I really need help with Part B of this question
I really need help with Part B of this question Problem 2: a) If F(a) is...
Answers are: 9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of iw 4 + 9 w2 9 w2 (b) The function f(t) satisfies the integral equation: OO -4u Н(u) du + 6sgn(t) е З, f(t) 0- ft - u) е" = 4 e -OO Find the Fourier transform of the function f(t) and hence find the solution f(t) 7 "(1-)н, (b) Transform the equation by using the convolution Theorem:...
(b) The signal f(t) is shown in the figure below 3 2 f(t) _ 0 I 1 -4 -3 -2 -1 0 1 2 3 4 5 6 7 t and is given by 21 (1) + 3A (132), where A is the triangle function defined as 10-{ It a It <a It > a 0 Write the Fourier transform F [A(t)] (s) of f(t) exploiting the fact that FA(t)](s) = sinc-(s) where sin(TTS) sinc(s) ITS and the theorem for...
(8). The one dimensional neutron diffusion equation with a (plane) source at x-0 is d'f(x) n (2) +002 f (x)-00(x) dx where f(x) is the flux of neutrons (f(x)→0 as x→±o), Q δ (x) is the (plane) source at x-0 (5(x) is the Dirac delta function), and o is a constant. This problem involves finding the solution to this equation using Fourier Transforms. You may use the formulas derived in class for the Fourier Transform of derivatives, but otherwise compute...
The fourier Transform of a dirac delta function, 8(t) is: (a) X(f) = 11-20,00)(f) (b) X(f) = 8(f) (c) X(f) = 0 (d) None of the Above
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
where M=7 322-M2 4) Find the inverse - transform of F(z) = (2-1)(2-2M)' (15 marks) 0 t<-M/2 M <t< - 5) Show that the Fourier transform of function f(t) sin 7 s (10 marks) au 6) Show that u = ln(x2 + xy + y2) satisfies the partial differential equation x x ди +y 2. (7 marks) au 7) Solve the partial differential equation = e-cos(x) where at du x = 0, at =tet ax at and t = 0,...
Need solution pls... 2. Find the Fourier transform of f() = {6 1 – 12 \t <1 1t| > 1 Use the first shift theorem to deduce the Fourier transforms of e3jt (1-12) 11 <1 (a) g(t) 1t| > 1 {" (b)h() = {**"1 –1) "151 It| > 1 Answer: 63 4 cos o 4 sin o + -62 -4 cos(w – 3) (a) (0 – 3)2 -4 cos(w – j) (b) (w – j)2 + 4 sin(0 – 3)...
For full credit, you must show all work and box answers 1. If functions f and g are piecewise continuous on the interval [0, oo), then the convolution of f and g is a function defined by the integral The Convolution Theorem (theorem 7.4.2 in your book and formula 6 in your table) states: If j(t) and g) are piecewise continuous on [0, oo) and of exponential order, then We are going to use convolution to solve y"-y,-t-e-,, y(0)-0, y'(0)-0....
Question: Required formulae from Question 4: Other formulae: 8. (a) If f(t) /2 show thattf. Use formulae from Question 4 to show thatpwF (the same equation in the transformed variables). It follows that F(w) - Ae-/2; evaluate the arbitrary constant A by putting w 0. Deduce that F(w) f(w) (i.e., this function is equal to its Fourier transform) (b)" Using Question 4(i), show that Fe-t2/202)-ơe_ơ2w2/2. There is a general theorem that the more widely spread out a function is, the...
hi i need help with the following & can you please put solutions in syntax form 1). f(t) satisfies the integral equation: Find the solution of the integral equation using Fourier transforms. Your answer should be expressed as a function of t using the correct syntax. f(t) = 2). A signal f(t) has a Fourier transform given by Use Parseval's theorem to find the total energy content of the signal. Your answer can be expressed as a number accurate to...