Question

Fourier transform of f(x)= |sin(x)|

Answer 1

over what period?

Answer 2

\[a_0 ={1 \over π} \int_{-π}^π|sin(x)|dx\]\[ ={2 \over π} \int_{0}^π sin(x) dx\]\[={-2 \over π} cos(x)]_0^π dx\]\[={-2 \over π} (-1-1)\]\[=4/π\]

Answer 3

@imranmeah91
the sin function has a period of 2π

Answer 4

\[a_n ={1 \over π} \int_{-π}^π|sin(x)|cos(nxdx\]\[ ={1 \over π} \int_{0}^π 2sin(x)cos(nx) dx\]\[={1 \over π} \int_{0}^π sin((1+n)x)+sin ((1-n)x) dx\]