教學觀摩會 電信系 謝世福
課程網頁進度表 學習指標 難度 : ★☆ 重要性 : ★★★ ★★★ 厭惡感 : ★★★ 上課日期課程進度、內容、主題 Feb 18(Mon) 1.Definitions of Signals and Systems. 2.Signal classifications. 3.Analog x(t), digital x[n] 4.Size of a signal: (total) Energy and (average) Power [ 難度 : ★, 重要性 : ★ ] 5.§1.5 Basic Signal operations: time shift(delay): x(t-b), time-scale: x(at), time-reverse x(-t) [ 難度 : ★☆, 重要性 : ★★ ] 6.combined operation: 口訣 : 先減加 x(t+b), 後除乘 x(at+b) Feb 25(Mon) 1.§1.6.6 Impulse function δ[n] & δ(t), Text-pp-53. [ 難度 : ★☆, 重要性 : ★★ ] a) Sifting properties b) Decomposition of a signal into sum/integral of scaled shifted impulses. i). useful to derive convolution of LTI systems, y=x*h, the output is a scaled, shifted impulse responses ii). A signal is decomposed onto time-orthogonal bases. Another frequency-orthogonal bases use complex exponentials. 2. Properties: a) u(t) = integral of δ(t) b) δ(t) = d/dt u(t) [Q] Find and plot the derivative of a 'birthday cake' function.
Homework Textbook reading: [Interconnected systems] Draw the block diagrams of a cascaded} and a parallel connected systems, respectively. [pp 54] [3 basic functional blocks] What are the input/output relationships of a time-shifter, an adder, and a scalar multiplication, respectively? [pp 54] 請分別利用 數學式, 方塊圖, 與 物理意義來描述一個 線性 系統. [pp 63-7] … Problems (10%) [Modulator] Haykin Problem 1.84, pp 95. (30%) [System property validation] Haykin Problem 1.64(a,d,i,j,k), pp 91. (30%) [MATLAB simulation] Use MATLAB to generate a 440Hz periodic square wave..... Use MATLAB to generate a 440Hz periodic square wave.....
Fourier Transform
Fourier Transform: Time/Freq 數學式 : x( t) X(f/ )/| | 音樂例子 : x(t) 大提琴原音 x(t) 大提琴原音 x(t) 大提琴原音 x(2t) 音調略高的中提琴 x(2t) 音調略高的中提琴 x(2t) 音調略高的中提琴 x(3t) 更尖銳的小提琴 x(3t) 更尖銳的小提琴 x(3t) 更尖銳的小提琴 x(t/2) 低沉的 doublebass x(t/2) 低沉的 doublebass x(t/2) 低沉的 doublebass
Sampling theorem DDDD Demo: (a) goldberg 原音 goldberg 原音goldberg 原音 (b) aliasing( 取樣不足 ): sol-la-si mi-re-do (b) aliasing( 取樣不足 ): sol-la-si mi-re-doaliasing( 取樣不足aliasing( 取樣不足 Demo: (a) goldberg( 原音 ), (b) aliasing( 取樣不足 ): la-si-DO mi-re-do
LTI System and Convolution
Convolution demo
Conclusions 教學相長 生活化的觸媒 知識的鍊結 簡化, 單純