In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform. [1]

In mathematical analysis, Parseval's identity, named after Marc-Antoine Parseval, is a fundamental result on the summability of the Fourier series of a function. The identity asserts the equality of the energy of a periodic signal (given as the integral of the squared amplitude of the signal) and the energy of its frequency domain ...

vector. The following theorem is called the Parseval’s identity. It is the Pythagoras theorem for Fourier series. Theorem: jjfjj 2= a 0 + X1 n=1 a2 n + b 2 n:

在 數學 中， 帕塞瓦爾定理 （或稱 帕塞瓦爾等式），經常指「傅立葉轉換 是 么正算符」這一結論；簡而言之，就是說函數平方的和（或積分）等於其傅立葉轉換式平方之和（或者積分）。 這個定理產生於法國數學家 馬克-安托萬·帕塞瓦爾 （Marc-Antoine Parseval）在1799年所得到的一個有關 級數 的定理，該定理隨後被應用於 傅立葉級數。 它也被稱為 瑞利能量定理 或 瑞利恆等式，以物理學家 瑞利 命名。 雖說 帕塞瓦爾定理 這一術語常用來描述 任何 傅立葉轉換的么正性，尤 …

在 数学 中， 帕塞瓦尔定理 （或称 帕塞瓦尔等式），经常指“ 傅里叶转换 是 幺正算符 ”这一结论；简而言之，就是说函数平方的和（或积分）等于其傅里叶转换式平方之和（或者积分）。 这个定理产生于法國數學家 马克-安托万·帕塞瓦尔 （Marc-Antoine Parseval）在1799年所得到的一个有关 级数 的定理，该定理随后被应用于 傅里叶级数。 它也被称为 瑞利能量定理 或 瑞利恒等式，以物理学家 瑞利 命名。 虽说 帕塞瓦尔定理 这一术语常用来描述 任何 傅里叶转换的幺正性，尤 …

Apr 18, 2023 · Parseval’s theorem states that the integral of the square of its function is equal to the square of the function’s Fourier components. This article covers the fundamentals of Parseval’s theorem and its proof. Learn when to apply the theorem and how to apply it given a particular function.

5 days ago · If a function has a Fourier series given by f(x)=1/2a_0+sum_(n=1)^inftya_ncos(nx)+sum_(n=1)^inftyb_nsin(nx), (1) then Bessel's inequality becomes an equality known as Parseval's theorem. From (1), (2) Integrating (3) so 1/piint_(-pi)^pi[f(x)]^2dx=1/2a_0^2+sum_(n=1)^infty(a_n^2+b_n^2).

Marc-Antoine Parseval des Chênes (27 April 1755 – 16 August 1836) was a French mathematician, most famous for what is now known as Parseval's theorem, which showed that the Fourier transform is unitary.

There exists a linear operator f 7!f^ on L. 2([0;1]) that coincides with the Fourier transform on bounded L. 1functions and satis es the identity (f;^ g^) = 2ˇ(f;g) for all f;g2L. 2([0;1]). This identity, or its special case jf^j2= 2ˇjfj2, is known as Parseval’s identity.

Sep 11, 2020 · Parseval’s theorem, also known as Plancherel’s theorem or Rayleigh’s energy theorem, is a fundamental result in Fourier analysis and signal processing. It relates the energy (or power) of a function (or signal) to the energy (or power) of its Fourier transform.