7. a) Find the Fourier transform of the function y = e-al=| (a > 0). b) Find the Fourier transform of the function y = (a > 0). (Hint: Use a). r2 + a?

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: (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: (11) The Fourier cosine transform of the function f(x) e; x>0, is

A:

Q: 4 Find the Fourier Transform of f(x) where S(x) =e*

A:

Q: Find the Fourier transform of ƒ (t) = 2 for -T≤t≤0 2 for 0 ≤ t ≤T

A: We have to solve given problems:

Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

A: The given problem is to find the Fourier sine transform of the given function, we have a general…

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: 3) Find the Fourier transform of the following signals L. x(t) x(t) + 3 + 2 -2 2 -1 -1 1 -2 using…

A:

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

A:

Q: Q4) Find Z transform for the functions 3) x(t) = te-at

A:

Q: Find the Z transform of [cos (ax), x20 f(x)=: 0, x<0

A: Given, fx=cosax,x≥00,x&lt;0 As we know that, Ze-ax=1+e-aτ+e-2τz-2+...=11-e-aτz-1=zz-e-aτ

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

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

A:

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: 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: 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: 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: 6. Suppose you are working out the Laplace transform of f(t) = e'+4t using the definition of the…

A: Answer

Q: 1. f(t) = cos(6t)

A:

Q: b) Find the Fourier sine transform of f(x) = 12π, 0 < x < 6π

A: Fourier coefficients represent the amplitude of each harmonically-related sinusoid present in the…

Q: Use the Fourier transform method to solve du k at ax2-Yu, -o∞ 0 u(x, 0) = f(x).

A:

Q: Find the fourier sine transform of a) f(x) = exp(-ar) and deduce sin(sz) -ds = 2+a² -az b) f(x)= re'…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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

A:

Q: 2 What is the Laplace transform of 2cos t?

A:

Q: Find the Fourier transform for S(2)%3D sin a, 2 0.

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: -2 20(x+2y?

A:

Q: Q2:Find the inverse Laplace transform of e-2s F (s) s2 – 2s – 3 - -

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

Q: Q.5. Determine the Discrete-Time Fourier Transform and z-Transform of the signal given below. x(n) =…

A: Calculate DTFT: XNk=∑n=-∞∞xne-i2πkNn           =∑n=-∞∞3nu-n-1e-i2πkNn           =∑n=-∞-13ne-i2πkNn…

Q: (a) By making appropriate use of Jordan's lemma, find the Fourier transform of T³ f(x) = (x² + 1)²*

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: 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: 3.44. Find the Laplace transform of x() given by otherwise

A: Given xt=1t1≤t≤t20otherwise

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

A:

Q: 4. Calculate Fourier transform : for a >0 r(t) = e-a'u(1)

A:

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

A:

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

A:

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: 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: 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…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.