將單位脈衝(Unit Impulse)輸入系統時,其響應即是此系統的特性函數 h(t),
此h(t)稱為脈衝響應。
●時域的脈衝響應為Convolution 函數式
●頻域的脈衝響應為乘積函數式:


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               border-radius: 8px;                padding: 16px;                font-size: 16px;                color: #535150;                line-height: 180%;                text-align: left;              }              .lexical__textBold {                font-weight: bold;              }              .lexical__textItalic {                font-style: italic;              }              .lexical__textUnderline {                text-decoration: underline;              }              .lexical__textStrikethrough {                text-decoration: line-through;              }              .lexical__textUnderlineStrikethrough {                text-decoration: underline line-through;              }              .lexical__textSubscript {                font-size: 0.8em;                vertical-align: sub;              }              .lexical__textSuperscript {                font-size: 0.8em;                vertical-align: super;              }              .lexical__textCode {                background-color: rgb(240, 242, 245);                padding: 1px 0.25rem;                font-family: Menlo, Consolas, Monaco, monospace;                font-size: 94%;              }            </style></head><body><div class="article-container"><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/cfa0e001-533d-4ec8-a681-7e11cb8470fa.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2Fcfa0e001-533d-4ec8-a681-7e11cb8470fa.jpg&width=740&sign=xjgUMsQFaw0D13pHYmDv40ACL-IjNyu-i7Il93lX4bA" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/cfa0e001-533d-4ec8-a681-7e11cb8470fa.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="https://www.dspguide.com/ch9/2.htm"></div><div class="captionTheme__wrapper"><p class="captionTheme__paragraph">https://www.dspguide.com/ch9/2.htm</p></div></div><p class="graf--p" style="text-align: left;"><br></p><p class="graf--p" style="text-align: left;"><span style="white-space: pre-wrap;">將單位脈衝(Unit Impulse)輸入系統時,其響應即是此系統的特性函數 h(t),</span></p><p class="graf--p" style="text-align: left;"><span style="white-space: pre-wrap;">此h(t)稱為脈衝響應。</span></p><p class="graf--p" style="text-align: left;"><span style="white-space: pre-wrap;">●時域的脈衝響應為Convolution 函數式</span></p><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/1b9e6b72-91ae-4cf2-b1ca-e009273364f4.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2F1b9e6b72-91ae-4cf2-b1ca-e009273364f4.jpg&width=740&sign=j3FfgeEqolVV82-wEf4dCkYiJUUlzpe_i204yGxO7FY" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/1b9e6b72-91ae-4cf2-b1ca-e009273364f4.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="graf--p" style="text-align: left;"><span style="white-space: pre-wrap;">●頻域的脈衝響應為乘積函數式:</span></p><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/f59f5537-b8cd-40e2-906c-96017e8f0fc3.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2Ff59f5537-b8cd-40e2-906c-96017e8f0fc3.jpg&width=740&sign=jkx-ofzziD0FNj9cyVAKfLq50LNQImRjcXigSFBYarU" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/f59f5537-b8cd-40e2-906c-96017e8f0fc3.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="graf--p" style="text-align: left;"><span style="white-space: pre-wrap;">可推導如下:</span></p><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/71323301-2c21-4f8a-a24c-ec98f46e5648.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2F71323301-2c21-4f8a-a24c-ec98f46e5648.jpg&width=740&sign=oVxpFM2bBo0tPYfbBbpCVmKn7d-BxHJjtlcNHBfPsl4" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/71323301-2c21-4f8a-a24c-ec98f46e5648.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/dbfda050-eba3-417c-a2dd-0aa558b83ece.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2Fdbfda050-eba3-417c-a2dd-0aa558b83ece.jpg&width=740&sign=0GcnY0W03QJNf4E7ZSqfN3XlithUx6zM9HMbqcaVzGk" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/dbfda050-eba3-417c-a2dd-0aa558b83ece.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/a1ad216d-7384-4ead-9e88-4d5676cb5206.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2Fa1ad216d-7384-4ead-9e88-4d5676cb5206.jpg&width=740&sign=fboGRhDJWWTC59GIC6-dLqzzh-6dpVgSWvHE85tlDI0" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/a1ad216d-7384-4ead-9e88-4d5676cb5206.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/ac735fc8-56da-4e01-9d91-ffe8e52ade82.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2Fac735fc8-56da-4e01-9d91-ffe8e52ade82.jpg&width=740&sign=lwdFAfuC0z8pOEv0kpIM-MzMn5uJpPbLj6OHNhp1jNo" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/ac735fc8-56da-4e01-9d91-ffe8e52ade82.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><div class="graf--img center"><div class="lexical__imageWrapper"><img src="https://images.vocus.cc/a83ca9d8-ff86-41db-b114-2bcf251c774e.jpg" data-src="https://resize-image.vocus.cc/resize?norotation=true&quality=80&url=https%3A%2F%2Fimages.vocus.cc%2Fa83ca9d8-ff86-41db-b114-2bcf251c774e.jpg&width=740&sign=ULMOKUayBpYE9P0trTGr7XTyNvoiR5epiRjxJB5uD-o" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/a83ca9d8-ff86-41db-b114-2bcf251c774e.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><div><a class="embed-wrapper" href="undefined" target="_blank"><div class="embed-title">前往觀看 YouTube 影片</div></a></div><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><div><a class="embed-wrapper" href="undefined" target="_blank"><div class="embed-title">前往觀看 YouTube 影片</div></a></div><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><div><a class="embed-wrapper" href="undefined" target="_blank"><div class="embed-title">前往觀看 YouTube 影片</div></a></div><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><div><a class="embed-wrapper" href="undefined" target="_blank"><div class="embed-title">前往觀看 YouTube 影片</div></a></div><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p><p class="graf--p" style="text-align: left;" dir="ltr"><br></p></div></body></html>

圖文插畫

將單位脈衝(Unit Impulse)輸入系統時,其響應即是此系統的特性函數 h(t),

●時域的脈衝響應為Convolution 函數式

●頻域的脈衝響應為乘積函數式:

(Reading Practice (Improve your pronunciation in English

'Return To Love' featuring Ellie Goulding is out now! Listen here: https://andreabocelli.lnk.to/ReturnToLoveID Pre-order "Sì Forever", the new album from Andrea Bocelli, here: https://andreabocelli.lnk.to/SiForever Watch the Music for Hope full event here: https://andreabocelli.lnk.to/LiveFromDuomoID Listen to the Music for Hope full event here: https://andreabocelli.lnk.to/MusicForHope1ID Music video by Andrea Bocelli performing "Quizas, Quizas, Quizas" ft.

Andrea Bocelli - Quizas, Quizas, Quizas (Audio) ft. Jennifer Lopez

Barry White - Love's Theme (Charlize Theron)

Provided to YouTube by JVCKENWOOD Victor Entertainment Corp. なみだの操 · Mina Aoe Onna no Namida o Utau ℗ JVCKENWOOD Victor Entertainment Released on: 2008-10-01 Auto-generated by YouTube.

なみだの操

<div class="draft--imgNormal draft-block"><div><div style="height:662px" class="image-block-prerender" data-src="https://images.vocus.cc/cfa0e001-533d-4ec8-a681-7e11cb8470fa.jpg" data-width="662" data-height="254" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block">https://www.dspguide.com/ch9/2.htm</figcaption></div></div>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left">將單位脈衝(Unit Impulse)輸入系統時,其響應即是此系統的特性函數 h(t),</p>
<p class="draft-block draft--p left">此h(t)稱為脈衝響應。</p>
<p class="draft-block draft--p left">●時域的脈衝響應為Convolution 函數式</p>
<div class="draft--imgNormal draft-block"><div><div style="height:567px" class="image-block-prerender" data-src="https://images.vocus.cc/1b9e6b72-91ae-4cf2-b1ca-e009273364f4.jpg" data-width="567" data-height="135" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block"></figcaption></div></div>
<p class="draft-block draft--p left">●頻域的脈衝響應為乘積函數式:</p>
<div class="draft--imgNormal draft-block"><div><div style="height:609px" class="image-block-prerender" data-src="https://images.vocus.cc/f59f5537-b8cd-40e2-906c-96017e8f0fc3.jpg" data-width="609" data-height="101" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block"></figcaption></div></div>
<p class="draft-block draft--p left">可推導如下:</p>
<div class="draft--imgNormal draft-block"><div><div style="height:617px" class="image-block-prerender" data-src="https://images.vocus.cc/71323301-2c21-4f8a-a24c-ec98f46e5648.jpg" data-width="617" data-height="129" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block"></figcaption></div></div>
<div class="draft--imgNormal draft-block"><div><div style="height:671px" class="image-block-prerender" data-src="https://images.vocus.cc/dbfda050-eba3-417c-a2dd-0aa558b83ece.jpg" data-width="671" data-height="374" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block"></figcaption></div></div>
<div class="draft--imgNormal draft-block"><div><div style="height:489px" class="image-block-prerender" data-src="https://images.vocus.cc/a1ad216d-7384-4ead-9e88-4d5676cb5206.jpg" data-width="489" data-height="474" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block"></figcaption></div></div>
<div class="draft--imgNormal draft-block"><div><div style="height:518px" class="image-block-prerender" data-src="https://images.vocus.cc/ac735fc8-56da-4e01-9d91-ffe8e52ade82.jpg" data-width="518" data-height="462" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block"></figcaption></div></div>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>
<div class="draft--imgNormal draft-block"><div><div style="height:1592px" class="image-block-prerender" data-src="https://images.vocus.cc/a83ca9d8-ff86-41db-b114-2bcf251c774e.jpg" data-width="1592" data-height="1080" data-position="center"></div><figcaption class="imageCaption draft-block" style="cursor:text;display:block"></figcaption></div></div>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>
<div class="embed-block-prerender" data-type="html" data-url="https://www.youtube.com/watch?v=HDpLkfddGR4&amp;t=278s"></div>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>
<div class="embed-block-prerender" data-type="html" data-url="https://www.youtube.com/watch?v=xYz5CiEy5bY"></div>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>
<div class="embed-block-prerender" data-type="html" data-url="https://www.youtube.com/watch?v=NCorVfa-QZ0"></div>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>
<div class="embed-block-prerender" data-type="html" data-url="https://www.youtube.com/watch?v=P8_TORzTn1M"></div>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>
<p class="draft-block draft--p left"></p>

這篇要來分享關於「頻率」這件事，談到頻率，不免就要順便談談「吸引力法則」，現在訪間已經有多書籍、影片都有詳細描述吸引力法則的運行方式。它並不是什麼怪力亂神也不是什麼偽科學，實則吸引力法則是個再科學不過的量子力學，同頻相吸的概念而已。

Intern Human 的沙龍

淺談「振動頻率」－以修電腦為例

跨元探索的沙龍

【訊號處理】脈衝響應(Impulse Response)

DSP技術的基本原理
訊號取樣 : 依 Nyquist Rate & Interval 法則進行取樣(連續-->離散)
訊號重建 : 抽取、內插(如 ZOH, FOH)等方式進行重建
(離散-->新的離散或重建回連續)
========================================

【訊號處理】取樣及重建

續傳遞函數離散化的核心環節，就是將控制器的s轉移函數(s-TF)轉換為z轉移
函數(z-TF)。
一般情況下，由連續到離散的設計最好多實驗幾種方法（通過模擬，得出滿意的
結果）。
用於PID連續系統映射轉換成PID離散系統的方塊圖如下:
■離散化演算法摘要
■離散化演算法比較
■MATLAB 指令說

【MATLAB】  連續系統與離散系統的轉換

調變（modulation）
是一種將一個或多個週期性的載波混入想傳送之訊號的技術，常用於無線電波的傳播與通訊、利用電話線的資料通訊等各方面。



【類比信號調變】漫畫詮釋AM_FM技術

系統響應是指系統針對其輸入而產生相對應的輸出結果
針對系統不同的特性，可以進行以下分析：
1.穩定度分析
2.暫態與穩態分析
3.時域與頻域分析
當系統的響應無法達到目標時，此時才會再加上控制器進行設計，以讓系統能達
到控制目標
===================================

【MATLAB】控制系統響應及穩態誤差

■控制系統分類
●依開閉路系統區分
(1)開路系統
(2)閉路控制系統
A.線性系統與非線性系統。
B.時變系統與時不變(非時變)系統。
C.線性時不變系統(俗稱LTI系統)
D.因果系統與非因果系統。
●依系統之訊號性質區分
(1)連續性（類比）控制系統：控制系統內部所處理的信號均為時間的


自動控制-連續時間系統的PID控制原理

=============================================
根軌跡的定義
=============================================
■根軌跡的定義
●控制系統轉移函數
●特性方程式及特性根
亦即  1+開迴路轉移函數=0
●根軌跡


【自動控制】根軌跡圖

職場

學習

以行動支持創作者！付費即可解鎖

神秘力量

地球實習日記

歡迎來到我的沙龍，平台主要紀錄我致力於身心靈領域至今所體悟到的人生哲理以及分享我的洞見，將這些豐沛的思想轉化為文字創作。


音樂藝文

職場產業

通訊無界

閱讀書評

智控_AI

創作

■視頻重點摘要
●符號及運算
單位脈衝 δ[n]=u[n]-u[n-1]
單位步階 u[n]
脈衝信號 h[n]
序列信號 x[n]
●Z轉換               
y[n]=h[n]*x[n] 為 Time - Domain 的差分方程式 (式中*為卷積)
頻率響應指頻率的放大倍數


投資理財

信號與控制:傅立葉轉換、拉普拉斯轉換、Z轉換

Analgesia nociception index (ANI) 的原理介紹

健康與情感

文化生活

麻醫踅踅唸 (碎碎唸)的沙龍

[麻醉][進階專業知識][臨床][進階監控-疼痛]ANI

西洋占星

LED彩光

咖啡精萃

晶片神山

印度占星

醒思三觀

卦算風水

虛實錢道

‘Return To Love’ featuring Ellie Goulding is out now! Listen here: https://andreabocelli.lnk.to/ReturnToLoveID
Pre-order "Sì Forever", the new album from Andrea Bocelli, here: https://andreabocelli.lnk.to/SiForever 

Watch the Music for Hope full event here: https://andreabocelli.lnk.to/LiveFromDuomoID
Listen to the Music for Hope full event here: https://andreabocelli.lnk.to/MusicForHope1ID

Music video by Andrea Bocelli performing "Quizas, Quizas, Quizas" ft. Jennifer Lopez. (C) 2011 Sugar Srl

<div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fcfa0e001-533d-4ec8-a681-7e11cb8470fa.jpg&amp;width=740&amp;sign=xjgUMsQFaw0D13pHYmDv40ACL-IjNyu-i7Il93lX4bA" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fcfa0e001-533d-4ec8-a681-7e11cb8470fa.jpg&amp;width=740&amp;sign=xjgUMsQFaw0D13pHYmDv40ACL-IjNyu-i7Il93lX4bA" data-loaded="true" data-original-src="https://images.vocus.cc/cfa0e001-533d-4ec8-a681-7e11cb8470fa.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="https://www.dspguide.com/ch9/2.htm"></div><div class="captionTheme__wrapper"><p class="captionTheme__paragraph">https://www.dspguide.com/ch9/2.htm</p></div></div><p class="lexical__paragraph" style="text-align: left;"><br></p><p class="lexical__paragraph" style="text-align: left;"><span style="white-space: pre-wrap;">將單位脈衝(Unit Impulse)輸入系統時,其響應即是此系統的特性函數 h(t),</span></p><p class="lexical__paragraph" style="text-align: left;"><div class="ad-placeholder" style="min-height: 124px;"></div><span style="white-space: pre-wrap;">此h(t)稱為脈衝響應。</span></p><p class="lexical__paragraph" style="text-align: left;"><span style="white-space: pre-wrap;">●時域的脈衝響應為Convolution 函數式</span></p><div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2F1b9e6b72-91ae-4cf2-b1ca-e009273364f4.jpg&amp;width=740&amp;sign=j3FfgeEqolVV82-wEf4dCkYiJUUlzpe_i204yGxO7FY" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2F1b9e6b72-91ae-4cf2-b1ca-e009273364f4.jpg&amp;width=740&amp;sign=j3FfgeEqolVV82-wEf4dCkYiJUUlzpe_i204yGxO7FY" data-loaded="true" data-original-src="https://images.vocus.cc/1b9e6b72-91ae-4cf2-b1ca-e009273364f4.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="lexical__paragraph" style="text-align: left;"><span style="white-space: pre-wrap;">●頻域的脈衝響應為乘積函數式:</span></p><div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Ff59f5537-b8cd-40e2-906c-96017e8f0fc3.jpg&amp;width=740&amp;sign=jkx-ofzziD0FNj9cyVAKfLq50LNQImRjcXigSFBYarU" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Ff59f5537-b8cd-40e2-906c-96017e8f0fc3.jpg&amp;width=740&amp;sign=jkx-ofzziD0FNj9cyVAKfLq50LNQImRjcXigSFBYarU" data-loaded="true" data-original-src="https://images.vocus.cc/f59f5537-b8cd-40e2-906c-96017e8f0fc3.jpg" data-lowquality="false" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="lexical__paragraph" style="text-align: left;"><span style="white-space: pre-wrap;">可推導如下:</span></p><div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=1&amp;url=https%3A%2F%2Fimages.vocus.cc%2F71323301-2c21-4f8a-a24c-ec98f46e5648.jpg&amp;width=550&amp;sign=GNHaLHDePTFIeOTAVM8Ntk29cOpHwEeJNHiBhi4PSe4" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2F71323301-2c21-4f8a-a24c-ec98f46e5648.jpg&amp;width=740&amp;sign=oVxpFM2bBo0tPYfbBbpCVmKn7d-BxHJjtlcNHBfPsl4" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/71323301-2c21-4f8a-a24c-ec98f46e5648.jpg" data-lowquality="true" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=1&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fdbfda050-eba3-417c-a2dd-0aa558b83ece.jpg&amp;width=550&amp;sign=BUozewKlOzvo6LS5sADRbRhVuQ9FAIb1n9PPaNZHG7Y" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fdbfda050-eba3-417c-a2dd-0aa558b83ece.jpg&amp;width=740&amp;sign=0GcnY0W03QJNf4E7ZSqfN3XlithUx6zM9HMbqcaVzGk" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/dbfda050-eba3-417c-a2dd-0aa558b83ece.jpg" data-lowquality="true" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=1&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fa1ad216d-7384-4ead-9e88-4d5676cb5206.jpg&amp;width=550&amp;sign=xh86U1UvLwDnwG0bGbsmoUfrggt0IQ4JDI8TOr2ukAI" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fa1ad216d-7384-4ead-9e88-4d5676cb5206.jpg&amp;width=740&amp;sign=fboGRhDJWWTC59GIC6-dLqzzh-6dpVgSWvHE85tlDI0" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/a1ad216d-7384-4ead-9e88-4d5676cb5206.jpg" data-lowquality="true" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=1&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fac735fc8-56da-4e01-9d91-ffe8e52ade82.jpg&amp;width=550&amp;sign=pEjZAWWfSdIHNewIjS1gIkFG0jn6Q3L5BG2SQCgcDMc" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fac735fc8-56da-4e01-9d91-ffe8e52ade82.jpg&amp;width=740&amp;sign=lwdFAfuC0z8pOEv0kpIM-MzMn5uJpPbLj6OHNhp1jNo" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/ac735fc8-56da-4e01-9d91-ffe8e52ade82.jpg" data-lowquality="true" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><div class="lexical__image center"><div class="lexical__imageWrapper"><img src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=1&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fa83ca9d8-ff86-41db-b114-2bcf251c774e.jpg&amp;width=550&amp;sign=9IaKzwYo_nnqt5g_og31RQCjzqrnrEyUksrArDtYxbY" data-src="https://resize-image.vocus.cc/resize?norotation=true&amp;quality=80&amp;url=https%3A%2F%2Fimages.vocus.cc%2Fa83ca9d8-ff86-41db-b114-2bcf251c774e.jpg&amp;width=740&amp;sign=ULMOKUayBpYE9P0trTGr7XTyNvoiR5epiRjxJB5uD-o" class="lazy" data-loaded="false" data-original-src="https://images.vocus.cc/a83ca9d8-ff86-41db-b114-2bcf251c774e.jpg" data-lowquality="true" data-width="undefined" data-height="undefined" data-retry="0" onerror="Number(this.dataset.retry) > 4 ? this.src='/static/default-error-img.svg': (() => {this.src=this.dataset.originalSrc; this.dataset.retry = Number(this.dataset.retry)+1;})()" alt="raw-image"></div><div></div></div><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><div class="lexical__youtube"><iframe data-lexical-youtube="HDpLkfddGR4" width="600" height="340" src="https://www.youtube-nocookie.com/embed/HDpLkfddGR4" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="true" title="YouTube video"></iframe></div><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><div class="lexical__youtube"><iframe data-lexical-youtube="xYz5CiEy5bY" width="600" height="340" src="https://www.youtube-nocookie.com/embed/xYz5CiEy5bY" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="true" title="YouTube video"></iframe></div><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><div class="lexical__youtube"><iframe data-lexical-youtube="NCorVfa-QZ0" width="600" height="340" src="https://www.youtube-nocookie.com/embed/NCorVfa-QZ0" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="true" title="YouTube video"></iframe></div><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><div class="lexical__youtube"><iframe data-lexical-youtube="_e9MMjyUhVs" width="600" height="340" src="https://www.youtube-nocookie.com/embed/_e9MMjyUhVs" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="true" title="YouTube video"></iframe></div><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p><p class="lexical__paragraph" style="text-align: left;" dir="ltr"><br></p>

繪畫／手作

♪《莫奔跑》
（英語：Buttons and Bows），《中文翻譯成紐扣與蝴蝶結》
 是一首風靡全世界的美國暢銷流行歌曲，
 🍎大西洋飲料公司將♪《莫奔跑》，作為🍎蘋果西打廣告曲，
 輕鬆愉快，朗朗上口，家喻戶曉的歌詞內容 :
「你一瓶，我一瓶，請喝蘋果西打🍎」讓人印象深刻!!
 中文版翻唱為《莫奔跑》
 中文版的作詞者是司徒明先生，原唱是民國時期著名歌手姚莉。
 ♪《莫奔跑》
 在1947年出版，Jay Livingston作曲和Ray Evans作詞，
 是電影The Paleface的主題歌曲，
 這首歌並且贏得了奧斯卡最佳原創歌曲獎。
 最受歡迎的版本是在1947年由美國女歌手Dinah Shore🎤主唱的，
     https://www.youtube.com/watch?v=jfW9-0EzYxA
  並在1948登上美國告示牌冠軍單曲。2004年，
 ♪《莫奔跑》在AFI百年百大電影歌曲中評鑑獲得了第八十七名。

【台灣最暢銷歌曲100首】♪ 莫奔跑(🍎 蘋果西打)~ 🍎 Buttons and Bows 🍎

Sarah Brightman (Christine) and Antonio Banderas (Phantom) duet in this rendition of the titular number from Andrew Lloyd Webber's Phantom of The Opera.

From Andrew Lloyd Webber: The Royal Albert Hall Celebration -  A celebratory tribute to musical compositions of Lord Andrew Lloyd Webber, live from the Royal Albert Hall. Featuring hits from some of his most renowned productions, such as Starlight Express, Evita, Cats, Phantom of the Opera, Jesus Christ Superstar, and more.

If you enjoyed that why not check out these other hit musicals! :


Cats: /bsi5lz
Joseph and The Amazing Technicolor Dreamcoat: /fri5lz
Phantom of The Opera: 
Love Never Dies: Welcome to The Shows Must Go On the channel bringing you showtunes, backstage access and full performances from some of the best loved musicals in history!

Featuring melodic moments, show-stopping solos and high notes for the history books. 

#PhantomOfTheOpera #SarahBrightman #AntonioBanderas #AndrewLloydWebber #Musicals #MusicalTheatre #stayhome #withme

'The Phantom of The Opera' Sarah Brightman & Antonio Banderas

授課教師：電機工程學系 吳炳飛老師
自動控制系統 YouTube Playlist：https://www.youtube.com/playlist?list=PLj6E8qlqmkFsk7Cyj1ZNLfDjZ_Yh4iySU
課程資訊：https://ocw.nycu.edu.tw/course_detail.php?nid=623&bgid=8&gid=0
授權條款：Creative Commons BY-NC-SA 4.0
更多課程歡迎瀏覽交大開放式課程網站：https://ocw.nycu.edu.tw/
#NYCUOCW #自動控制系統 #Automatic Control Systems

自動控制系統 - Ch3 轉移函數、方塊圖、信號流程圖 Transfer Functions, Block Diagrams, Signal-Flow Graphs (4/6)

自動控制系統 - Ch3 轉移函數、方塊圖、信號流程圖 Transfer Functions, Block Diagrams, Signal-Flow Graphs (5/6)

通过简单的平衡实验展示PID控制算法。

接线图与代码：
CSDN（机器人工坊） https://blog.csdn.net/robotixworkshop

【Arduino 101】五分钟搞懂PID控制算法

A closed loop control system for position control is comprised of proportional, integral, and derivative circuits and is often referred to as a PID. Watch this video to learn more.

See this and over 140+ engineering technology simulation videos at http://www.engineertech.org.

Simulations provided free under a Department of Labor grant awarded Eastern Iowa Community Colleges. To learn more visit http://www.eicc.edu.

PID Controller

迴響國樂團
指揮：陳慶文
地點：國家音樂廳
日期：2019年7月22日

傾聽台灣~傳唱台灣的聲音 - 台東人     ( 演唱：劉福助 )

How to find the range of the gain K for a system is stable using the system's open loop root locus plot. You will learn to use the MATLAB functions rlocus, step, and how to navigate root locus plots.

Find Range of Gain K For Stability Using Root Locus Plot

代表作
三橋美智也/瞼の中に故里が
天童よしみ/春が来た/夢うぐいす/幸せはすぐそこに…
門倉有希/ノラ
坂本冬美/凛として
長山洋子/蜩
美空ひばり/人恋酒/おまえに惚れた
佐良直美/国東半島ぶらり旅
小林旭/氷雪海峡
増位山太志郎/そんな女のひとりごと
細川たかし/置き手紙
石川さゆり/命燃やして
石原詢子/淡墨桜/なごり雨/寿契り酒/雪散華〜ゆきさんげ〜
キム・ヨンジャ/北の雪虫
山川豊/海峡本線/しぐれ川
三船和子/この冬すぎれば春が来る
上杉香緒里/おんな酒
西方裕之/遠花火/紀ノ川/夢追い川/海峡列車
藤あや子/花のワルツ/女泣川
田川寿美/しゃくなげの雨
テレサ・テン/逢う時はいつも他人/冬日和
都はるみ/草枕
美川憲一/赤い鴎
加門亮/男の慕情/麗子/夜霧
前川清/窓
新沼謙治/ヘッドライト
香田晋/お宝女房
山口ひろみ/女の波止場
和田青児/夢さすらい
佳山明生/男の水割り
滝里美・徳久広司/ちいさな酒場
花咲ゆき美/冬の蛍
小柳ルミ子/桜前線
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This video covers a purely geometric way to understand both Fourier and Laplace transforms (without worrying about imaginary numbers). 

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The intuition behind Fourier and Laplace transforms I was never taught in school

工程數學之拉普拉斯轉換 (i.e.拉普拉斯變換 Laplace Transform) ! 這裡包含了所有你該熟練的一般函數的拉式轉換 L{e^(at)}, L{t^n}, L{sin(bt)}, L{cos(bt)}, L{U(t-a)}, L{δ(t-a)}, ... 和你該知道的拉普拉斯轉換特性 L{e^(at)f(t)}, L{tf(t)}, L{f'(t)}, L{integral of f(u)}, L{f(t)*g(t)},...., 還有一些例子. 這會對你微分方程的課 或是 訊號學的課有幫助. 喜歡數學請訂閱 @黑筆紅筆 

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題目: https://www.blackpenredpen.com/_files/ugd/287ba5_bb285a61a06745e6a7452c4c379a7de0.pdf
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0:00, 24題拉普拉斯轉換 (i.e. 拉普拉斯變換 or 拉氏轉拉氏轉換)
Q1, 3:23, L{e^(at)}, 
Q2, 6:49, L{t^n} (用級數)
Q3, Q4, 17:40, L{sin(bt)}, L{cos(bt)} 
Q5, 25:04, L{sinh(bt)}, hyperbolic sine
Q6, 27:34, L{cosh(bt)}, hyperbolic cosine
Q7, 30:50, L{U(t-a)}, unit-step function
Q8, 36:38, L{Πa,b(t)}, the window function
Q9, 41:30, L{δ(t-a)}, Dirac Delta function
Q10, 46:58, L{f(t-a)U(t-a)}, shifting theorem in the t-domain
          part 2, 53:33, L{f(t)U(t-a)}
Q11, 59:03, L{(t-2)^2*U(t-2)} vs. L{t^2 U(t-2)}, 拉普拉斯轉換例子
Q12, 1:05:11, L{f(at)} 
         1:10:04, 例子 L{sin(t)} vs L{sin(bt)}
Q13, 1:13:28, L{e^(at) f(t)}, shifting theorem in the s-domain
Q14, 1:17:14, L{t^3 e^(2t)}
Q14*, 1:19:18, L{e^(3t)cos(2t)}
Q15, 1:22:26, L{tf(t)} = -d/ds(F(s))
Q16, 1:29:23, L{tsin(bt)}
          1:31:29 的分母應該是(s^2+b^2)^2
          Honorable metions: L{t^nf(t)}=(-1)^n d^n/ds^n(F(s))
Q17, 1:37:22, L{f(t)/t}
Q18, 1:50:28, L{sin(t)/t}=pi/2-tan^-1(s)
          1:54:30 積分sin(t)/t, 積分sin(t)/(te^t), 積分sin(e^t)?
Q19, 2:01:43, L{f'(t)}
Q20, 2:08:31, L{f''(t)}
Q21, 2:13:00, L{integral of f(u)}
Q22, 2:19:55, L{f(t)*g(t)}, the convolution theorem
         Honorable mentions: L{sin(t)cos(t)} vs. L{sin(t)*cos(t)}
Q23, 2:39:24, L{sqrt(t)}, ft. Gamma function
          (1/2)階乘 https://youtu.be/EE3Y0-j9tRE, 高斯積分 https://youtu.be/QdYsbx0SVKA
Q24, 2:47:34, 壓軸 L{ln(t)}
做完啦, 好爽!!

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#黑筆紅筆 不是為了考試的數學頻道

拉普拉斯轉換 Laplace Transform (終極複習)

Explains how the Fourier Series (FS), Fourier Transform (FT), Discrete Time Fourier Transform (DTFT), Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), Laplace Transform (LT) and Z-Transform (ZT) are all Related?
Related videos: (see http://www.iaincollings.com)
• Fourier Series and Eigen Functions of LTI Systems https://youtu.be/gRq3K4ZQKi8
• What is the Fourier Transform? https://youtu.be/G74t5az6PLo
• What is the Fourier Transform used for? https://youtu.be/VtbRelEnms8
• Fourier Transform Equation Explained https://youtu.be/8V6Hi-kP9EE
• Typical Exam Question on Fourier Transform Properties https://youtu.be/hPZ08BdjHL4
• Discrete Time Basis Functions https://youtu.be/P7q2YMQiat8
• How does the Discrete Fourier Transform DFT relate to Real Frequencies? https://youtu.be/pIFz84oj9cA
• Laplace Transform Equation Explained https://youtu.be/F_XmgIryugU
• Laplace Transform Region of Convergence Explained https://youtu.be/SexBL1OlhhU
• What is the Z Transform? https://youtu.be/n6MI-nEZoL0
• Z Transform Region of Convergence Explained https://youtu.be/uq_qv3Spzbs
• Is Phase important in the Fourier Transform? https://youtu.be/WyFO6yBQ0Cg

For a full list of Videos and accompanying Summary Sheets, see the associated website: http://www.iaincollings.com

(* Note that for the DFT, unfortunately I forgot to say the last part of the explanation. I made the point that the DFT effectively assumes that the finite-length sampled signal is actually one period of an infinitely long periodic signal. I then drew the Fourier transform for the infinitely long discrete time signal. What I forgot to do, was to then say that the output of the DFT is only the finite part of that Fourier transform between omega=0 and omega=2pi. And that it is a discrete sequence with the same number of elements as the number of samples in the time domain sampled signal. For more details see: https://youtu.be/pIFz84oj9cA)  
.

How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related?

Link to a video explaining how poles and zeros influence a systems frequency response https://youtu.be/m5TP2uG_O2M

An explanation of the z transform part 4  - the transfer function

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This video goes through an overview of what you would learn in a discrete time signals (or digital signal processing) course. Sampling, digital filters, the z-transform, and the applications of these are some of the things included. I had to over simplify a lot to barely keep this video under 30 minutes but hopefully it gives you an idea of how this type of math is used in the real world.

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The Mathematics of Signal Processing | The z-transform, discrete signals, and more

All i know about this piece of music is, it was written at  the end of the nineteenth century by a Polish composer named Karol Namyslowski. It is a piece of music you love or hate.