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X(ja)= 3 2.148(N12), k=-0 2. A square wave x(t) = 1, lok To I 4 K...
4. (4.5 pts) Consider a 3D electromagnetic plane wave in vacuum, described in usual complex form by, (r, t) = Ēelkr-wt) in which ło = Epein/2y. Where k = -kx is the wave vector (assume k > 0) and w > 0 is the angular frequency. As usual, the real field is Er, t) = ReLEr, t)] (a) In which direction is the wave propagating? In terms of the given values k and w, what is the speed, wavelength, and...
Problem 4 Let x(t) be a continuous time signal whose Fourier transform has the property that Xe(ja)0 for lal 2 2,000. A discrete time signal aIn]x(n(0.5x 10-3)) is obtained. For each of the following constra ints on Xa(e/n), the Fourier transform of xaln], determine the coresponding constraint on Xe(ja) a) X(en) is real b) The maximum value of X4 (ea) over all is 1 c) Xa(ea)= Xa(e/ a-) Problem 4 Let x(t) be a continuous time signal whose Fourier transform...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
ffset sawtooth wave x(t). 1-7 A binary signal x(t) = 0 for t <0. For posi- tive time, x(t) toggles between one and zero as follows: one for 1 second, zero for 1 second, one for 1 second, zero for 2 seconds, one for 1 1-11 second, zero for 3 seconds, and so forth. That is, the "on" time is always one second but the “off” time successively increases by one sec- ond between each toggle. A portion of x(t)...
Problem 2: Consider the following periodic signals x(t), a square wave, and yt), a saw tooth 2T The pulses width of x(t) т, wave. Both have the same amplitude A and the same frequency - equal T. The duty-cycle of x(t) is defined as d- T. -A From tables of Fourier Series ofvarious periodic signals, the following formulas are given for your convenience x(= Ad+2Adnacos at+2Ad sna cos 2at+2Adl sun 3xdcos3at яd 2лd Зяd 24 (sin a 1 sin 2asin3ajain...
Question 4 (2+4+4+1+4 = 15 marks) Consider the function y = 4 sin (2x-π) for-r below to sketch the graph of y. x < π. Follow the steps (a) State the amplitude and period in the graph of this function 4 sin (22-9 ) for-r (b) Solve y π to find the horizontal intercepts x (a-intercepts) of the function. (c) Find the values of x for-π π for which the maximum. and the x minimum values of the function occur...
Consider the signal 2, defined for allt e Ras sin(at) 1<t<4 (t) 0 otherwise. Define the signal y as y(t) = x(4 – t) for allt ER For which value of t does (x+y)(t) assume its maximum value? 3 2 6 none of the other answers 4 0
help on all a), b), and c) please!! 1. A particle in an infinite square well has an initial wave function Alsin sin 4 0 < x < L otherwise s(x, t = 0) 0 (a) Find A so that the wavefunction is normalized. (b) Find '(z,t). (c) Find the expectation value(E) of the energy of ψ(x,t = 0). You may use the result mx n 2 0 1. A particle in an infinite square well has an initial wave...
For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition: For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive real constants. (a) Normalize Y. (b) Determine the expectation values of x and x?. (c) Find the standard deviation of x. Sketch the graph of V', as a function of x, and mark the points (x) + a) and (x) -o to illustrate the sense in which represents the spread" in x. What is the probability that the particle would be found outside this...