Question

What is the fourier convergence theorem?

(a) Fourier series approximation oscillates about the numerical value

(b) Fourier coefficients converge near a discontinued point

(c) In any finite interval, x (t) is of unbounded variation

(d) In majority finite interval, x(t) is of unbounded variation

This question was posed to me during a job interview.

This interesting question is from Gibb’s Phenomena, Convergence of Fourier Series topic in chapter Fourier Series of Signals and Systems

Answer 1

Correct answer is (a) Fourier series approximation oscillates about the numerical value

For explanation: According to fourier convergence theorem, near a point of discontinuity the fourier series approximation oscillates about the numerical value it should achieve. This is valid in an infinite series limit.