4) Find the Fourier transform (FT) of the rectangular pulse signal x(t) analytically by using FT pairs and sketch it in the interval Jw|<.x(t) (Fig. 5-16) defined by a x(1) = P,(t) = 0 (5.135) lel> a a (a)

Q: Use laplace transform to find the initial-value problem of; a) y''-4y'=6e^3t-3e^-t; y(0)=1,…

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Q: Find the Fourier Sine Transform of e-t and hence find the Fourier Cosine Transform of te-t.

A: Fourier sine transform of e-t is ∫0∞e-tsinωtdt. Calculate it:  ∫0∞e-tsinωtdt=∫0∞e-teiωt-e-iωt2idt…

Q: 3. Use the Laplace transform method to solve the initial value problem r = 6x1 + 11r2, r = -4x1 –…

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

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Q: 4. Using the "final value theorem" predict the final value in time for signal having the following…

A: The Final value theorem states that, limt→∞x(t) =lims→0 s X(s)  We have, limt→∞ f(t) = lims→0s F(s)…

Q: A damping system with a negligibly small spring constant is modelled by x"+bx'=aebt with x(0)=0 and…

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Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

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Q: Use a Fourier transform to solve the following initial value problem for the free Schrödinger…

A: Given: Let us consider the given ut=iuxx ; ux,0=e-x2

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: Use laplace transform to solve the initial value problem; a) y''+y=alpha(t-1/2pi)+alpha(t-3/2pi),…

A: Given                     y''+y=α(t-1/2π)+α(t-3/2π),and      y(0)=0,        y'(0)=0…

Q: 4) Consider the square wave function f(x) = { 1, 0 <x<n -1, T < x < 2n a. Find the Fourier series…

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Q: . Find Fourier cosine transform of - and deduce that 2. bx e 1 e V2m log р ға cos px dx

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Q: is de -Idc 0 K f (at) = { 1 de (b) Fourier coefficient, a If ripple-free load current in…

A: As per the question we are given the periodic function f(ωt) and we have to find the Fourier series…

Q: compute the Fourier Transform of the signal given by the relation:  x(t) = [cos(2*pi*t) +…

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

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

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Q: 1. Find the Fourier Coefficients and Fourier Series of the square wave function defined by: 0 if…

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

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Q: 2. Use the Laplace Transform to solve the following system x'= x-5y, y'=-5x+y, x(0)=1, y(0)=1.

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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: 3. Use the Laplace transform method to solve the initial value problem x₁ = 6x₁ + 11x2, x2 = −4x1-…

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Q: Determine continuous time Fourier transform for the given signals. x(t) 1 1, t20 0, t < 0

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Q: 3. Find the Fourier transform 4. Find the Fourier transform of of 6e-ltl of of 1/(1+ t²).

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Q: 1. Below is given the FT-IR (Fourier Transform Infra Red) data of a 1:1 (by weight) mixture of…

A: The regression analysis is done to fit a dataset into an equation. It is provided that P=f(m). Here,…

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

A: Given function is,

Q: 7) Use the Laplace transform method to solve the Volterra integral equation: u(x) =1-x - (x -t u (1…

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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: The Laplace transform of signal xi(t) is shown below. Determine the initial value x(0)

A: Above question is solved.

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

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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: of the function. 4. Find the Fourier transform of of 1/(1+t²).

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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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: 4) Derive an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in…

A: Given:

Q: 1. (a) Given the Z-transform of sinwt and coswt, find the Z-transform of -at sinwt and e-at coswt by…

A: Introduction: Z transformation follows many different properties. These properties are widely used…

Q: 3. Use a Fourier transform to solve the equation d²y dx2 y 0 with initial conditions y(0) = yo and y…

A: Given: d2ydx2-y2=0 To find: Solving the equation by using Fourier transform.

Q: 2. Prove the following properties of Discrete-time Fourier transform (DTFT). DTFT DTFT (a) ifx[n]…

A: Given x[n]⇔DTFTXejω then we have to show x[n-n0]⇔DTFTXejωe-jn0ω=Z(ejω) (say) Proof: we have…

Q: Б) у —у +Зу — 5у%3D—-бе-t У () %3 1, у (0) %3D2, у' (0) %3D— 4

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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: Consider the following initial value problem, in which an input of large amplitude and short…

A: The given differential equation is: y''+4π2y=2πδ(t-1) ;              y(0)=0,  y'(0)=0

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

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

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Q: 5. Find the Fourier Transform of the given signal and plot its frequency spectrum. x(t) = 2 e"u(-t)

A: The given signal is defined as x(t) = 2 e3t u(-t).The Fourier transform is defined by F(w) =…

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

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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: 5. Use the Laplace Transform solve the IVP: x' + y = t (4x + y' = 0 x(0) = 1, y(0) = 2

A: Theory : The Laplace transform of a second order linear differential equation : y" +α y' +βy =f(t)…

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

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