NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Introduction to Digital Filter Analysis

The subject of digital filtering is quite large, and many books are devoted entirely to that subject from different points of view. This chapter discusses only the filter structures we need, such as basicFIR filters and BiQuads. The last section summarizes the main point of digital filter theory.

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Subsections

• Motivating Example and Overview
• FIR Filters
  • Convolution Representation
  • Finiteness
  • Causal FIR Filters
  • Transfer Function
  • Order
• The BiQuad Section
• Digital Filter Theory Summary
  • Linearity and Time-Invariance
  • Difference Equation
  • Convolution Representation of LTI Filters
  • Frequency Response
  • Phase Delay and Group Delay

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