1. Signals and Systems
Lecture 18:
FIR Filters

2. Today's lecture FIR Structures: Building Blocks
Linear Time-invariant Systems
System Properties:
Linearity
Time-invariance
Filters as Building Blocks

3. Hardware Structures

4. Linear Time-invariant Systems

5. Linear Time-invariant Systems: FIR Filters

6. Overview

7. Digital Filtering

8. Building Blocks

9. LTI: Convolution Sum

10. Convolution Example

11. System Properties

12. Time Invariance

13. Testing Time-Invariance

14. Examples of Time-Invariance
Square Law system
y[n] = {x[n]} 2
Time Flip system
y[n] = x[- n]
First Difference system
y[n] = x[n] - x[n-1]
Practice: Prove the system given Exercise 5.9 is not time-invariant

15. Linear System

16. Testing Linearity