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sgn傅立葉 在 [微積] F.T.{d/dt sgn(t)} = jw F.T.{sgn(t)} - 看板Math - 批踢踢實業坊 的推薦與評價


作者JefferyChiu (betta fish)
看板Math
標題[微積] F.T.{d/dt sgn(t)} = jw F.T.{sgn(t)}
時間Wed May 26 01:32:45 2021


已知當函數趨近正負無限大皆為零時，
對函數做微分再做傅立葉轉換，
等於虛數j*omega*(函數做傅利葉轉換)

但如題，sgn(t)趨近正負無限大時，
sgn函數都不為零，
然而為什麼上式卻依然成立？

ps: sgn(t)= 1 ,t>0
-1 ,t<0
-----
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※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 1.165.193.195 (臺灣)
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1621963969.A.61C.html
※ 編輯: JefferyChiu (1.165.193.195 臺灣), 05/26/2021 01:39:43
推 Vulpix : 直接查一般的表示式，不相等。05/26 01:49
→ JefferyChiu : 請問樓上是查什麼一般的表示式？05/26 09:51
→ JefferyChiu : 可以讓我看一下嗎？謝謝05/26 09:51
→ JefferyChiu :05/26 09:58
→ JefferyChiu : 我是在算sgn(t)的傅立葉轉換用到那個特性，最後計算05/26 09:59
→ JefferyChiu : 結果也是對的05/26 09:59
→ JefferyChiu :05/26 10:01
→ JefferyChiu : 在yt上也有查到有人用一樣的算法05/26 10:05
→ JefferyChiu : https://youtu.be/GCxCHP6QSNM05/26 10:05
→ JefferyChiu : 在影片6:20處05/26 10:06
推 cplalexandta: 我猜你標題問的是d/dt? 然後這個實際上要用distribu05/26 12:55
→ cplalexandta: tion來做05/26 12:56
推 cplalexandta: 參考這門課的notes: https://see.stanford.edu/Cour05/26 13:00
→ cplalexandta: se/EE26105/26 13:00
推 cplalexandta: 不過如果你是工數要拿來應用的話其實你自己貼的那些05/26 13:04
→ cplalexandta: 影片看熟就好了 不然Fourier Transform如果要講的很05/26 13:04
→ cplalexandta: 嚴謹的話需要有一點分析的基礎05/26 13:04
→ JefferyChiu : 回c大，沒錯，是d/dt，我改一下05/26 13:05
※ 編輯: JefferyChiu (1.165.193.195 臺灣), 05/26/2021 13:06:54
→ JefferyChiu : c大你貼的連結打不開耶05/26 13:08
→ JefferyChiu : 想請問c大，那我便利貼畫紅色底線的做法是對的嗎05/26 13:09
→ JefferyChiu : ？05/26 13:09
※ 編輯: JefferyChiu (1.165.193.195 臺灣), 05/26/2021 13:09:49
推 Vulpix : 其實在你遇到的其他函數夠好的時候，確實會一樣。 05/26 13:20
→ Vulpix : 不過要挑出不同也還是很好挑。你可以分別查wiki。 05/26 13:20
推 wohtp : 貼圖的u又是啥鬼，step function嗎？ 05/26 14:11
→ wohtp : 拉它來救援sgn沒有比較好啊，FT積分照樣不收斂。 05/26 14:11
→ wohtp : 反過來說，如果你知道FT(u)是怎麼搞出來的，你也不 05/26 14:11
→ wohtp : 需要問這個問題了。 05/26 14:11
推 annboy : https://reurl.cc/R0djy9 05/26 14:13
→ annboy : 你想知道比較嚴謹的答案就這篇的一樓 05/26 14:13
→ wohtp : 照貼圖做法就是w加個虛部逼它收斂。不管你怎麼操作 05/26 14:17
→ wohtp : 都好，精神就是要假裝有其他東西讓整個被積函數在無 05/26 14:17
→ wohtp : 限遠處收斂到零，如果沒有就自己放一個進去。 05/26 14:17
推 cplalexandta: 我晚點回你一篇好了 05/27 02:48






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sgn wj. 2. Sa (x) = sin(x) / x sinc function. Page 2. Signals & Systems - Reference Tables. 2 t j p. 1. ) sgn(w. )( tu w wpd j. 1. )( + å. ¥. -¥= n t jn n.

#61. 6 傅立葉轉換範例- 方波函數

單元：連續F轉換-6. 傅立葉轉換範例- 方波函數. 授課老師： 連豊力. Page 2. 單元學習目標與大綱. • 根據傅立葉轉換的公式與關係式. • 計算方波函數的傅立葉轉換 ...

#62. Inverse Fourier Transform Questions and Answers - Sanfoundry

10. Find the inverse Fourier transform of sgn(ω). a) \frac{1}{πt} b) \ ...

#63. 高斯函数的傅里叶变换,sgn函数的傅里叶变换 - 花开半夏

高斯函数的傅里叶变换,sgn函数的傅里叶变换. admin 06-18 17:54 520次浏览. 文章目录序言1、box函数2、gaussian函数注意. 首先生成Box函数和aGaussian函数，进行傅立叶 ...

#64. HELM 24: Fourier Transforms

Write the unit step function in terms of the signum function and hence obtain. F{u(t)}. First express u(t) in terms of sgn(t):. Your solution. Answer. From the ...

#65. B: Laplace and Fourier Transforms - Wiley Online Library

sgn ω. 17. 1 xn. −i. √ π. 2. [. (−iω)n−1. (n − 1)! sgn ω. ] 18. 1 x − a. −i. √ π. 2 e. −iωa sgn ω ... −iaω (−iω)n−1. (n − 1)! sgn ω ...

#66. On Tricomi's relation for the Hilbert transformation

Proof. The result is equivalent to [1, Theorem 65]. As noted earlier, we shall be using the formula for the Fourier transform of Hf ...

#67. 線性系統

Find the Fourier transforms in frequency domain f, not in @ domain, of sgn(t) given. 1 t>0 below as sgn(t) = = (2%). V. 1 <0. 11. (a).

#68. On the parabolic equation sgn (x)|x|p u y −u xx =0 and a ...

Chandrasekharan,Fourier transforms, Annals of Mathematics Studies,19 (1949). Erdélyi - Magnus - Oberhettinger - Tricomi,Tables of integral transforms, McGraw- ...

#69. Bead-Fourier path integral Monte Carlo method applied to ...

We compared the analytically available exact result for the average of sign, 〈Sgn〉, dependence versus temperature with that from our simulations and ...

#70. [SF] Serie di Fourier - INFN Roma

Sviluppare la funzione f(x) = sgn(x) in serie di Fourier nell'intervallo [-π, π]. Scrivere esplicitamente i primi 6 termini non nulli dello sviluppo.

#71. Table of Fourier Transform Pairs - Rose-Hulman

Given the F.T. pair sgn( ). 2 t jω. ⇔. , what is the. Fourier transform of x(t)=1/t? First, modify the given pair to. 2sgn( ) 1.

#72. arXiv:2306.09731v1 [math.AP] 16 Jun 2023

A numerical approach for the Serre-Green-Naghdi (SGN) equations in 2D based on a Fourier spectral method with a Krylov subspace technique is.

#73. part (07): fourier transform (fourier integral) - upatras eclass

This yields the Fourier transform pair: sgn ↔. which is real odd in time, hence imaginary odd in frequency. NOTE: Some authors denote the Fourier ...

#74. Fourier Coefficients - William Chen

sgn (x) cos nx dx = 0, since the integrand is an odd function. On the other hand, for every n ∈ N, we have bn = 1 π ∫ π. −π sgn(x) sin nx dx =.

#75. Table of Fourier Transform Pairs

sgn wj. 2. Page 2. Signals & Systems - Reference Tables. 2 t j p. 1. ) sgn(w. )( tu w wpd j. 1. )( +. Е. ¥. -¥= n t jn n. eF 0 ω. Е. ¥. -¥= - n n n. F. ) (.

#76. hilbert transforms for - sampled data - J-Stage

sgn (w). Various properties of the Hilbert transform are the direct conse- ... The Fourier transform of x(t) is —i sgn (@)X(∞) by definition.

#77. Best of Etherwood: Artist Liquid Drum and Bass Mix #12

Stream Best of Etherwood: Artist Liquid Drum and Bass Mix #12 by U:FOURIER on desktop and mobile. Play over 320 million tracks for free on ...

#78. A Transformada de Fourier

Para encontrar a transformada de Fourier da funç˜ao sgn(t) definimos uma funç˜ao que pode ser aproxi- mada para a funç˜ao sinal da seguinte forma:.

#79. [理工] 步階函數之傅立葉轉換- 看板Grad-ProbAsk - PTT網頁版

透過計算，我知道要把單位步階跟sgn扯上關係，但是這樣感覺好像繞了一大圈來做計算，想請問板上神人，為什麼步階函數不能直接以傅立葉轉換的積分公式去算？

#80. Generalized Fourier transforms applied to fractional ...

Θ(x)=12+12sgn(x), (10) ... ∫∞−∞eikxxdx=iπsgn(x), (13) ... F[x−n](k)=πkn−1in(n−1)!sgn(k),n∈N, (16) ...

#81. Problem Set 4 w/ soln - WINLAB, Rutgers University

where m(t), M(f) and mH(t), MH (f) are Fourier transform pairs and sgn(f) is the signum function. Using the definition of the Hilbert transform, ...

#82. TransfFourier de sgn(t) - Sistemas Lineares - Passei Direto

Transformação no Limite: A Transformada de Fourier de sgn(t). Método 1. A função sinal, representada por signum(x), signal(x) ou sgn(x), é uma função real ...

#83. Exercises, Fourier transform and Hausdorff dimension, spring ...

What is the Fourier transform of the sign function sgn;sgn(x) = 1, when x ≥ 0, sgn;sgn(x) = −1, when x < 0? 7. Show that if µ is a finite Borel measure on ...

#84. Ch. 5 Fourier Transform - Dr. Jingxian Wu

APPLICATIONS: FILTERING. • Filtering. – Filtering is the process by which the essential and useful part of a signal is separated from undesirable components ...

#85. [Fourier transform] Convolution product with sin and cos

And I can't see anything that may help me... Wolfram says this is the solution: 1/4 sqrt(pi/2) (sgn(-w-20pi+1)+ ...

#86. Chapter 7. WKB in dimension $\ge 2

In particular, $\sgn(\tilde{S}_{pp})=\sgn(S_{xx})$. where $\sgn(S_{xx})$ is a sign of $S_{xx}$. For partial Fourier transform we arrive to the similar formulae.

#87. Computing Fourier series using the package Fourier

Find the Fourier series of the function f(x)=sgn(cos x) on the interval Maple Equation and draw the plots of partial sums Maple Equation ...

#88. A Fourier Series Method for Numerical Kramers-Kronig Analysis

... domain method the Kramers-Kronig integrals are derived without recourse to complex analysis (except in evaluating the Fourier transform of sgn (t)).

#89. Answered: -1, t<0 1) Given that sgn(t) = { 1,… | bartleby

Hence, find the inverse Fourier a+jw transform for F(w) = 1/[(2 +jw)(3 +jw)]. 3) Find the complex exponential Fourier series representation of the function ...

#90. White-light stereoprojection through Fourier spectrum ...

sgn (cosP0x)Δ¯{1,cos(P0x)≥0−1,cos(P0x)≤0,. where P0 is the sampling frequency; T01 and T02 are ...

#91. 施圖姆定理 - 中文百科全書

這個方法是以雅克·夏爾·弗朗索瓦·施圖姆命名的，但實際上是約瑟夫·傅立葉發現的。施圖姆定理與代數基本定理的一個 ... 是sgn(an)，而sgn(P(−x))則是sgn((−1)an)。

#92. Transformées de Fourier de la fonction signe et ... - Culture Diff

La transformée de Fourier de la fonction sgn(t) peut s'écrire : ̂ sgn(f) = lim. T→∞,a→0. {∫ T/2. −T/2 sgna(t) exp(−j2pf t) d t. }.

#93. ¿Cómo calcular la transformada de Fourier de la función ...

función Signo (f(t)= Sgn (t))?. Bienvenidos a este vídeo sobre la transformada de. Fourier de la función signo a partir de la definición de

#94. Explicit Inverse Fourier Transformation TM- 70-1033-2 of a ...

K sgn(t)sinwot. P +wo. (24). In this section we derived the inverse Fourier transforms. The inverse Laplace transforms of. ofE,&,and. KWO 2 .

#95. [傅里叶变换及其应用学习笔记] 十四. 分布傅里叶变换的性质

与传统傅里叶变换的导数定理不同的是，这两个等式是联合分布于测试函数进行匹配后推导得来的，在这里不再记录推导过程。 导数定理应用的例子. 1.求$sgn$的傅里叶变换. $\ ...

#96. 简易法证明1/t的傅立叶变换原创 - CSDN博客

-i*pi*sgn(ω); 看到很多人只给了结论，这里简单说一下证明思路： 其中有一些符号变换注意一下就可以了继续访问 · 实验4 快速傅立叶变换(FFT).

#97. Fourier transforms of commonly occurring signals

Fourier transform of sgn(t). This function is often used to model a voltage comparitor in circuits. Example 4: Unit Step#. Use the signum function to show ...

#98. Find out the Fourier transform of the signum function sgn(t)

VIDEO ANSWER: Hello students in this question. We have to find out the Fourier transform of the function f of t is equal to s g n of t where this is the ...