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Consider the following problems related to the exponential Fourier series. (a) The exponential Fourier series of a periodic signal x(t) of funda- 4.7 mental period To is 3 i. Determine the value of the fundamental period To 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(ST) 0- What is A? (b) A train of pulses x(t), having a period XI (t)-u(t) _ 2u(t _ π ) + u(t-2π) has a Fourier series 0O 4 x(t) = π Σ 2k-1 sin((2k-1)t) Figure out how to use these results to find an expression for π. Obtain an approximation oft using the first three terms of the Fourier series. Answers: (a) To 2: x(t) even; A-6/4 + 9π 2); (b) use x(1)=1 or instance.

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