5. FIR Filters

Overview: In chapter 5 the class of FIR (finite-impulse-response) filters is introduced. These filters use a running weighted average to form the output from the input. In this chapter, we will exhibit the basic input-output structure of the FIR filter as a time-domain computation based on a feed-forward difference equation. The impulse response of the filter will be defined and shown to characterize the filter. The general concepts of linearity and time-invariance will also be presented. These properties characterize the class of filters that can be analyzed thoroughly by the mathematical methods of Fourier analysis.

Homework

Labs - MATLAB

Lab 07: Sampling, Convolution, and FIR Filtering

The goal of this lab is to learn how to implement FIR filters in MATLAB, and then study the response of FIR filters to various signals, including images and speech. As a result, you should learn how filters can create interesting effects such as blurring and echoes. In addition, we will use FIR filters to study the convolution operation and properties such as linearity and time-invariance. [Files]

mp02: Discrete Convolution GUI

This mini project concentrates on the use of dconvdemo a GUI for discrete-time convolution. This demo is exactly the same as the MATLAB functions conv() and firfilt() used to implement FIR filters. This demo illustrates an important point about the behavior of a linear, time-invariant (LTI) system. It also provide a convenient way to visualize the output of a LTI system.

Demos

5.18 Discrete Convolution Demo

p120 - This program helps visualize the process of discrete-time convolution.