Question

What is the polar form of the fourier series?

(a) x(t) = c0 + ∑cncos(nwt+ϕn)

(b) x(t) = c0 + ∑cncos(ϕn)

(c) x(t) = ∑cncos(nwt+ϕn)

(d) x(t) = c0+ ∑cos(nwt+ϕn)

I have been asked this question by my college professor while I was bunking the class.

This is a very interesting question from Fourier Series & Coefficients in section Fourier Series of Signals and Systems

Answer 1

Correct option is (a) x(t) = c0 + ∑cncos(nwt+ϕn)

Easiest explanation: x(t) = c0 + ∑cncos(nwt+ϕn), is the polar form of the fourier  series.

C0=a0 and cn = √a2n+ b2n for n≥1

And ϕn = tan^-1 bn/an  .