Signals and Systems Lecture 18: FIR Filters.

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Presentation transcript:

Signals and Systems Lecture 18: FIR Filters

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

Hardware Structures

Linear Time-invariant Systems

Linear Time-invariant Systems: FIR Filters

Overview

Digital Filtering

Building Blocks

LTI: Convolution Sum

Convolution Example

System Properties

Time Invariance

Testing Time-Invariance

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

Linear System

Testing Linearity

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