Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 217

CHAPTER

7

Finite Impulse Response
Filter Design

CHAPTER OUTLINE

7.1 Finite Impulse Response Filter Format ........................................................................................... 217
7.2 Fourier Transform Design .............................................................................................................. 219
7.3 Window Method ........................................................................................................................... 230
7.4 Applications: Noise Reduction and Two-Band Digital Crossover....................................................... 253
7.4.1 Noise Reduction........................................................................................................253
7.4.2 Speech Noise Reduction ............................................................................................256
7.4.3 Noise Reduction in Vibration Signals...........................................................................257
7.4.4 Two-Band Digital Crossover ........................................................................................258
7.5 Frequency Sampling Design Method .............................................................................................. 262
7.6 Optimal Design Method................................................................................................................. 269
7.7 Realization Structures of Finite Impulse Response Filters ............................................................... 280
7.7.1 Transversal Form.......................................................................................................280
7.7.2 Linear Phase Form.....................................................................................................281
7.8 Coefficient Accuracy Effects on Finite Impulse Response Filters...................................................... 282
7.9 Summary of FIR Design Procedures and Selection of FIR Filter Design Methods in Practice .............. 285
7.10 Summary ................................................................................................................................... 288
7.11 MATLAB Programs ...................................................................................................................... 288

OBJECTIVES:
This chapter introduces principles of the finite impulse response (FIR) filter design and investigates design
methods such as the Fourier transform method, window method, frequency sampling method, and optimal
design method. Then the chapter illustrates how to apply the designed FIR filters to solve real-world
problems such as noise reduction and digital crossover for audio applications.

7.1 FINITE IMPULSE RESPONSE FILTER FORMAT
In this chapter, we describe techniques for designing finite impulse response (FIR) filters. An FIR filter
is completely specified by the following input-output relationship:
yðnÞ¼ K

i ¼ 0 b i xðn iÞ
¼ b 0 xðnÞþb 1 xðn 1 Þþb 2 xðn 2 Þþ / þ b K xðn KÞ

(7.1)