Chapter 16 - Adaptive Filters

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 2

Learning Objectives



Introduction to adaptive

filtering.



LMS update algorithm.



Implementation of an adaptive

filter using the LMS

algorithm.

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 3

Introduction



Adaptive filters differ from other filters such as FIR and IIR in the

sense that:



The coefficients are not determined by a set of desired specifications.



The coefficients are not fixed.



With adaptive filters the specifications are not known and change with

time.



Applications include: process control, medical instrumentation, speech

processing, echo and noise calculation and channel equalisation.

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 4

Introduction



To construct an adaptive filter the

following selections have to be made:



Which method to use to update the

coefficients of the selected filter.



Whether to use an FIR or IIR filter.

D ig ita l

F ilte r

A d a p tiv e

A lg o r ith m

e [n ] ( e r r o r s ig n a l)

d [n ] ( d e s ir e d s ig n a l)

y [n ] ( o u tp u t s ig n a l)

x [n ] ( in p u t s ig n a l)

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 5

Introduction



The real challenge for designing an adaptive filter

resides with the adaptive algorithm.



The algorithm needs to have the following properties:



Practical to implement.



Adapt the coefficients quickly.



Provide the desired performance.

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 6

The LMS Update Algorithm



The basic premise of the LMS algorithm

is the use of the instantaneous

estimates of the gradient in the steepest

descent algorithm:



It has been shown that (Widrow and Stearns, 1985):



Finally:



step size parameter



n,k

= gradient vector that makes

H(n) approach the optimal

value H

opt

 











  









 

  













e(n) is the error

signal, where: e(n) =

d(n) - y(n)

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 7

LMS algorithm Implementation

I n itia lis a tio n 1

h [ n ] = 0

I n itia lis a tio n 2

y = 0

A c q u is itio n

r e a d th e in p u t s a m p le s : x [ n ] ,

d [ n ]

C o m p u ta tio n 1





]

[

]

[

C o m p u ta tio n 2

e = d - x





C o m p u ta tio n 3

 















U p d a te

x ( i ) = x ( i - 1 )

O u tp u t y

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 8

temp = MCBSP0_DRR;

// Read new sample x(n)

X[0] = (short) temp;
D = X[0];

// Set desired equal to x(n) for this
// application

Y=0;

for(i=0;i<N;i++)

Y = Y + ((_mpy(h[i],X[i])) << 1) ;

// Do the FIR filter

E = D -(short) (Y>>16);

// Calculate the error

BETA_E =(short)((_mpy(beta,E)) >>15);

// Multiply error by step size parameter

for(i=N-1;i>=0;i--)
{

h[i] = h[i] +((_mpy(BETA_E,X[i])) >> 15);

// Update filter coefficients

X[i]=X[i-1];

}

MCBSP0_DXR = (temp &0xffff0000) | (((short)(Y>>16))&0x0000ffff);

// Write output

LMS algorithm Implementation

Dr. Naim
Dahnoun,
Bristol U
niversity
, (c) Te
xas Instr
uments 20
04

Chapter 16, Slide 9

Adaptive Filters Codes



Code location:



\Code\Chapter 16 - Adaptive Filter\



Projects:



Fixed Point in C:

\Lms_C_Fixed\



Floating Point in C:

\Lms_C_Float\



Fixed Point in Linear Asm:

\Lms_Asm_Fixed\



Further reading:



Widrow and Stearns, 1985...

Document Outline