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1、BEIJING JIAOTONG UNIVERSITYThe Course Group of Signals and Systems,Beijing Jiaotong University.P.R.CHINA.Copyright 2020Dr.Yanfeng LISignals and Systems Basic Operations on D-T Signals Time reversal Time shifting Decimation Interpolation Addition Multiplication Difference Summation1.Time Reversalxk x
2、-kFlip xk horizontally about the origin2.Time Shiftingxk xk n n0 xk-n to shift xk right by n units xk+n to shift xk left by n units 3.DecimationDownsampling MPick every M point(keeping the point at the origin)xkxMk,M is a positive integerM=23.Decimation originaldecimated by 4x,Fs,bits=wavread(我的祖国);
3、%Fs=22,050 Hzdecimated by 8x1=x(1:4:end);%Fs=22,050/4 Hzx2=x(1:8:end);%Fs=22,050/8 Hz The signal is distorted3.Interpolation Upsampling LInsert L-1 more points between the original neighboring pointsL=2Example 1:Given a D-T sequence,get x-3k+2.Shifting right by 2Decimation by 3 Sequence Decimation a
4、nd InterpolationSolution:Exercise 1:Given the waveform of a sequence xk,show the waveform of x-2k+3.4.AdditionSeveral sequences added together pointwise5.MultiplicationSeveral sequences multiplied together pointwise6.Difference The unit impulse sequence is the 1st order backward difference of the un
5、it step sequence1st order backward2nd order backwardNth order backward1st order forward difference7.Summation 7.Summation The unit step sequence can be represented with the summation of the unit impulse sequenceThe ramp sequence rk+1 can be represented with the summation of the unit step sequenceNot
6、 rk Summary Time reversal Time shifting Decimation Interpolation Addition Multiplication Difference SummationBasic Operations on D-T SignalsApplied on the independent variableApplied on the dependent variableAcknowledgmentsMaterials 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 D-T Signals