Portal of "Dieu* de Briefcase"

* The French word 'Dieu' means 'God'. Used here solely for the sake of its resemblance to Cantonese.

Signals and Systems

 

FUN STUFF IN SIGNAL/SYSTEM THEORY

Cover - Annals of Improbable Research - Special Wiener Sausage Issue!: You'll appreciate it once you get into this field and eventually know who Norbert Wiener is.

How to Write a Scientific Paper: Publish or Perish!

M.T.T.F from probability theory, often used by industrial engineers:

 

ELECTRICAL ENGINEER'S TIP TO HKCEE/HKALE (SYSTEMS)

This is a short 9 page book in attempt to offer alternative (easier) methods to Math, Physics and Electronics candidates in HKCEE/HKALE. Download in PDF.

 

FAKE NEWS

FCC regulates the use of 20Hz-20kHz band

 

MY SYSTEM THEORY ARGUMENT

反饋系統 (Feedback Control System) 解說欣宜瘦身/扮白雪公主被投訴:

要分析欣宜減肥,先要理解它體重暴增的原由。在訊號學的角度來說 [見下圖],那隻肥豬正在一個不穩的系統的設定 (unstable configuration). 理由是肥肥不斷提供鮑魚 (abalone) 鼓勵 作為反饋訊號(feedback signal),令整個係統成為了正面反饋系統 (positive feedback system)。不用多說,這個系統會不斷自我膨脹,如個沒有把那些正面訊號切斷,那隻肥豬不久便會爆炸,像各位網上所見用炸藥解決巨鯨的結果一樣,要是想到便會嘔心不安。

要幫助欣宜回復正常體重,這個可傷腦筋。那隻肥豬自信心爆棚,不是一般的干預 (interference) 可以解決的,簡直是無可救藥。對付欣宜這種高膨脹 (high gain/amplification) 系統我們可以利用訊號學基本的負面反饋原理 (negative feedback principle)  [見下圖]。要用甚麼作為反訊號呢?最有效的還是鏡子。看到自己的衰樣,如果它沒有超凡的免疫力,便會像普通人見到佢扮白雪公主的反應一樣:嘔吐,失去食欲 。

以鏡子作為反饋系統的增訊值 (Gain) 很接近 100%,是一個很有效的单一負面反饋 (unity negative feedback) 系統

把欣宜的自信心以 A(s) 來表達,那麼系列整體的擴充功能 (transfer function)

H(s) = A(s)/(1+A(s))

有了這一套良好的反饋系統,它的體重的確是穩定下來,把 |H(s)| 控制在 1 以內。 基於它無比的自信,A(s) 催近無限,導使 |H(s)| 非常接近 1 ,穩定體重 (steady state weight)未降到一般人可以接受的地步。要進一步減磅,便要把 |H(s)| 降至遠低於 1 的上限。從以上的擴充功能 (transfer function) 可見,唯一可做的是從減低 A(s) 入手,換言之,先要解決它的自信心膨脹的問題。

不約而同地,不少對控制系統 (Control System) 有所領會的香港人,為了支持欣宜瘦身,不致於半途而廢,搞盡腦汁才想到向廣管局投訴的妙計,設法打擊欣宜令人驚嘆(嚇驚,嘆息)的自信,令它重拾瘦肉的外,卻遭光名頂的名咀譴責。我本來也很喜歡聽光明頂的,但今天也要為這些有工程常識,忍肉(辱)負重的智者討公道

 

SIGNALS AND SYSTEMS

My field of interest is in signal processing. So, I hope to help people to overcome this hurdle course. Here's a short article highlighting the preparations and strategies needed to excel in this gateway course to communications, signal processing and control systems. This article will be updated at any time whenever the author feels appropriate. It can be downloaded here.

Here are some other useful resources:

Dr. Sebald (UW-Madison) wrote a very impressive summary on what kind of Mathematics which will be handy in signals, systems and communications. You don't need all of them for the course, but they are good stuff if you plan to enter this Mathematical field. It can be download from this site or his site.

 


 

Engineering & Mathematics

 

How many mathematicians does it take to change a light bulb? If you understand the punch lines, you know math.

PHYSICS (OPTICS)

 

APPLIED PHYSICS IN BUSINESS & FINANCE


The Uncertainty Principle. That's also used in signal analysis (time and frequency resolution).

 

MATH IN DILBERT


Who said the boss can't do math? It's a brilliant exploit!

 

MY MATHEMATICAL ARGUMENTS

羅文唱的「家變」中的歌詞提及到「不必怨世時變,變幻才是永恆」,表達了一個很大膽的理論: 「世界是線性的」,這是學術界不可思議的一大奇聞。如果世事真的是線性,那麼股市只可以永遠不停地上升,下降,或停滯。從微積分學中,我們可以看到為何如此簡單的一句歌詞醞含著那麼大的玄機:

我們先以 f(x) 代表世界的事情, x 陣列代表可變的事物,K 是永恆不變的固定數,那麼世事變幻便是 f'(x)。「變幻才是永恆」亦即譯作 f'(x) = K,把恆等式的兩邊積分,我們便得到 f(x) = Kx + C,不用多說,C 當然是隨意常數。從此可見世界是線性方程式!

- Sep 17, 2005

 

MATHEMATICS IN TV/MOVIES


大和拜金女 Ep 1
Looks fancy but these are just basic calculus!

 

My favorite topics of discussion, which sometimes I enjoy upsetting people with those:

Reasoning behind Comedy

Brainwashing (Education, Cognitive systems, Psychology) and cult(ure), religion and ethics.

Economics and Psychology