use Sine transform to solve this.
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Use the time-shifting property and the result for the Fourier Transform of a cosine function to calculate the Fourier Transform of a sine function. Show that the phase response at positive and negative frequencies matches the expected result for a sine function.
Problem 6 [30 points Use Fourier transform to solve the heat equation U = Ura -o0<x< t> 0 subject to the initial condition -1, 1 u(x,0) = -1 < x < 0 0 < x <1 x € (-00, -1) U (1,00)
Problem 5: Use the duality property of the Fourier transform to find the Fourier transform of x(t) = sinc(Wt). Please solve clearly, not copy paste old solutions.
This is a Fourier Analysis Question TO SOLVE: Exercise 31.6 Compute the Fourier transform of pv(-). Use this to com pute the Fourier transform of signx) FOR REFERENCE, DO NOT SOLVE TO SOLVE: Exercise 31.6 Compute the Fourier transform of pv(-). Use this to com pute the Fourier transform of signx) FOR REFERENCE, DO NOT SOLVE
fourier analysis 2. (a) Find the Fourier sine transform of b) Write f(x) as an inverse sine transform Hint: Don't directly calculate F,[f (x)(w). Begin with showing the representation sin wxdw. x >0 ㄧㄨ and then interchanging x and w in the representation. Now look at it carefully, what does the equation tell you?
Integral Transform Find the Fourier Sine transform of the following functions: (a) F {e-a2} (b) Fo{qz1a2}
1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and initial condition; denote this function U(w, t). (b) Find u u(z, t) by taking the inverse transform of the U(w, t) you found in part (a). 1. Use the Fourier Transform to solve the following problem with W1 21 (a) Find the Fourier Transform of u by applying F to the equation and...
Problem 6 [5ptsl Find the Fourier Transform of the pulses shown below. More specifically, find the Fourier transform of the half-cosine pulse shown in (a), the half-sine pulse shown in (b), the negative half- sine pulse shown in (c) and the single sine pulse shown in (d). g(Ct) g(t) 0 T 0 g(t) g(t) 0 T
Solve using the Fourier Transform Method. 2.24) Solve Laplace's equation in a strip using Fourier transforms: u,)+ e-lal, u(x, L) = 0, u(x, y)0 as0o.
Fourier transform of a rectangular pulse is a: Tan function Cosine function Sinc function Sine function Question 28 1 pts Every periodic function can be expressed as a linear combination of: Sine and cosine functions Sine functions Logarithmic functions None of the above