Frequency Domain Adaptive Filtering

Project SupervisorDr. Edward Jones

Myles Ó Fríl

Adaptive Filters

Digital Filter Adaptive Algorithm Convolution Time Domain Algorithms The LMS Algorithm

Updated Valueof tap-weight

vector

Old Value oftap-weight

vectorx

Learningrate

parameter+ Tap-input

vectorx ErrorSignal

System Identification

UnknownSystem

AdaptiveFilter

+

X(n) d(n)

e(n)

-

+

y(n)

Echo Cancellation

Transmitter

Receiver

HybridAdaptive

Filter

+

-+

Hybrid

Transmitter

AdaptiveFilter

Receiver+

-+

CommonLine

X(n) X(n)

e(n) e(n)

Speaker A

Speaker EchoReturn Paths

CleanSignal

CleanSignal

Speaker B

Y(n) Y(n)

Speaker Bsignal + echo of A

Speaker Asignal + echo of B

Frequency Domain Filtering

Discrete Fourier Transform Fast Fourier Transform N a power of two Time Convolution Theorem Efficiency Overlap Save

Overlap Save Filtering

Input Block Length 2N N Zeros + Impulse Response

2N point FFT 2N point FFT

Y(f) = X(f) x H(f)

2N point IFFT

Y(n) + circular artifacts

Frequency Domain AdaptiveFiltering Algorithm

Fast LMS Overlap Save Filtering Block Diagram of Fast LMS

FFT IFFTX Save Last Block

+ Delay

X

FFT

AppendZero Block

Delete LastBlock

IFFT

X FFT AppendZero Block +

Conjugate

d(n)

y(n)

GradientConstraint

u(n)

mu

U(k) Y(k)

U*(k) E(k) e(n)

Memory Comparison

LMS

N inputs + N filter coefficients

= 2N

Fast LMS

15 N in total

Computational Comparison

LMS2N x N

Fast LMS 15N log2 (2N) + 10N for 5 FFTs

+ 28N for rest of algorithm Cross Over Point

N a power of two

128

LMS V Fast LMS

0 100 200 300 400 500 6000

2

4

6

8

10

12x 10

6

Num

ber

of o

pera

tions

Length of impulse Response

Frequency V Time Domain Operations

Time Domain

Frequency Domain

Implementation

The NIDAQ Card

Threads

Main Program

Write and ReadValues from

the NIDAQ card

Start Fast LMSThread

Get morevalues

N

Y

End Program

Further Applications

Training Period Decision Maker Time Domain Frequency Domain

AdaptiveEqualizer

DecisionDevice

TrainingSequenceGenerator

+-

+

e(n)

y(n) d1(n) d(n)x(n)

Adaptive Equalizer

Summary

Adaptive Filters System Identification Frequency Domain Filtering Frequency Domain Adaptive Algorithm Memory/Computational Comparison Implementation

Any Questions?