CT321 Digital Signal Processing Yash Vasavada Autumn 2016

CT-321 Digital Signal Processing Yash Vasavada Autumn 2016 DA-IICT Lecture 13 Z Transform 7 th September 2016

Review and Preview • Review of past lecture: – Inverse Z Transform • Preview of this lecture: – Properties of Z Transform and their Applications – Linear Constant Coefficient Difference Equations • Reading Assignment – OS: Chapter 3 and Chapter 4 – PM: Chapter 3 and Chapter 4 section 4. 4 Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 2

Properties of Z Transform • Refer to Section 4 of Chapter 3 Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 3

Application of the Properties of Z Transform • We will make use of only the following Z Transform Pair: • Time-shifting property: • Time reversal property: • Differentiation property: • Exponential multiplication property: Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 4

Linear Constant-Coefficient Difference Equations • Take Z Transform of both sides of LCCDE: Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 5

Accumulator Expressed as LCCDE • Representation of the accumulator in time domain: • …and in Z domain: Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 6

A Moving Sum Expressed as LCCDE • • Therefore: • LCCDE representation of Moving Sum: • Z Transform Representation Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 7

Z Transform of Finite Duration Sequences • ROC ROD Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 8

Frequency Response of LTI Systems • Yash Vasavada DA-IICT. Autumn 2016 CT-321. Lecture 13: 7 th September 2016. 9