PROPERTIES OF Z-TRANSFORM Pamarthy.Chennarao HOD ECE Dept. PALADUGU PARVATHI DEVI COLLEGE OF ENGINEERING

Slide 2:

PROPERTIES OF Z- TRANSFORM 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 2

Slide 3:

LINEAR PROPERTY: Let x 1 (n), x 2 (n) are two discrete sequences and ZT[ x 1 (n) ] = X 1 (z), ZT[ x 2 (n) ] = X 2 (z), then according to linear property of z transform ZT[ a x 1 (n) + b x 2 (n) ] = a X 1 (z) + b X 2 (z) PROOF: From basic definition of z transform of a sequence x(n) Replace x(n) by a x 1 (n) + b x 2 (n) 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 3

Slide 4:

TIME SHIFTING PROPERTY: Let x(n) be a discrete time sequences and ZT[ x(n) ] = X(z), then according to time shifting property of z transform ZT[ x(n – n 0 ) ] = z -no X(z) PROOF: From basic definition of z transform of a sequence x(n) Replace x(n) by x(n – n o ) 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 4

Slide 5:

TIME REVERSAL PROPERTY : Let x(n) be a discrete time sequence and ZT[ x(n) ] = X(z), then according to time reversal property of z transform ZT[ x(– n) ] = X(1/z) PROOF: From basic definition of z transform of a sequence x(n) Replace x(n) by x(– n) 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 5

Slide 6:

TIME CONVOLUTION THEOREM: Let x 1 (n), x 2 (n) are two discrete time sequences and ZT[ x 1 (n) ] = X 1 (z), ZT[ x 2 (n) ] = X 2 (z), then according to time convolution theorem of z transform ZT[ x 1 (n) x 2 (n) ] = X 1 (z) X 2 (z) PROOF: From basic definition of z transform of a sequence x(n) Replace x(n) by x 1 (n) x 2 (n) 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 6

Slide 7:

CONJUGATE PROPERTY : Let x(n) be a discrete time sequence and ZT[ x(n) ] = X(z), then according to conjugate property of z transform ZT[ x*(n) ] = X*(z*) PROOF: From basic definition of z transform of a sequence x(n) Replace x(n) by x*(n) 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 7

Slide 8:

DERIVATIVE PROPERTY : Let x(n) be a discrete time sequence and ZT[ x(n) ] = X(z), then according to derivative property of z transform ZT[ n x(n) ] = - d/dz [ X(z) ] PROOF: From basic definition of z transform of a sequence x(n) Differentiate w.r.t z 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 8

Slide 9:

INITIAL VALUE THEOREM : Let x(n) be a discrete time causal sequence and ZT[ x(n) ] = X(z), then according to initial value theorem of z transform PROOF: From basic definition of z transform of a sequence x(n) Apply as z 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 9

Slide 10:

FINAL VALUE THEOREM : Let x(n) be a discrete time causal sequence and ZT[ x(n) ] = X(z), then according to final value theorem of z transform PROOF: From basic definition of z transform of a causal sequence x(n) Replace x(n) by x(n) – x(n – 1) Apply as z 1 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 10

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

Send to Blogs and Networks

Processing ....

Premium member

Use HTTPs

HTTPS (Hypertext Transfer Protocol Secure) is a protocol used by Web servers to transfer and display Web content securely. Most web browsers block content or generate a “mixed content” warning when users access web pages via HTTPS that contain embedded content loaded via HTTP. To prevent users from facing this, Use HTTPS option.

By: haichenna (68 month(s) ago)

nice it is good