14 Digital Signal Processing W.K. Jenkins, A. D. Poularikas, B. W. Bomar, L.M. Smith, J.A. Cadzow Fourier Transforms er Transforms and the Fast Fourier Transform. Design and Imple of Digital Filters.Signal Restoration

1 具紧支集的光滑函数 2 广义函数 3 缓增分布及 Fourier 变换 Fourier 变换 Schwarz 函数类 缓增分布

S14-2 Exponential Fourier series f(t)=+ cosot+a2 cos 2ot+.] sinot+ b2 sin

Any periodic waveform f(t)f(t) can be expressed by a Fourier series provided that (1) If it is discontinuous, there are only a finite number of discontinuous in the period T (2)It has a finite average value over the period T (3)It has a finite number of positive and negative maximums in the period T

1.由例16.1.2的结果

1.设y(x)在[0,+∞)上连续且单调,limy(x)=0,证明

一、Fourier变换的几种可能形式 二 、周期序列的DFS及其性质 三、离散傅里叶变换（DFT） 四、离散傅里叶变换的性质 六 、抽样z变换——频域抽样理论 七 、用DFT对模拟信号作频谱分析 八 、序列的抽取与插值

时域分析方法 变换域分析方法： 连续时间信号与系统 Laplace变换 Fourier变换 离散时间信号与系统 z变换 Fourier变换 一、z变换的定义及收敛域 二、z反变换 三、z变换的基本性质与定理

2.1 Discrete-time signals:sequences 2.1.1 Definition 2.1.2 Classification of sequence 2.1.3 Basic sequences 2.1.4 Period of sequence 2.1.5 Symmetry of sequence 2.1.6 Energy of sequence 2.1.7 The basic operations of sequences 2.2 Discrete-time system 2.2.1 Definition：input-output description of systems 2.2.2 Classification of discrete-time system 2.2.3 Linear time-invariant system（LTI） 2.2.4 Linear constant-coefficient difference equation 2.2.5. Direct implementation of discrete-time system 2.3 Frequency-domain representation of discrete-time signal and system 2.3.1 definition of fourier transform 2.3.2 frequency response of system 2.3.3 properties of fourier transform

1.设交流电的变化规律为E(t)=Asin ot,将它转变为直流电的整流过程有两种类型: (1)半波整流(图16.1.5(a))