Consider the following problems related to periodicity and Fourier series:

(a) For the signals

x₁(t) = 1 + cos(2Ï€ t) ˆ’ cos(6Ï€ t),

x₂(t) = 1 + cos(2Ï€ t) ˆ’ cos(6t)       ˆ’ˆž < t < ˆž

i. Determine which of these signals is periodic and the corresponding fundamental period.

ii. For the periodic signal, find a trigonometric Fourier series representation.

iii. Indicate why it is not possible to obtain a trigonometric Fourier series representation for the non-periodic signal.

(b) Consider the signal

i. Is this signal periodic? If so, what is its fundamental period T₀?

ii. Find the Fourier series of x(t).

Transcribed Image Text:

sin(2t + 1) x(t) sin(t)