A) write a function that calculates the continuous time fourier transform of a periodic signal x (t). syntax: [w, x]- ctft(, x) the outputs to the function are: w = the frequencies in rad/s, and x = the continuous fourier transform of the signal the inputs to the function are: x- one period of the signal x(t), and t the time vector the continuous time fourier transform of a signal x(t) is given by: | x(t)e-jatdt x(a))= b) write a function that calculates the inverse continuous time fourier transform. the inverse continuous-time fourier transform is given by: 2π syntax: x ictft(t, w. x) the output to the function is: the signal x(t) the inputs to the function are: the time vector, w = the frequencies in rad/s, and x = the continuous fourier transform c) test both ofyour functions ctft and ictft with x(t) =sin(t) , where t =-50: 0.1 : 50, and use subplot to plot each of x(c), and the output of icft to verify its accuracy. label all plots and axes appropriately

An charge with mass m and charge q is emitted from the origin, (x,y)=(0,0). a large, flat screen is located at x=l. there is a target on the screen at y position y(h), where y(h) > 0. in this problem, you will examine two different ways that the charge might hit the target. ignore gravity in this problem. 1.assume that the charge is emitted with velocity v(0) in the positive x direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l. 2.now assume that the charge is emitted with velocity v(0) in the positive y direction. between the origin and the screen, the charge travels through a constant electric field pointing in the positive x direction. what should the magnitude e of the electric field be if the charge is to hit the target on the screen? express your answer in terms of m, q, y(h), v(0), and l.