logging in or signing up PROPERTIES OF Z-TRANSFORM haichenna Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 1281 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: February 03, 2011 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... By: haichenna (15 month(s) ago) nice it is good Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript PROPERTIES OF Z-TRANSFORM: PROPERTIES OF Z-TRANSFORM Pamarthy.Chennarao HOD ECE Dept. PALADUGU PARVATHI DEVI COLLEGE OF ENGINEERINGSlide 2: PROPERTIES OF Z- TRANSFORM 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 2Slide 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 3Slide 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 4Slide 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 5Slide 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 6Slide 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 7Slide 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 8Slide 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 9Slide 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.
PROPERTIES OF Z-TRANSFORM haichenna Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 1281 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: February 03, 2011 This Presentation is Public Favorites: 0 Presentation Description No description available. Comments Posting comment... By: haichenna (15 month(s) ago) nice it is good Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript PROPERTIES OF Z-TRANSFORM: PROPERTIES OF Z-TRANSFORM Pamarthy.Chennarao HOD ECE Dept. PALADUGU PARVATHI DEVI COLLEGE OF ENGINEERINGSlide 2: PROPERTIES OF Z- TRANSFORM 2/3/2011 P.CHENNARAO,HOD ECE DEPT,PPDCET 2Slide 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 3Slide 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 4Slide 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 5Slide 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 6Slide 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 7Slide 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 8Slide 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 9Slide 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