仔细观察上一节中的几幅图像后可以得到这样的直觉:对于一般 的以2为周期的函数f(x),除了个别点之外(看来是不连续点),当 m→∞时,它的 Fourier级数的部分和函数序列{m(x)}

一、傅立叶变换 一离散时间傅立叶变换(Discrete-Time- Fourier Transform,DTFT)(定义、收敛条件、性质)离散傅立叶变换( Discrete Fourier Transform,DFT)(定义、性质) 二、Z变换(定义、收敛条件、逆变换、性质)

(1)x(n)是有限长序列,且长度为M。与 Fourier换和z变换不同,n仅定义在o,m-1]的整数区间上; (2)变换核为W=eN,将时域序列x(n)变换为频域序列X(k)

A.1 The Fourier transform The Fourier transform permits us to decompose a complicated field structure into elemental components. This can simplify the computation of fields and provide physical insight into their spatiotemporal behavior. In this section we review the properties of the transform and demonstrate its usefulness in solving field equations

人们最熟悉的简单函数无非两类：幂函数和三角函数。英国数学 家 Taylor 在 18 世纪初找到了用幂函数的（无限）线性组合表示一般 函数 f x( )的方法，即通过 Taylor 展开将函数化成幂级数形式

一、主要内容 1。 Fourier 级数 2。收敛定理（Dirichlet充分条件）

4.1 Representation of Aperiodic Signals :The Continuous-Time Fourier Transform

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

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