《信号与线性系统分析基础 》 课件 6.3 常系数线性差分方程的解.ppt

信号与系统SignalsandSystems吉林大学

Propertiesofthez-Transform——Linearity

Iff1(k)?F1(z),?1?z??1，f2(k)?F2(z),?2?z??2，thenLinearityExample:

Iff1(k)?F1(z),?1?z??1，f2(k)?F2(z),?2?z??2，thenLinearityExample:

信号与系统SignalsandSystems吉林大学

Propertiesofthez-Transform——TimeShifting

TimeShiftingExample:Bilateralz-TransformIff(k)?F(z),??z??,thenwheremisapositiveinteger.

TimeShiftingProof:Unilateralz-Transform——RightshiftIff(k)?F(z)，?z??，thenwheremisapositiveinteger.

TimeShiftingUnilateralz-Transform——RightshiftIff(k)=0,k0,thenExample:Iff(k)?F(z)，?z??，thenwheremisapositiveinteger.

TimeShiftingUnilateralz-Transform——LeftshiftIff(k)?F(z)，?z??，thenwheremisapositiveinteger.Proof:

TimeShiftingUnilateralz-Transform——LeftshiftIff(k)?F(z)，?z??，thenwheremisapositiveinteger.Example:?(k+1)

信号与系统SignalsandSystems吉林大学

Propertiesofthez-Transform——Scalinginthez-Domain

Scalinginthez-DomainProof:Iff(k)?F(z),R1|z|R2，thenaisanonzerorealorcomplexnumber.ROCofF(z):ROCof:

Scalinginthez-DomainIff(k)?F(z),R1|z|R2，thenaisanonzerorealorcomplexnumber.Example:aksin(?k)?(k)，0a1

Scalinginthez-DomainIff(k)?F(z),R1|z|R2，thenaisanonzerorealorcomplexnumber.Example:(-1)k?(k)

信号与系统SignalsandSystems吉林大学

Propertiesofthez-Transform——Convolution

ConvolutionProof:Iff1(k)?F1(z),?1?z??1,f2(k)?F2(z),?2?z??2,then

ConvolutionIff1(k)?F1(z),?1?z??1,f2(k)?F2(z),?2?z??2,thenExample:(k+1)?(k)LTIsystems:

信号与系统SignalsandSystems吉林大学

Propertiesofthez-Transform——DifferentiationandIntegralinthez-Domain

Differentiationinthez-DomainProof:Iff(k)?F(z),??z??,then wherekisanypositiveinteger.

Differentiationinthez-DomainIff(k)?F(z),??z??,then wherekisanypositiveinteger.Example:Ifa=1,then

Differentiationinthez-DomainIff(k)?F(z),??z?