Question

What is the sum of the series at a point when the signal is discontinuous?

(a) Average of the previous limits

(b) Previous limits are considered

(c) Future limits are added

(d) Average of left hand limit and right hand limit are taken

The question was asked in an international level competition.

This interesting question is from Dirichlet’s Conditions topic in division Fourier Series of Signals and Systems

Answer 1

Right option is (d) Average of left hand limit and right hand limit are taken

The best I can explain: If the signal is discontinuous at a point t, then an average of left hand limit and right hand limit of the signal x(t) are taken.

That is x(t) = ½[ x(t+)+x(t-)].