A sinusoid x(t) = cos(t) is a band-limited signal with maximum frequency max = 1 (a)

A sinusoid x(t) = cos(t) is a band-limited signal with maximum frequency ­Ω_max = 1

(a) Using Fourier transform properties determine the maximum frequency of x²(t). What sampling period T_s can be used to sample x²(t) without aliasing. Verify your results using trigonometric identities.

(b) Can you generalize the above results to x^N(t), for integer N > 2? Is x^N(t) band-limited for all the given values of N? Consider the case N = 3 and use trigonometric identities to verify the results.