Question

The first two components of trigonometric Fourier series of the given signal is ____________

(a) 0, 4/π

(b) 4/π, 0

(c) 0, -4/π

(d) -4/π, 1

I got this question in unit test.

My doubt is from Trigonometric Fourier Series in chapter Fourier Series of Signals and Systems

Answer 1

The correct choice is (a) 0, 4/π

Explanation: Signal is odd and ω = \(\frac{2π}{t}\) = π

Here, c0 = a0 = 0

So, cn = bn = \(2\int_0^t f(t).sin⁡ωt \,dt\)

∴ c1 = b1 = \(2\int_0^t  sin⁡ωt \,dt\)

= \(\frac{2}{ω}[cos⁡ωt]_0^t\)

= \(-\frac{2}{π}\)[-1-1] = 4/π

So, the first two components are 0, 4/π.