Chapter 16

Chapter 16

Adaptive Filters

Adaptive Filters

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

Chapter 16, Slide 2

Learning Objectives

Learning Objectives



Introduction to adaptive

Introduction to adaptive

filtering.

filtering.



LMS update algorithm.

LMS update algorithm.



Implementation of an adaptive

Implementation of an adaptive

filter using the LMS

filter using the LMS

algorithm.

algorithm.

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

Chapter 16, Slide 3

Introduction

Introduction



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

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

sense that:

sense that:



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

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



The coefficients are not fixed.

The coefficients are not fixed.



With adaptive filters the specifications are not known and change with

With adaptive filters the specifications are not known and change with

time.

time.



Applications include: process control, medical instrumentation, speech

Applications include: process control, medical instrumentation, speech

processing, echo and noise calculation and channel equalisation.

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

Introduction



To construct an adaptive filter the

To construct an adaptive filter the

following selections have to be made:

following selections have to be made:



Which method to use to update the

Which method to use to update the

coefficients of the selected filter.

coefficients of the selected filter.



Whether to use an FIR or IIR 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

Introduction



The real challenge for designing an adaptive filter

The real challenge for designing an adaptive filter

resides with the adaptive algorithm.

resides with the adaptive algorithm.



The algorithm needs to have the following properties:

The algorithm needs to have the following properties:



Practical to implement.

Practical to implement.



Adapt the coefficients quickly.

Adapt the coefficients quickly.



Provide the desired performance.

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 LMS Update Algorithm



The basic premise of the LMS algorithm

The basic premise of the LMS algorithm

is the use of the instantaneous

is the use of the instantaneous

estimates of the gradient in the steepest

estimates of the gradient in the steepest

descent algorithm:

descent algorithm:



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

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



Finally:

Finally:





=

=

step size parameter

step size parameter





n,k

n,k

= gradient vector that makes

= gradient vector that makes

H(n) approach the optimal

H(n) approach the optimal

value H

value H

opt

opt

 

 

.

,

1

k

n

n

n

k

h

k

h











  



.

,

k

n

x

n

e

k

n







 

 

  



.

1

k

n

x

n

e

k

h

k

h

n

n











e(n) is the error

e(n) is the error

signal, where: e(n) =

signal, where: e(n) =

d(n) - y(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

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

å







1

0

]

[

]

[

N

i

i

x

i

h

y

C o m p u ta tio n 2

e = d - x

e

e

´







C o m p u ta tio n 3

 

 





k

n

x

e

k

h

k

h

n

n











1

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

LMS algorithm Implementation

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

Chapter 16, Slide 9

Adaptive Filters Codes

Adaptive Filters Codes



Code location:

Code location:



\Code\Chapter 16 - Adaptive Filter\

\Code\Chapter 16 - Adaptive Filter\



Projects:

Projects:



Fixed Point in C:

Fixed Point in C:

\Lms_C_Fixed\

\Lms_C_Fixed\



Floating Point in C:

Floating Point in C:

\Lms_C_Float\

\Lms_C_Float\



Fixed Point in Linear Asm:

Fixed Point in Linear Asm:

\Lms_Asm_Fixed\

\Lms_Asm_Fixed\



Further reading:

Further reading:



Widrow and Stearns, 1985...

Widrow and Stearns, 1985...

Chapter 16

Chapter 16

Adaptive Filters

Adaptive Filters

- End -

- End -