Adaptive Filters and Applications - Digital Signal Processing: Fundamentals and Applications - page 494

Noise source

Primary noise

Error

Reference Secondary

speaker

m c m c n

yn ()

xn ()

ANC

en ()

(a)

Physical model

dn ()

xn ()

P z ()

yn () en ()

xn ()

W z () S z ()

-

un ()

Adaptive
Algorithm

S z ()

(b)

Simulation model

FIGURE 10.32

An active noise control system.

Note that eðnÞ is measured from the error microphone.
The completed filtered-x LMS algorithm is summarized below:
1. Initialize wð 0 Þ , wð 1 Þ , . wðN 1 Þ to arbitrary values.
2. Read xðnÞ and perform digital filtering:

yðnÞ¼wð 0 ÞxðnÞþwð 1 Þxðn 1 Þþ / þ wðN 1 Þxðn N þ 1 Þ
3. Compute the filtered inputs:

uðnÞ¼sð 0 ÞxðnÞþsð 1 Þxðn 1 Þþ / þ sðM 1 Þxðn M þ 1 Þ

4. Read eðnÞ and update each filter coefficient:

for i ¼ 0 ; / ; N 1 ; wðiÞ¼wðiÞþ 2 meðnÞuðn iÞ;
Assuming the following:

Sampling rate ¼ 8,000 Hz and simulation duration ¼ 10 seconds
Primary noise: xðnÞ¼ 500-Hz sine wave
Primary path: PðzÞ¼ 0 : 2 þ 0 : 25 z 1

þ 0 : 2 z 2
Secondary path: SðzÞ¼ 0 : 2 5 þ 0 : 2 z 1
Secondary path estimate: SðzÞ¼SðzÞ¼ 0 : 2 þ 0 : 2 z 1 (can have slight error as compared

to SðzÞ )