基本素養 Basic Literacy

核心能力 Competence

掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
處理數字及符號運算的能力
Ability to operate with symbols and digits.
透視形像與空間的能力
Ability to visualize space, shape, and images.
利用計算機處理數學的能力
Ability of using computer to do mathematics.
應用隨機理論的能力
Ability to apply stochastic mathematics.
處理大量數據的能力
Ability to handle large amount of data.
處理離散型數學的能力
Ability to do mathematics relating to discrete models.
獨立研究的能力
Ability to do independent studies of mathematics.
使用計算機的能力
Abilities to use computer as a tool.

課程概述 Course Description

本課程談論聲波、聲波訊號、語音訊號及數位訊號處理。 內容包括:(1) 時間域聲波的特徵 (2) 質點振動的常微分方程、特徵值與頻率 (3) 波動方程的邊界值問題 (4) 傅立葉轉換與時頻分析(5)週期函數與傅立葉級數 (6)數位語音合成、識別與診斷
In this course, we will talk about sound waves, acoustic signals, voice signals and digital signal processing. The contents include (1) the features of sound waves in time-domain (2) ordinary differential equations of particle vibration and the corresponding eigenvalues and frequencies (3) boundary value problem of wave equation (4) Fourier transform and time-frequency analysis (5) periodic functions and Fourier series (6) digital speech synthesis, recognition and diagnosis.

課程學習目標 Course Objectives

  • 熟悉聲音訊號
  • 學習使用數學處理聲音訊號
  • 學習使用計算機處理數學問題
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1 聲音訊號簡介 ..空氣中的應力波
    2 C程式語言複習, 聲音訊號的離散化與數位化
    3.wav 檔與 .wav 檔的讀寫
    4 .wav 檔讀寫實習
    5正弦波的頻率: 周期函數與傅立葉級數
    6樂器的音色: 弦樂器 弦波
    7 弦樂的合成實習
    8樂器的音色: 鼓
    9鼓樂的合成實習
    10其他樂器的音色
    11衰退,合成實習
    12 樂曲合成與實習
    13 傅立葉轉換
    14 傅立葉轉換
    15時頻分析
    16樂曲識別與實習
    17語音訊號
    18 期末作業
     以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

    有關課程其他調查 Other Surveys of Courses

    1.本課程是否規劃業界教師參與教學或演講?
    Is there any industry specialist invited in this course? How many times?
    2.本課程是否規劃含校外實習(並非參訪)?
    Are there any internships involved in the course? How many hours?
    3.本課程是否可歸認為學術倫理課程?
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
    4.本課程是否屬進入社區實踐課程?
    Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?