Sketch the Fourier transforms of the following functions assuming |w1|> [w2| a. f(t) = [cos(wit) + i sin(@¡t)] - [cos(@zt) + i sin(@2t)] b. f(t) = [cos(wot)]e¬t/T2

Q: Determine the laplace transform of the following functions: 1. sin?t cos²t

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

Q: F(z)=z tan:

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

Q: 5 sin [ -5TT X<ST %3D otherwise

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Q: then prove that i) F, [ƒ (x) cos ax] = [f, (p + a) +f, (p a)] 1 ii) F.[f(x) sin ax] 2 [f. (p + a) –…

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Q: Q: The Fourier representation of a function f(x): f(x) = {-10 V, 10 V, ーTくX x > 0 40 sinx sin3x…

A: Given f(x) = -10v.  When -π &lt; x &lt; 0              = 10v when 0 &lt; x &lt; π.   Graph of this…

Q: 8 The inverse Laplace transform of the function is sin(3t) (A) t – 3 sinh(3t) (B) t- 3 sin(3t) (C)…

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Q: cos x, 0 a

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Q: f(x) cos (at) if t 20 %3D 0 if t<0

A: Given: f(x)=cos αt if t≥0o if t&lt;0

Q: 2) Find the Fourier transforms of: a) b) f(x) = cos(ax), where a > 0. f(x) = x² cos(ax) + x sin(ax),…

A: Since the given problem has multiple sub parts, as per our company guidelines we will solve only the…

Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: Compute the fourier transform of f(x) = e -│x│ Sin2πx , sketch f and its fourier transform , x in R

A: Given function is, fx=e-xsin2πx;x∈ℝ. Graph of f(x) is given by,

Q: cos x, 0a

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Q: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x&lt;a0,x&lt;aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

Q: Q3// Find the value of sin лz²+ сos лZ² $c dz (z-1)(z-2) Where C is a rectangular with vertices at…

A: As per the question first we have to evaluate a conture integral, then we have to find the laplace…

Q: -t cos(3t

A: To solve this problem, we  use the  result of laplace transformation.

Q: f(d) = 2e+d[2 sin(4d) cos(2d) – 2 sin(2d) cos(4d)]

A: The given problem is to find the Laplace transform of the given function, we can use basic…

Q: State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms…

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Q: If v(r, y) is a harmonic conjugate of a harmonic function u(x, y) show that the function g(r, y) =…

A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

Q: Find Fourier transform for : A) f(t) = e-3t cos² (3t) B) f(t) = te tu(t - 3)

A: (A)Given f(t)=e−3tcos2⁡(3t).Now, we'll find the Fourier transforms for individual terms.The Fourier…

Q: Determine the Z-transforms of the following expressions (ii) (cos+isin)"

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Q: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

A: As per the question we are given the Fourier transform of a function f(x) as f̂(p) From that we have…

Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: Find the Fourier transform of the following function. f(t) = sin2t [H(t+1) - H(t-1)]

A: Given : Function : ft = sin 2t Ht + 1 - Ht - 1   To find : Fourier transform of the given function.

Q: 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…

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Q: 1. Find the forier tansform of f(t) = 8(t) + 2e-3lt| %3D

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

Q: Q1) a) Find L[ (k - ht)².t²] RI Find the Laplace transform of: f (t)= et, cos² (3t)

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Q: Inverse Laplace transform of s2+9 is given by O cosh(3t) O cos(9t) O cos(3t) O sin(3t)

A: Find the inverse Laplace transform of ss2+9 we know that L-1ss2+a2=cosat

Q: f(x) = (sinx if 0 π

A: This is a question of Fourier Analysis.

Q: 2. Find the Fourier transform of f(t) defined by: -5. -T st<0 0<tST 0 Elsewhere f() = 5. where T is…

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Q: .2 TX e cos(x)

A: Given, fx=e-πx2cosx ∴ℱfx=f~p=12π∫-∞∞eipxfxdx⇒ℱe-πx2cosx=12π∫-∞∞eipxe-πx2cosxdx…