Fourier series and LTI systems ?Time domain inputoutputSystem functionWhen input is periodic , the output is also periodic ! Fourier series and LTI systems ?Frequencydomain TransformFrequency respons
连续时间系统用N阶常系数微分方程描述则连续时间LTI系统的响应利用卷积积分可求出零状态响应(1) 特征根是不等实根s1 s2 ? sn齐次解yh(t)3) 求方程的全解[解] 系统的特征方程为(两相等实根) 冲激平衡法求系统的单位冲激响应2) 由动态方程右边d(t)的最高阶导数与方程 左边h(t)的最高阶导数确定d (j)(t)项.例1系统的单位冲激响应为h(t -τ)已知定义在区间( –
第三章 连续信号与系统的频域分析则可以展开为三角型傅里叶级数1. 偶函数: 则 只含有常数项和余弦项3. 偶谐函数: 则 只含偶次谐波由欧拉公式指数型和三角型傅里叶级数系数之间的关系称为抽样函数或取样函数 频谱图清晰地表征了周期信号的频域特性从频域角度反映了该信号携带的全部信息画频谱图时注意
冲激串抽样47对f (t): f m = 20kHz f s = 2 f m = 40kHz 信号 频谱所占带宽(包括负频率)为______ 1s若将它进行冲激抽样为使抽样信号频谱 不产生混叠最低抽样频率 f s=______Hz奈奎斯特间 隔 Ts =______ s H1(j?)H2(j?)H2(j?)f (t)5cos(1000? t)?(1cos4000?t)下一节
Imaginaryexponential signals Single frequency signal FrequencyPeriod Chapter 3Fourier Series Representation of Periodic SignalsEigenfunction of LTI systems Simple way to determine the output from inpu
The properties of LTI systems LTI System can be represented by its impulse response , so its properties Memoryless systems Amplifier ,adder, multiplier, …sas2-31Invertible systems sas2-32Causal system
Properties of continuous-time Fourier series ?Linearity If Then All signals must have same period T !sas3-21Linearity sas3-22Time shifting Magnitude will not change, but add a linear phase !sas3-23Ti
The Laplace transform and LTI systemSystem functionsas9-31The properties of LTI systems Memoryless systems Invertible systems sas9-32The properties of LTI systems Causal systemsis rational and its ROC
The z transform and LTI systemSystem functionsas10-31Representation of the LTI systems Pole-zero plot PolesZerosGain sas10-32The properties of LTI systems Memoryless systems Invertible systems sas10-3
Fourier transform and LTI systems In time domain System represented by its impulse response In frequency domain System represented by its frequency response sas4-31 The frequency response You can get
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