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1、BEIJING JIAOTONG UNIVERSITYThe Course Group of Signals and Systems,Beijing Jiaotong University.P.R.CHINA.Copyright 2020Signals and Systems Basic Operations on C-T Signals Time reflection Time compression Time extension Time shifting Addition Multiplication Differentiation Integration1.Time Reflectio
2、nx(t)x(-t)Flip signal x(t)about the origin2.Time Compression and Extension0a1,time compressionx(t)x(at)a02.Time Compression and Extensionx(t)x(t/2)x(2t)normalfasterslowerSimulate acoustic signals played faster or slower Chinese audioSample rate:22050Hz3.Time Shiftingx(t)x(t t0)t00 x(t-t0)shifted to
3、the right by t0 x(t+t0)shifted to the left by t0Signal delay in telecommunicationTransmitting endReceiving endChannel3.Time Shifting Example 1:Given x(t),plot the waveform of x(6-2t)Solutions:Invariant Function Values at TerminalsPrinciple:the time reflection,scaling and shifting are linear changes
4、of the independent variable,which do not change the function values at the terminals.Plot the waveform of x(6-2t)Invariant Function Values at TerminalsPrinciple:the time reflection,scaling and shifting are linear changes of the independent variable,which do not change the function values at the term
5、inals.Invariant Function Values at TerminalsPrinciple:the time reflection,scaling and shifting are linear changes of the independent variable,which do not change the function values at the terminals.Example:Given the waveform of x(3t+2),plot the waveform of x(6-2t)Example 2:Given x(t)shown below,plo
6、t the waveform of x(3t).Summary Time reflection Time compression Time extension Time shiftingx(t)x(-t)x(t)x(at)a1x(t)x(at)0a0 The time reflection,scaling and shifting are linear changes of the independent variable,which do not change the function values at the terminals.Invariant Function Values at TerminalsAcknowledgmentsMaterials used here are accumulated by authors for years with help from colleagues,media or other sources,which,unfortunately,cannot be noted specifically.We gratefully acknowledge those contributors.Basic Operations on C-T Signals