Question

For a fullwave rectified sine wave shown in figure below:

Fourier series coefficient $|C_1|$ is

• A. 0.21

Answer 1

The correct option is A 0.21

Time period of the signal is T = 1

Signal signal $x\left(t\right)=\sin \pi tfor0\le t\le 1$

$C_0=\frac{1}{T}{\int }_0^{1}x\left(t\right)dt={\int }_0^1\sin \pi tdt$

$C_0=\frac{2}{\pi }$

$C_n=\frac{1}{T}{\int }_0^{1}x\left(t\right)e^{-jd\omega t}dt=\frac{1}{T}{\int }_0^1\sin \pi t{e}^{-j2\pi nt}dt$

$=\frac{1}{2j}[{\int }_0^1{e}^{j\pi t}{e}^{-j2\pi nt}-{\int }_0^1{e}^{-j\pi t}{e}^{-2j\pi nt}dt]$

$=\frac{1}{2j}[\frac{-2}{j(1-2n)\pi }-\frac{2}{j(1+2n)\pi }]$

$C_n=\frac{2}{(1-4n^2)\pi }$

$|C_1|=\frac{2}{3\pi }=0.212$