Download presentation

Presentation is loading. Please wait.

Published byVictoria Grant Modified over 6 years ago

1
**Signals and Systems Fall 2003 Lecture #3 11 September 2003**

1) Representation of DT signals in terms of shifted unit samples 2) Convolution sum representation of DT LTI systems 3) Examples The unit sample response and properties of DT LTI systems

2
**Exploiting Superposition and Time-Invariance**

Question:Are there sets of “basic” signals so that: a) We can represent rich classes of signals as linear combinations of these building block signals. b) The response of LTI Systems to these basic signals are both simple and insightful. Fact: For LTI Systems (CT or DT) there are two natural choices for these building blocks Focus for now: DT Shifted unit samples CT Shifted unit impulses

3
**Representation of DT Signals Using Unit Samples**

4
**SignalsThe Sifting Property of the Unit Sample**

That is .. Coefficients Basic Signals SignalsThe Sifting Property of the Unit Sample

5
**Suppose the system is linear, and define hk[n] as the**

response to δ[n -k]: From superposition:

6
**Now suppose the system is LTI, and define the unit **

sample response h[n]: From TI: From LTI: Convolution Sum

7
**Convolution Sum Representation of Response of LTI Systems**

Interpretation Sum up responses over all k

8
**Visualizing the calculation of**

Choose value of n and consider it fixed View as functions of k with n fixed prod of overlap for prod of overlap for

9
**Calculating Successive Values: Shift, Multiply, Sum**

10
**Properties of Convolution and DT LTI Systems**

A DT LTI System is completely characterized by its unit sample response There are many systems with this repsonse to There is only one LTI Systems with this repsonse to

11
- An Accumulator Unit Sample response

12
Step response of an LTI system step input “input” Unit Sample response of accumulator

13
**The Distributive Property**

Interpretation

14
**The Associative Property**

Implication (Very special to LTI Systems)

15
**Properties of LTI Systems**

Causality Stability

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google