演習問題

周期関数

${\displaystyle f\left(x\right)=\left\{\begin{array}{cc}-1& \left(-\pi \leqq x<0\right)\\ 1& \left(0\leqq x<\pi \right)\end{array}\right.}$ ，${\displaystyle f\left(x+2\pi \right)=f\left(x\right)}$

のフーリエ級数を求めよ．

周期関数

${\displaystyle f\left(x\right)=\left|x\right|}$   ${\displaystyle \left(-\pi \leqq x\leqq \pi \right)}$，${\displaystyle f\left(x+2\pi \right)=f\left(x\right)}$

のフーリエ級数を求めよ．

周期関数

${\displaystyle f\left(x\right)=\left\{\begin{array}{cc}-1& \left(-1\leqq x<0\right)\\ 2& \left(0\leqq x<1\right)\end{array}\right.}$，${\displaystyle f\left(x+2\right)=f\left(x\right)}$

のフーリエ級数を求めよ．

周期関数

${\displaystyle f\left(x\right)=\left\{\begin{array}{cc}2& \left(-2\leqq x<0\right)\\ 2-x& \left(0\leqq x<2\right)\end{array}\right.}$ ，${\displaystyle f\left(x+4\right)=f\left(x\right)}$

のフーリエ級数を求めよ．

周期関数  ${\displaystyle f\left(x\right)=x}$ ( ${\displaystyle -l\leqq x<l}$  ) ， ${\displaystyle f\left(x\right)=f\left(x+2l\right)}$ のフーリエ級数を求めよ．