the connection of Chebyshev to Fourier.

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Q: Find the domain of the function 3x -1 A. f(x)= 1- 2x + 3 sin 2.

A:

Q: Find the Fourier Cosine Transform of the function ƒ(x) = (ae-4x + be-³x + ce-²x)² if x > 0 if a = 4,…

A:

Q: I am not fully grasping the transformation from sinx to tanx and from cosx to tanx in step 2 of the…

A: To evaluate the following integral by using the substitution .Note: Since, the student has mentioned…

Q: (ii) Evaluate J dx. COS TI

A:

Q: Express sinh (i) in the form a + ib

A:

Q: Question 1.i.) A truncated sine wave { sin5x, y = f(x) = 0, %3D otherwise

A:

Q: the value of (yn)o If y= Sin (msin , find

A: Given that We need to find the value of

Q: y = cos(-4x)

A:

Q: 2 Find the reflection of v = | 5| on the line with equation II

A: Let v=25-1,  w=11-2 (vector of line) Projection of v→ onto line vector w→ is…

Q: Let y = sinx, if y(n) = sin x then n =

A: This question can be solved using the concept of higher order derivatives.