Review of Progress in Quantitative NDE 2007 Colorado School of Mines Golden, Colorado July 22 – July 27, 2007 Digital Audio Signal Processing and NDE:

Review of Progress in Quantitative NDE 2007Review of Progress in Quantitative NDE 2007Colorado School of MinesColorado School of Mines

Golden, ColoradoGolden, ColoradoJuly 22 – July 27, 2007July 22 – July 27, 2007

Digital Audio Signal Processing and NDE:Digital Audio Signal Processing and NDE:an unlikely but valuable partnershipan unlikely but valuable partnership

Patrick GaydeckiPatrick Gaydecki

School of Electrical and Electronic EngineeringSchool of Electrical and Electronic EngineeringThe University of ManchesterThe University of Manchester

PO Box 88PO Box 88Manchester M60 1QDManchester M60 1QD

United KingdomUnited Kingdom

[email protected]@manchester.ac.uk

[UK-44] (0) 161 306 4906[UK-44] (0) 161 306 4906

www.eee.manchester.ac.uk/research/groups/sisp/research/dspwww.eee.manchester.ac.uk/research/groups/sisp/research/dspwww.signalwizardsystems.comwww.signalwizardsystems.com

Characteristics of Real-Time DSP Systems

• DSP offers flexibility, allowing a single platform to be rapidly reconfigured for different applications

• Operations such as modulation, phase shifting, signal mixing and delaying are simply performed in software

• System performance is far more accurate than equivalent analogue systems

• However, considerable intellectual investment is required to design and program DSP platforms

analogue to digital converter

amplifier

loudspeakersystem

10100100100100100111111010101010010010101011010101001010110110101001011010010101010010100101001110100101010100101010010101

PC…PC…

…or DSP system

The Sound Transduction Process:sound energy electrical signal binary processed binary electrical signal sound energy

digital to analogue converter

amplifier

Sample frequency,

kHz

Nyquist frequency,

kHz

Filter coefficients, DSP56309

Filter coefficients, DSP56321

10 5 9888 55000

20 10 4888 27500

40 20 2489 13750

100 50 888 5500

200 100 450 2750

500 250 195 1100

1000 500 85 550

FIR Performance Figures forDSP56309 and DSP56321

DSP Systems at UoM:Generations II and III Processing Repertoire

• Standard filters, e.g. Butterworth etc.• Arbitrary FIR filters• Arbitrary IIR filters• Adaptive filters• Inverse filters• Echo• Real-time gain control• Mixing• Phase delays• Time delays• Real-time FFT and waveform capture• Sine and arbitrary wave synthesis

• Standard filters, e.g. Butterworth etc.• Arbitrary FIR filters• Arbitrary IIR filters• Adaptive filters• Inverse filters• Echo• Real-time gain control• Mixing• Phase delays• Time delays• Real-time FFT and waveform capture• Hilbert transform• Quadrature Signal Processing• Envelope detection• Sine and arbitrary wave synthesis• Tone generation• Shaped noise generation• Modulation, encoding and decoding• Vocoding• JTAG support• 3rd party software support (C++ design tools)

Generation II Generation III

24-bit Dual 24-bit Dual Channel CodecChannel Codec

24-bit Dual 24-bit Dual Channel CodecChannel Codec

Fla

sh

Fla

sh

me

mor

ym

em

ory

Fla

sh

Fla

sh

me

mor

ym

em

ory

Serial InterfaceSerial InterfaceSerial InterfaceSerial Interface

DSPDSPCoreCoreC

on

tro

l C

on

tro

l sy

stem

syst

emC

on

tro

l C

on

tro

l sy

stem

syst

em

Signal Wizard 2 Hardware Concept

Signal Wizard 2 Hardware

Signal Wizard 2 Software

FIR and IIRdesign area

Graphical display of filter

Hardware control: control: download, gain, adaptive, download, gain, adaptive,

delay, mixing etc.delay, mixing etc.

24-bit multichannel24-bit multichannel(6 in 8 out) 200 kHz Codec(6 in 8 out) 200 kHz Codec

24-bit multichannel24-bit multichannel(6 in 8 out) 200 kHz Codec(6 in 8 out) 200 kHz Codec

Flash Flash memorymemoryFlash Flash

memorymemory

USB InterfaceUSB InterfaceUSB InterfaceUSB Interface

DSPDSPCoreCore

Control Control systemsystem

Control Control systemsystem

Signal Wizard 3 Hardware Concept

JTAG InterfaceJTAG InterfaceJTAG InterfaceJTAG Interface Parallel InterfaceParallel InterfaceParallel InterfaceParallel Interface

S/PDIF S/PDIF interfaceinterfaceS/PDIF S/PDIF interfaceinterface

Signal Wizard 3Signal Wizard 3

550 million 550 million multiplications multiplications and additions and additions per secondper second

Signal Wizard 3 Software

Output signal

Transfer function

Unconditional stability yes no

Word length immunity good poor

Design ease easy unwieldy

Arbitrary response yes not in practice

Computational load high low

Analogue equivalent yes yes

1

0

][][][M

k

knxkhny

H zY z

X zh n z

n

n( )( )

( )[ ]

0

M

k

N

k

knykbknxkany10

][][][][][

N

n

n

M

m

m

n

m

znb

zma

znb...zbzma...zaa

zH

1

01

1

][1

][

][]1[1

][]1[]0[)(

FIRProperty / Filter type IIR

Basic Linear Filter Theory: dtxhty )()()(

Noise in audio can be classified into two types: narrowband (easy to remove) or broadband (difficult)

frequency

ampl

itude

audio signal

narrow bandnoise

frequency

ampl

itude

audio signal

broad band noise

easy

difficult

Finite Impulse Response (FIR) Filter Designusing the Frequency Sampling Approach

1

0

][][][M

k

knxkhny

elsewhere0][

elsewhere0][

][][

][][

][][][ 1

kH

kH

fkfkbkH

fkfkakH

kHFnwnh

i

r

li

lr

Arbitrary filter impulse response h[n] obtained by:

Output signal y[n] obtained by discrete-time convolution:

Precise phase control for each harmonic, to a resolution of 0.0001 degree. Application: real-time Hilbert transform.

)()()( 1 hh YFtyHty

0),(

0),()(

jY

jYYh

Phase Control

Infinite Impulse Response (IIR) Filter Design

M

k

N

k

knykbknxkany10

][][][][][

Digital Emulation of Analogue Networks I:Laplace to z-domain mapping

sL

1/sC

R

vin(t)

vout(t)

sL

1/sC

R

vin(t)

vout(t)

j

-j

-

j

-j

-

j

-j

1-1

j

-j

1-1

1)(

2

sRCLCs

sRCsH

s-domain

z-domain

js

TjTeez

1)(

2

sRCLCs

sRCsH

1

1

1

12

z

z

Ts

11

12

1

12

1

12

)(

1

12

1

12

1

1

z

zRC

Tz

zLC

T

z

zRC

TzH

LCT

b

T

RCa

22

2

11

1

1

1

1

1

1

1

)(

1

1

1

1

1

1

1

1

z

za

z

z

z

zb

z

za

zH

21

2

)1()22()1()(

zabzbba

azazH

)1(

)1(

)1(

)22(

)1(

2

1

0

ba

ab

ba

b

ba

a

22

11

20

1

)1()(

zz

zzH

]2[]1[]2[][][ 2100 nynynxnxny

Substitutions:

Digital Emulation of Analogue Networks II:The Bilinear z-transform (BZT)

Final difference equation:

Digital Emulation of Analogue Networks III:Real-Time Performance

-15

-10

-5

0

5

10

15

0 0.005 0.01 0.015 0.02

Time, s

Vo

lts

-15

-10

-5

0

5

10

15

0 0.005 0.01 0.015 0.02

Time, s

Vo

lts

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 2000 4000 6000 8000 10000

Frequency, Hz

Rel

ativ

e m

agn

itu

de

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 2000 4000 6000 8000 10000

Frequency, Hz

Rel

ativ

e m

agn

itu

de

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.005 0.01 0.015 0.02

Time, s

Vo

lts

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.005 0.01 0.015 0.02

Time, s

Vo

lts

0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0 2000 4000 6000 8000 10000

Frequency, Hz

Rel

ativ

e m

agn

itu

de

0.00

0.01

0.01

0.02

0.02

0.03

0.03

0.04

0 2000 4000 6000 8000 10000

Frequency, Hz

Rel

ativ

e m

agn

itu

de

Design

Realised

IIR Comb Filters and Pole-Zero Placement

))((

))((

))((

))((

))((

))(()(

12

12

32

32

10

101

0

nn

nnn

k k

k

pzpz

zzzz

pzpz

zzzz

pzpz

zzzz

pz

zzzH

))((

))(()(

10

10

pzpz

zzzzzH

111

110

001

000

jp

jp

jz

jz

21

211

20

200

2

11

20

10

1111

0000

21

21

)()(

)()()(

z

zz

jzjz

jzjzzH

]2[]1[2]2[]1[2][][ 1100 nynynxnxnxny 0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

0 2000 4000 6000 8000

Frequency, Hz

Rel

ativ

e m

agn

itu

de

0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

0 2000 4000 6000 8000

Frequency, Hz

Rel

ativ

e m

agn

itu

de

-600

-400

-200

0

200

400

600

0 0.01 0.02 0.03 0.04 0.05

Time, s

Vo

lts

-600

-400

-200

0

200

400

600

0 0.01 0.02 0.03 0.04 0.05

Time, s

Vo

lts

j

-j

1-1

j

-j

1-1

Use of Super Narrowband Filters in the Detection of Low Amplitude Ultrasonic Pulses Propagated through Seawater

via a Steel Structure

(Rito Mijarez)

7 m structure being lowered into the dockat Liverpool, UK

Location of transmitter

Instrumentationamplifier(x 400)

DigitalOscilloscope

super narrowband

filter

digital gain(x 2048)

DSPDSP

Microcontrolledpulser

Transmittingtransducer

Receivingtransducer

100 m

Signal type Tone burst

Frequency 40 kHz

Transmission amplitude

20 V

Divergence angle hemispherical

Attenuation Geometric (1/r2)

Peak received signal 650 nV

Experimental Configuration

Time

Am

plitu

de

Time

Am

plitu

de

Time

Am

plitu

de

Typical Results

(a) Detail of original received signal degraded by noise.

(b) Detail of received signal, recovered by super narrowband filter.

(c) Complete tone burst signal detected after transmission through water, recovered using a super narrowband IIR filter.

(a)

(b)

(c)

Signal Shape Reconstruction

Essential Equations Describing Time Domain Deconvolution (Inverse Filtering)for Real-Time and Off-Line Processing

)()()()(*)()( HXYthtxty

)(

)()( 1

H

YFtx

)()(*)()( tsthtxty

)(

)(

)(

)()( 1

H

S

H

YFtx

otherwisesH

ifs

,10)(

1,0

sHFth

)(

1)(

~ 11

)(~

*)()( 1 thtytx

Simple Fourier domain scheme (rarely successful):

Fourier domain scheme with noise estimate:

Time domain scheme with noise estimate (surprisingly useful):

Finally:

Signal Shape Reconstruction in Practice

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

time (s)

volts

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

time (s)

volts

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

time (s)

volts

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

time (s)

volts

Signal comprising three impulses

Signal after inverse filtering in real-timeSignal after low-pass distortion

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

time (s)

volts

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

-0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004

time (s)

volts

Loudspeaker Equalisation

System operation: • Signal Wizard software generates

a swept sine or white noise test signal and downloads it to the hardware.

• The hardware sends the signal to the speaker, simultaneously recording its response.

• Signal Wizard software analyses the response and generates an equalization filter based on deconvolution.

• The hardware convolves the filter with the test signal and the analysis is repeated.

DSP systemDSP systemDSP systemDSP system

amplifieramplifieramplifieramplifier

amplifieramplifieramplifieramplifier loudspeakerloudspeakerloudspeakerloudspeaker

-90

-85

-80

-75

-70

-65

-60

-55

-50

-45

-40

500 1000 1500 2000 2500 3000 3500

Frequency, Hz

Re

lati

ve

Inte

ns

ity

, dB

-90

-85

-80

-75

-70

-65

-60

-55

-50

-45

-40

500 1000 1500 2000 2500 3000 3500

Frequency, Hz

Re

lati

ve

Inte

ns

ity

, dB

-90

-85

-80

-75

-70

-65

-60

-55

-50

-45

-40

500 1000 1500 2000 2500 3000 3500

Frequency, Hz

Re

lati

ve

Inte

ns

ity

, dB

-90

-85

-80

-75

-70

-65

-60

-55

-50

-45

-40

500 1000 1500 2000 2500 3000 3500

Frequency, Hz

Re

lati

ve

Inte

ns

ity

, dB

Loudspeaker Equalisation Results

After

Before

Noise in audio can be classified into two types: narrowband (easy to remove) or broadband (difficult)

frequency

ampl

itude

audio signal

narrow bandnoise

frequency

ampl

itude

audio signal

broad band noise

easy

difficult

Adaptive Filters

broadbandbroadbandnoisenoise

broadbandbroadbandnoisenoise

FIR filter sectionFIR filter sectionwithwith

tap modifiers (LMS)tap modifiers (LMS)

FIR filter sectionFIR filter sectionwithwith

tap modifiers (LMS)tap modifiers (LMS)

++

__

frequencyfrequency

ampl

itude

ampl

itude

RecoveredRecoveredsignalsignal

RecoveredRecoveredsignalsignal

][][][][

][][][

][][][1

0

knxnekhkh

nyndne

knxkhny

oldnew

M

k

InputInputsignal +signal +noisenoise

InputInputsignal +signal +noisenoise

Adaptive filter theory is complex but its implementation simple. It is ideally suited to real time DSP systems.

Conclusions

• Flexibility ensures that real time DSP is suitable for many applications in both real time NDE and audio signal processing

• Software-realized processing yields very significant improvements with regard to stability, precision and repeatability

• New generation DSP devices are extending the range of signal

frequencies over which real time discrete processing can be applied