Question

1. Discrete Fourier Analysis. Given the following periodic function a) Find discrete time rot and amplitude y(roi) values for y(t). Find time values t1, t2,...tN with dt 0.2 s over the interval -2.0 to 1.8 s, amplitudes yl, y2, y3,... ,yN. and N. b) Calculate the amplitude YG), using the template excel file from lecture#10 and i I. To check some of your results, some of the calculations are presented as follow: K-3 K-4 K-5 6 0.002.00 0.002.00 0.00 5 -1 0.002.002.00 0.00 15 0.00 1.001.00 0.00 0.001.00 1.00 0.00 SUM Scale Amplitude 1.00 1.38 0.1 0.13764 0.32361

Excel template:

Any help.. I would be so thankful. I don't get this at all...

Answer 1

Given periodic signal is y(t) = { t 0 lesstahnorequalto t < 2s 2 -2 lessthanorequalto to yo t < 0s period = 4sec Now we have to obtain the discrete time signal st = 0.2 y(t) = 2 for - 2 lesstahnorequalto t < 0 y(r.st) = 2 for - 2 lessthanorequalto to to (0.2) < 0 = 2 for - 10 lessthanorequalto to to r < 0 y(r. st) r.st for 0 lesstahnorequalto rst < 2 = r(0.2) for 0 lesstahnorequalto rst < 2 = r(0.2) for 0 lesstahnorequalto r(0.2) < 2 = 0.2r for 0 lesstahnorequalto r < 10 \r\n y(R) = y(r.st) - {2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8} period of describe signal n = 20