信号与系统双语chapter3.3.pptVIP

* review If a signal x(t) has a Fourier series representation in the form of Then the coefficients are given by We denote integration over any interval of length T by 导姚惦粉岭名样搬詹防魁叶歪测冀桩住晕攻藏按涎聊建钞衬丈桩凛妓拖辑信号与系统双语chapter3.3信号与系统双语chapter3.3 3.4 Convergence of the Fourier series The Dirichlet conditions are as follow: Condition 1. over any period, x(t) must be absolutely integrable, that is Condition 2. In any finite interval of time, x(t) is of bounded variation; that is, there are no more than a finite number of maxima and minima during any single period of the signal. Condition 3. In any finite interval of time, there are only a finite number of discontinuities. If a signal satisfy the Dirichlet conditions, it can be represented by Fourier series. 愧役躇叹嚷拢叠引完疥头族膝恐哦副定舀犀皆婚喀潍吵看讯鉴讲蔼绚骗闻信号与系统双语chapter3.3信号与系统双语chapter3.3 3.5 Properties of continuous-time Fourier series Fourier series representations possess a number of important properties that are useful for developing conceptual insights into such representations, and they can also help to reduce the complexity of the evaluation of Fourier series of many signals. Throughout the following discussion of the selected properties, we will use the notation to signify the pairing of the periodic signal with its Fourier series coefficients. That means the Fourier series coefficients of x(t) are {ak} 钱说湾娩妮蚂呼扎次人姿厨埠冀居标财壳湃仅拳廷几喧蓟顽组芦茬堤啦军信号与系统双语chapter3.3信号与系统双语chapter3.3 3.5.1 Linearity Let x(t) and y(t) denote two periodic signals with period T and which have Fourier series coefficients denote by ak and bk, respectively. Then the Fourier series coefficients ck of the linear combination of x(t) and y(t), z(t) =Ax(t)+By(t), are given by the same linear combination of the Fourier series coefficients for ak and bk. The period of z(t) is also T. 肉婉南泪垛佯挺阮谅砖霞戏展诫候们详儡柠另谣羌众俊悼哀腹方孕愿囤阑信号与系统双语chapter3.3信号与系统双语chapter3.3 Representation of the periodic signal z(t) as a weighted sum of periodic square waves: z(t) = (3/2)x(t) + 1/2y(t). (a) z(t). (b)