4.0 引言 4.1 非周期信号的表示（连续时间傅里叶变换） 4.2 周期信号的傅里变换 4.3 连续傅里叶变换的性质 4.4 卷积性质 4.5 相乘性质 4.6 傅立叶变换性质和基本傅里叶变换对列表 4.7 由线性常系数微分方程表征的LTI系统

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

◆2.1 Discrete-Time Signals: Sequences ◆High and Low Frequencies in Discrete-time signal ◆2.2 Discrete-Time Systems ◆Memoryless (memory); Linear; Time-Invariant; Causality; Stability(BIBO) ◆2.3 Linear Time-Invariant (LTI) Systems ◆LTI Systems:Convolution( 系统适用吗?) ◆2.4 Properties of LTI Systems ◆Stability and Causality of LTI systems;FIR and IIR systems ◆2.5 Linear Constant-Coefficient Difference Equations ◆The output for a given input is not uniquely specified. Auxiliary conditions are required; initial-rest conditions ◆2.6 Frequency-Domain Representation of Discrete￾Time Signals and systems ◆ Eigenfunction and Eigenvalue for LTI systems ◆2.7 Representation of Sequences by Fourier Transforms ◆2.8 Symmetry Properties of the Fourier Transform ◆2.9 Fourier Transform Theorems ◆2.10 Discrete-Time Random Signals

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

Representation of ct signals Approximate any input x(t) as a sum of shifted, scaled

◆2.0 Introduction ◆2.1 Discrete-Time Signals: Sequences ◆2.2 Discrete-Time Systems ◆2.3 Linear Time-Invariant (LTI) Systems ◆2.4 Properties of LTI Systems ◆2.5 Linear Constant-Coefficient Difference Equations

◼ Introduction ◼ Discrete-time signals ◼ Discrete-time systems ◼ Time-domain characterization of LTI discrete-time systems ◼ Digitalization of Analog Digital

Modulation Representing digital signals as analog waveforms Baseband signals Signals whose frequency components are concentrated around zero Passband signals Signals whose frequency components are centered at some frequency fc away from zero Baseband signals can be converted to passband signals through modulation Multiplication by a sinusoid with frequency fc Eytan Modiano

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 COMPUTER LAB 2 Issued: October 7. 2003

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 PROBLEM SET 4 SOLUTION Home Study Exercise -o&e W 3.63