The smoothness of a period deter-mines the way the magnitude line spectrum decays. Consider the following periodic
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The smoothness of a period deter-mines the way the magnitude line spectrum decays. Consider the following periodic signals x(t) and y(t) both of fundamental period T0 = 2sec., and with a period from 0 ≤ t ≤ T0 equal to
x1(t) = u(t) − u(t − 1), y1(t) = r(t) − 2r(t − 1) + r(t − 2).
Find the Fourier series coefficients of x(t) and y(t) and use MATLAB to plot their magnitude line spectrum for k = 0, ±1, ±2, ... ±20. Determine which of these spectra decays faster and how it relates to the smoothness of the period. (To see this relate |Xk|to the corresponding |Yk|.)
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The signal xt with a period x 1 t ut ut 1 period T 0 2 0 has so that its Fouri...View the full answer
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