Question

For fourier series of piecewise function , do we take period of whole thing, just each pieces?

Answer 1

i wish i knew it!! it was have been a privilege helping you :P

Answer 2

f(x) = x 0<x<Pi
x+pi -pi<x<0

Answer 3

\[a_0=\frac{1}{\pi }\int_{-\pi }^0 (x+\pi ) \, dx+\int_0^{\pi } x \, dx\]

Answer 4

i should probably keep quiet because i know next to nothing about this, but i recall that in example i have seen you perform the transform on each piece separately
http://www.stat.ucla.edu/~dinov/courses_students.dir/04/Spring/Stat233.dir/STAT233_notes.dir/FFT.html

Answer 5

Let me try it

Answer 6

\[a_n=0\]

Answer 7

\[b_n=-\frac{1+(-1)^n}{n}\]

Answer 8

I got
\[\frac{\text{Pi}}{2}+\sum _{n=1}^{\infty } b_n\text{Sin}[n t]\]