Compute the Fourier Transform of the following function (3 , –n < x < o (1 , 0

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x,0) = e, -0 <r < oo.

A: Given ut=uxx, -∞&lt;x&lt;∞, t&gt;0u(x,0)=e-x2, -∞&lt;x&lt;∞

Q: 4. Find the inverse z- transform of the following 3 de XCZ)= tanh (z-)

A: Given: Let us find the inverse z-transform of the given following, xz=tanh-1z2-14

Q: Find the Fourier transform off (x) defined by Example 6. 1, |x| a f(x) = sin s ds (ii) 00 sin sa.…

A:

Q: 5. Compute the inverse z-transform of X(z)=log(1+z),z|<1.

A: Given: To explain the given statement as follows, To calculate Z transform, .

Q: Find the inverse Laplace transform of F(x) = 4s^2−2s+2/(s2−4)(s)

A: The inverse laplace transform of F(s)=4s2-2s+2s(s2-4)

Q: Find the inverse Laplace transform of 1 F(x) S- s2 (s + 1)

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s).…

Q: si |x| < a 1. f(x) = [1 0 en otro caso ||

A:

Q: 1. Calculate the Laplace transform of the function 2. 1-t when 0 <t < 1 when 2 <t<3 everywhere else…

A:

Q: Find the Laplace Transform of: e-2 -2t sin2t + e3tt2

A:

Q: 53. If Fs (n) is the Fourier sine transform of f (x) on 0<x<1, show that 2nt F.[f" (x)] = [f (0) –…

A:

Q: 3. Find the Fourier transform of the following: f(t) = {te-t -1<t<0 elsewhere

A: We have to find the Fourier transform of the given function.

Q: ) Determine the complex exponential Fourier transform for the following periodic signal shown. x(t)…

A: To find : Complex exponential Fourier transform for given signal

Q: 8. Find the function whose Fourier sine transform is the following function. S[u] - 2 0 x = [1, 2],…

A:

Q: WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS: F(t) = for…

A:

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

A:

Q: 2s3+ 4s²+1 F(s) = (s²+ 2s+17)(s²+ 4s+20)

A:

Q: What is the Fourier transform of the following e-j10ntx(t)

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-jktf(t)dt,…

Q: Determine the Fourier transform of e cl, with ca positive number.

A:

Q: Find the Fourier transform for x[t] = at*u[t], |a| &lt; 1

A: Given function is,

Q: determine the inverse Laplace transform of F.

A:

Q: Obtain the Fourier Series expansion of the periodic function f(t): Then, draw the periodic function.…

A:

Q: 1 Find the inverse Laplace transform of X(s) = given ROC: -1<o<3. (s + 1)(s – 3) x(t) =

A:

Q: Find the Laplace transform of the below function 1-1 01 1 1-t2 1

A: The given function is  f(x) = 1-t2  0≤t≤10              t&gt;1 We know that the Laplace…

Q: Determine the inverse Laplace 2s +3 transform of (s+4)

A:

Q: (2) Find Inverse Laplace transform for; 1 1-F(s)= s(s +1) 3 2-F(s)=- s' +4

A: We need to find the inverse Laplace transform. Part(1) We have 1ss+1 We use partial decomposition.…

Q: (c) Compute the inverse Fourier transform for the function ={ Is| 4 -s, F(s) 0,

A: The given function is  F(s) =        - s             |s|&lt;= 4         =           0.…

Q: *: Obtain Z-transform for the Followings 1) x(t) = Coswt 2) x(s) (sta)2 3) x(s) = s(s+1)

A: We have to use standard z transforms.

Q: The Laplace transform of th is valid for O s>n O s>0

A: The Laplace transform of tn is        Ltn=n!sn+1, for s&gt;0

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

A: 2-2e^(-t)

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: Determine the Laplace transform of the given generalized function. (3*e^(3t))(delta(t-5))

A:

Q: f(x) = = 1 2 cos: X x

A:

Q: (2) Compute the Fourier integral representation for the function f(x) = x² for 0< I< 27.

A:

Q: 4- Find the Fourier sine and cosine transform of: e-x 0 <x < a F(t) = otherwise

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: Find the exponential transform of the function {1, Pi/2<x<pi. and 0, otherwise} and write f(x) as a…

A:

Q: 7 Find the inverse Laplace transform of using Residue theorem. (s+3)(s²+5s+6)

A:

Q: find the inverse laplace transform of; a)  (S^2+1)/S(S-1)(S+1)(S-2)

A:

Q: find the Fourier expansion of the periodic function shown below f(x) = = sinx - n< x < T

A: we have to find the Fourier series of

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

A:

Q: 2. Compute the Fourier Transform of f(x) = e¬ax²

A:

Q: Prove the following continuous time Fourier transform relationship. Continuous Time 2л x(t) = E…

A: Given, xt=∑n=-∞∞δt-nT. Now, xt=∑n=-∞∞δt-nT is a periodic signal with period T. So, converting in…

Q: 3. Find the Fourier transform of f(x) = {1, |x| 1 Also evaluate .00 Sinx dx

A:

Q: 12. Find the Laplace transform of the period function to f(1) = 2n-t <tS2n

A:

Q: Find the inverse Laplace transform of, 1+s 1+s2.

A: we have to find the Inverse Laplace of  1+s1+s2

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:

Q: 4. Use the dilation principle to find the Laplace transform of 1- cos 5t cos t given L{- In g² +1 t

A: We want to find Laplace transform of 1 - cos5tt Given L1 - costt = 12lns2s2+1

Q: 9. Solve the IVP using Laplace transform: x' – x = 2cos5t, with x (0) = = 0.

A: Given equn isx'-x=2 cos 5t with x0=0taking both the side laplace transformation we get…

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

A: the Fourier transform of f(ax) as a function of the Fourier transform of f(x) is known as change of…