邬震宇-信号与系统 3.pptVIP

* * * * * Example 3.5.1: The real signal is Determine and the trigonometric function expression Solution: ， §3.5.8 Parseval’s Relation §3.5.9 Differentiations Total average power in a periodic signal equals to the sum of the average power in all of its harmonic components table 3.1 e.g. 3.9 * FS定义式 2. 周期方波和冲击串的FS 3. FS的性质 3.6.1 Linear Combination of Harmonically Related Complex Exponentials Periodic signal x[n] with period N: x[n]=x[n+N] § 3.6 Fourier Series Representation of Discrete-time Periodic Signals Discrete-time complex exponential orthogonal signal set: * Property of orthogonal signal set: * 3.6.2 Determination of the Fourier Series Representation of Periodic Signals Fourier series of periodic signal x[n]: Determine the coefficients ak by orthogonality: * The equations of Fourier series: ( ak is periodic ) * Example 3.10 3.12 x[n] ak * §3.7 Properties of DT FS Table 3.2 E.g. 3.14 * * 1 Fourier Series and CT LTI Systems Problem * (Linearity) Steps: (1). Take Fourier series expansion (2). Calculate system eigenvalue . is periodic with T 补充例题 * Example 3.8.1 The CT LTI system impulse response is Determine the system response y (t) to the input f(t). Solution： 1 So, * 2 Calculate the system eigenvalue System response Note: is imaginary and odd. * The magnitude and phase are: LTI Example 3.8.2 The CT LTI system impulse response is Determine the system response y (t) to the input Solution： * If h (t) is real， The system response should be * In this example The system response is * 2. FS and DT LTI system * 3.16, 3.17 § 3.9 Filtering 3.9.1 Frequency-shaping filters Example1: Equalizer * Example2: Image Filtering (Edge en