Question

The equation x(t)=\(a_0+\sum_{k=1}^∞(a_k cos2πkF_0 t – b_k sin2πkF_0 t)\) is the representation of Fourier series.

(a) True

(b) False

I had been asked this question in examination.

I'm obligated to ask this question of Frequency Analysis of Continuous Time Signal in section Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

Correct answer is (a) True

The best I can explain: cos(2πkF0 t+θk) = cos2πkF0 t.cosθk-sin2πkF0 t.sinθk

θk is a constant for a given signal.

So, the other form of Fourier series representation of the signal x(t) is

\(a_0+\sum_{k=1}^∞(a_k cos2πkF_0 t – b_k sin2πkF_0 t)\).