Find the limiting value of the first local minimum

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Reference no: EM131051366

The purpose of this problem is to explore the Gibbs phenomenon. This phenomenon occurs as a result of truncating the Fourier series of a discontinuous function. Examine, for example, this henomenon in detail for the function y3(x) given in P8. The function under consideration is given analytically by:

a. Find the value where the truncated Fourier series overshoots the value of 0.5. (Answer: The limiting value of this first maximum is 0.58949).

b. Find the limiting value of the first local minimum. (Answer: The limiting value of this first minimum is 0.45142).

c. Derive, from first principles, the answers to parts (a) and (b). (Hint: Look up in a standard integral table the sine integral function.)

NOTE An important goal of filter theory is to find methods to smooth these kinds of oscillations.

Reference no: EM131051366

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