Question

When a continuous function is synthesized by using the first N terms of the fourier series does the gibbs phenomenon occur?

(a) True

(b) False

I had been asked this question at a job interview.

The doubt is from Gibb’s Phenomena, Convergence of Fourier Series topic in chapter Fourier Series of Signals and Systems

Answer 1

Right answer is (b) False

Easiest explanation: The gibbs phenomenon present in a signal x(t), only when there is a jump discontinuity in the signal. When a continuous function is synthesized by using the first N terms of the fourier series, the synthesized function approaches the signal for all t↔∞. No gibbs phenomenon occurs.