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: 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: cos x, 0 a

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Q: Find the Fourier approximation with the specified order of the function on the interval [0, 2π].f…

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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: Let u(x,y)=4x+3x2y−y3. Part (a) Show that u is a harmonic function. Part (b) Find a harmonic…

A: The given problem is to show that the given function u(x,y) is harmonic function and also to find…

Q: cos x, 0a

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Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

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: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

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: 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: 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: f(x) = (sinx if 0 π

A: This is a question of Fourier Analysis.

Q: .2 TX e cos(x)

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

Q: [SK 23. Find the cosine transform of the function off(x), if f(x) = { CoS x, ) a

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Q: Find the Fourier transform of (а) f (г) %—D еxp (-ах?), () f (») — еxp (-а \x),

A: To find the Fourier transform of the below functions. fx=e−ax2 fx=e−ax