For each periodic signal shown below, compute its trigonometric Fourier series and sketch its amplitude and phase spectra (a) -20r 10m 20m 0m -T (b) N (b) -8 -6m -4m -2T 0 2m 4T 6m 8T

A function f(x) is given by (in the picture). Find the Fourier transform of f(x) with hint (in the picture to)

the second hand of a circular clock exhibits simple harmonic motion if the second hand moves continuosly and displacment of the tip of the hand around the circumference of the clock from its starting position (at 12) is measured. On a specific clock, the motion of the second hand causes maximal displacemement of 6pi inches. The second hand completes one revolution of the clock in 60 seconds. Assume the second hand is at 12 on the clock when you begin the modelling process. Determine the amplitude, frequency and period of the second hand of the clock. Write a mathematical model that decribes displacement in inches of the tip of the hand around the circumference of the clock from its starting position as a function of time in seconds. Sketch a graph of the model exhibiting two periods of motion.

Find Fourier coefficients for 0, 1st, and 2nd components of Fourier expansion for periodic rectangular signal represented in the figure.