The Fourier transform of a function f (x) is defined as: f (w) = Lf(x)e¬iwx dx Similarly, the inverse Fourier transform of a function f (x) whose Fourier transform is known is found as: f (x) Lo f (w) e-iwx dw So, find the Fourier transform f (w) for a> 0 of the function given below, and using this result, calculate the inverse Fourier transform to verify the form f (x) given to you: for x > 0 for x < 0 -ax e f(x) = {

Q: (a) Find the Fourier series of the function f(x) = x²,0 ≤ x < L with period L. (b) Use the previous…

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Q: (a) Show that the transformation Q = p + iaq, P = (p − iaq) / (2ia) is canonical and find a…

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Q: There is a pendulum in an elevator going down with constant velocity v. Assuming the mass of the…

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Q: Find the Z Transform for the following function: f(t)=e^(-ct) cos⁡(2πt/3)u(t)

A: To find the Z-transform of the given function, we can first write the function in terms of the…

Q: Suppose we know exactly two arbitrary distributions p(x|&#969;i) and priors P(&#969;i) in a…

A: (a) Introduction: Bayes' Theorem is a simple mathematical formula used for calculating conditional…

Q: Consider a thin hoop of mass (1.420 ± 0.001) kg and radius  (0.250 ± 0.002) m. The moment of inertia…

A: Given: M=1.420 kgδM = 0.001 kgR = 0.250 mδR =0.002 m

Q: Qualitatively sketch log(Ids) vs. Vg(assume Vds = Vdd) for the following Please pay attention…

A: Please find the sketch for log(Ids) vs. Vg

Q: (a) Write the wave function ų(x)= 4o•e'kx in the form w(x) = a + ib, where a and b are real…

A: a) The wave function is given by ψ(x)=ψ0 eikx        =ψ0( cos kx+i sin kx)        =ψ0 cos kx+iψ0 sin…

Q: Find the Fourier transform of rect(t/4). (a) sinc(w) (b) sinc(w) (c) sinc(2w) (d) 2 sinc(2w)

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Q: If f(x) is a function with period 2L = 4 given on the interval (−2, 2) with (in the picture) (a)…

A: Given: f(x)=2+x,    -2&lt;x&lt;02-x,       0&lt;x&lt;2 Calculation: First we will calculate…

Q: Problem 1: Use the Taylor expansion of the error function to estimate erf(0.1). How far off is that…

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Q: Prove that the expression e*/(1+ e*)² is an even function of x.

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Q: The eigenvalues a

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Q: Consider a thin hoop of mass (1.420 ± 0.001) kg and radius  (0.250 ± 0.002) m. The moment of inertia…

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Q: 8. A periodic function is defined as follows: f(t) = { (3 for-1<t <0 for 0 < t < 1 16 i. ii. iii.…

A: We have given a periodic function of time period 2 then we can express by the Fourier series as…