Motivation for the Laplace transform CT Fourier transform enables us to do a lot of things, e. g Analyze frequency response of lTi systems Sampling Modulation Why do we need yet another transform? One view of Laplace Transform is as an extension of the Fourier
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1.aM with an Arbitrary Periodic Carrier 2. Pulse Train Carrier and Time-Division Multiplexing 3. Sinusoidal Frequency modulation 4. DT Sinusoidal am 5. DT Sampling, Decimation,d Interpolation
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then, assuming we choose wM
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More efficient to transmit e&m signals at higher frequencies Transmitting multiple signals through the same medium using different carriers Transmitting through\channels, with limited passbands
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SAMPLING We live in a continuous-time world most of the signals we encounter are CT signals, e.g. x(). How do we convert them into Dt signals x[n? Sampling, taking snap shots of x(t) every Seconds
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Result: Linear phase e simply a rigid shift in time, no distortion Nonlinear phase e distortion as well as shift DT
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1. DTFT Properties and Examples 2. Duality in fs& ft 3. Magnitude/Phase of Transforms and Frequency Responses
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Convergence Issues Synthesis equation: None. since integrating over a finite interval Analysis Equation: Need conditions analogous to CTFT, e. g
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Fourier series: Periodic signals and lti Systems ()=∑H(k k= ak一→H(ko)ak “g Soak-→|H(jkco)lkl H(7k)=1H(k0e∠B(ko) or powers of signals get modified through filter/system ncludes both amplitude phase akeJhwon
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Convolution Property 0(t)=h(t)*(t)←→Y(j)=H(ju)X( where h(t)←→H(ju) A consequence of the eigenfunction property
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南京邮电大学：《数字电路与系统设计》课程教学资源（PPT课件讲稿）第四章 组合逻辑电路（4.2）比较器（3/3）电子技术：《模拟电路与数字电路》课程电子教案（PPT课件讲稿，数字电路）第五章 时序逻辑电路《C语言程序设计导论》课程电子教案（PPT教学课件）第一章 程序设计概述电子科技大学：《图像处理及应用 Image Processing and Application》课程教学资源（课件讲稿）Chapter 02 数字图像处理基础 Fundamentatals of Digital Image《数字信号处理》课程教学课件（2020讲稿）第三章 离散傅里叶变换 §3-1 引言 §3-2 傅里叶变换的几种形式北京交通大学：《光纤测量原理》课程教学课件（PPT讲稿）第三讲 光纤折射率分布测量海南大学：《通信原理》课程教学资源（PPT课件讲稿）第五章 数字基带传输系统（5.3）基带传输的常用码型中国矿业大学信电学院：《数字电子技术》课程教学资源（PPT课件讲稿）第四章 组合逻辑电路《电工学》课程PPT教学课件（电子技术）第06章 晶闸管及其应用《信号与系统》课程教学大纲 signals and systems《电子技术基础》课程PPT教学课件（数字部分）03 逻辑门电路