Consider the following problems related to the exponential Fourier series.

(a) The exponential Fourier series of a periodic signal x(t)of fundamental period T₀ is

i. Determine the value of the fundamental period T₀.

ii. What is the average or dc value of x(t)?

iii. Is x(t)even, odd, or neither even nor odd function of time?

iv. One of the frequency components of x(t)is expressed as Acos(3Ï€ t). What is A?

(b) A train of pulses x(t), having a period

x₁(t) = u(t) ˆ’ 2u(t ˆ’ Ï€) + u(t ˆ’ 2Ï€) has a Fourier series

Figure out how to use these results to find an expression for π. Obtain an approximation of π using the first three terms of the Fourier series.

Transcribed Image Text:

3 3 eikri x(t) = >) Σ 4+ (kл)* k=-00 4 x(t) sin((2k – 1)t) k=1 2k – 1