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개념 기사 기사 작성법
내가 아는 수학개념을 쉽게 설명해주세요!
[개념 기사] 음파를 분해한다고? 푸리에급수
유한의끝도못본남자 2020.03.18 08:06

여러분, 소리는 종파라는것을 들었죠? 하지만  경우에따라 횡파로 변환할때도있습니다

하지만 주변에는 잡음이 많이섞여 바로 녹음하면 뾰족점이있는 미분불가능형태로 표출됩니다

하지만 이것을 주파수를 잡거나, 연구용으로 써야한다면 정말로 골치가 아프겠죠?

그러려면 이를 횡파의 합으로 분해하여야합니다

그래서 소개해드릴것은

푸리에급수란

어떤 함수를 삼각함수의 가중치로 분해한함수입니다

일단 대학생분들의 설명으로하겠습니다

이과가아닌이상

일반인은 이걸 이해하지못합니다

{\displaystyle f(x)=f(x+T)}일때(T는주기)

{\displaystyle \int _{a}^{b}|f|^{2}\,dx}가 가능하다고하자

이때 f의 푸리에계수g_n

{\displaystyle g_{n}={\frac {1}{T}}\int _{t_{0}}^{t_{0}+T}\exp(-{\frac {2n\pi {i}x}{T}})f(x)\,dx,\quad t_{0}\in \mathbb {R} .}

라고 정의한다

임의의 x\in\mathbb R에 대하여, 다음 식이 성립하지 않는x의 집합은르베그측도 0을 가진다.

{\displaystyle f(x)=\sum _{n=-\infty }^{\infty }g_{n}\exp({\frac {2n\pi {i}x}{T}})}.

예, 한번에 알아들으면 천재입니다

 

이거는 "주기함수를 삼각함수n개로 분해한 공식이다"를 아주아주 길게 풀어쓴것입니다

예제로

엔트리에 "delta"라는 유저의 부계정이만든작품인

http://naver.me/Go6fKVTU

가있습니다(허락도받았습니다)

푸리에급수, 정말신기하지않나요?

잡음까지계산하여 소리로 분해하다니...

수학의 세계는 역시 광활합니다

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