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 evaluate

Q: What is the Fourier transform of the function 4 cos(5t) on the interval [-x, a]| Select one: O a. 4…

A: Here we have to find the Fourier transformation of the function x(t) = 4 cos (5t) Using the formula:…

Q: Find Fourier transform of i 1x ka f(x) = 1₁ 0 Ixl ya Then find: 05- Sin Pa Cospx dp , P of M.H sin…

A: Fourier transform of the function and deduce the given definite Integral

Q: 5. Determine the Laplace transform of tet sin? t using any methods introduced in the module.

A: Given ft=te4tsin2t

Q: Find the Fourier sine expansion of f(x)=x² (3L– 2x) on [0, L].

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find the Fourier transform of f if (e* jkax > 0 * ikax<0 Note : jika = if

A:

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: The best approximation of f(x) = cos(8 + x) by a Fourier polynomial of degree 1 is

A: The Fourier Polynomial of degree n is Fn(x)=a0 + ∑k=1nakcos(kx) +∑k=1nbksin(kx). Then, the Fourier…

Q: IS kept contact with ice at 0°C' and if initially the rod is submerged in hot water at 100°C. Use…

A:

Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

A:

Q: Find the finite Fourier Cosine Transform of f(x) = 1- in (0, x).

A:

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: Calculate the Fourier transform of f(x) = (1 – 2)e-(z-a)?/2_

A: Calculate Fourier transform of e-x-a2/2:  ∫-∞∞e-x-a2/2·e-jωxdx=e-jaω∫-∞∞e-x-a2/2·e-jωx-adx-a…

Q: Q.3. Find the fourier expansion for the function whose definition 一T х, (x) = 0, くxく- 2 <x< -

A: Given that function we have to find the Fourier series of that function.

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: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

A:

Q: 5. The fourier transform of the function f(x)=eI, is 2 4- w? O b. 2 w? -4 4 С. w? - 4 Od. 4+w? 4.

A:

Q: 2. Use Laplace transform properties to compute 2.1. {f(1 – e")du} -

A:

Q: Find the Fourier Cosine transform of e-t² Hint: Use the integral formula √π So e-u² du = 2

A:

Q: Find the Fourier sine and cosine transform of f (x), if х, 0 2

A: Fourier Cosine transform and Fourier sine transform

Q: Determine the Laplace Transform of e1- c cos /7t + sin V5 4. sin /5 12s-7 s2+7 none of the choices 4…

A:

Q: 27. Explain why this function does or does not have a Fourier transform. If it does, compute its…

A: Consider the given function. fx=0,        x&gt;1excosx,x&lt;1 Fourier transformation is defined as.…

Q: Find the Fourier transform of the following signals using sine and cosine integral. x(t) 1 -1 -1 1…

A: Given function from the graph is: fx=x+1 Fourier transform of a function fx is:…

Q: (1, |x| 15 Q.1 Find the Fourier transform of f (x) defined by f (x) = %3D Hence evaluate S: sins…

A:

Q: Compute the Fourier Transform of the following function (3 , –n < x < o (1 , 0<x< TI f(x) =

A:

Q: (sin³r} = {1-co52} and find the Laplace transform: S 1 2 -3²+2 S 1 2 O 1(1 1/1 S +4 +2

A: Given formula of sin^2 t is in terms of cos2t. For detailed solution, visit step 2.

Q: The Fourier transform of f(t) = -1<t<1 is otherwise O 2sin(w + 2) w +2 O 2sin(w – 2) w - 2 2…

A: Fourier transform of the function

Q: Show that the finite sine transform of , 0 < x < n is (- 1y*'- p

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: Find the z-transform of the following equations: a. 2un + n 2 b. cos(3n) + 2 sin(3n)

A:

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

A:

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: What is the Fourier Transform of f (t) = 3; -2<t< 2 O sin(2w) 0 음sin(w) o žsin(w) o 용sin(2u)

A:

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

A:

Q: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: Find the Z-transform for x(n) shown below * including ROC a(n) = (3)"sin(프n)u(n) |

A: It is given that, x(n)=13nsinπ4nu(n) The convolution property says that,   The z-transform of…

Q: The Laplace transform of L[2 sin 5t sin 4t is s+ (1)2 s2 + (9)2. 2s s2 +(1)2 s2 + (9)2 s2 + (1)2 s2…

A:

Q: Find z-transform for the functions (using properties) 1) x(t) = eat cos (w t)

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Let xfn] be a discrete-time signal whose Fourier transform between -r and r is 4 |w< 4 X(e) = 0, 4…

A: Given Discrete time signal xn whose Fourier transform between -π and π isXejw=4πw2,  w&lt;π40,…

Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

A:

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

A:

Q: x(t) 2 -1 -1 1 -2

A:

Q: Find the z-transform of the following equations: a. 2un+n b. cos(3n) + 2 sin(3n)

A: According to our guidelines I can answer only question no. (a)

Q: Show that d() = ñ[6(w − K) + 6(w + K)] is the Fourier transform of cos (Kt).

A: To prove dw=πδw-k+δw+k is the fourier series of cos(kt)

Q: Compute the coefficient Fourier a, of the { T - r, 0<r<* 0, f(r) =

A: We have to compute Fourier coefficient an.

Q: Find the complex Fourier series coefficients for the signal x(t)= (sin(nwot))5

A:

Q: Find the z-transform of the following equations: b. cos(3n) + 2 sin(3n)

A: We need to find z - transform of , un = cos3n + 2 sin3n That is , zun = zcos3n + 2 sin3n zun =…

Q: Find the inverse z-transform of the following: z|2| sin 3 i. z-15 , z²-(2|2|cos 3)z+|2|2]

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

Q: O Show that the Fourier transform of | 3 -2<1<2 0 otherwise f() = {0 6 sin 20 is given by F (@) =

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