fast and wideband identification of systems: fast and wideband identification of systems: broadband...

Fast and wideband Identification of SystemsFast and wideband Identification of Systems::

broadband excitation and the processing of responses(Impedance Spectroscopy)

Examples: electrical bioimpedance and electrochemical impedance

by Mart Min

Jäneda, 17. juuni, 2013

Introduction

• Fast frequency domain analysis of impedance is required when the system under test is not stationary, e.g. in high throuput microfluidic devices, fuel cell analysers, lab-on-chip devices, cardiac monitors, implantable pacemakers, pulmonary

• Joint time-frequency analysis is required, because the spectra are time dependent (time-frequency-intensity diagrams for Re and Im).

Questions: 1) what kind of waveforms are the most suitable for excitation when the

fast broadband analysis is required?2) what kind of signal processing methods could be used for processing

the responses to such excitations ?

2

vr(t)

ie(t)

Ż(ω,t) G Ż

excitation generator

impedance

Impedance Analyzer

response voltage


Wavelets, chirplets, chirplet transform

• Wavelets (Haar, 1908-1912) – the beginning of scalable signal basis• Gabor Transform (Dennis Gabor, 1946) – beginning of time-frequency analysis• Wilson – multiresolution FFT (1992), also fractional FFT• Chirp&Chirplet Transform – Simon Haykin and Steve Mann (1991)• Theoretical (mathematical) bases for joint time-frequency analysis – Leon

Cohen (1990ies).

Our task: developing of signal generation and processing modifications optimal for certain applications where time is relevant.

3Jäneda, 17. juuni, 2013

Focus: synthesis of appropriate excitation waveforms and developing signal processing methods for the fast time dependent spectral analysis – intensity and phase shift versus time and frequency.

Pump G

Delay

Measure-ment

and

time-frequency analysis

Response voltage

current excitation +

current excitation -

Synchro

Ż

Ż(ω,t)

a) b) c) d)


Rectangular pulses

10.707

time

ampl

itude

log f

1/2T

lin f

lin m

agn

lo

g m

agn

10kHz 20kHz 40kHz

T=50μs

20kHz 40kHz 10kHz

1/2T

a)

b)

c)

2T2/ of max value

1/T2/T

Waveforms for excitation signals


Sinc functions (sinus cardinalis)

sinc(ωt) = sin(ωt)/(ωt)

real sinc, limited to 6 periods real sinc, windowed by Hanning

2T

1.0

time

6 periods = 12T

0

6

Amplitude


Sinc & Gaussian pulses

sinc(ωt) =

max

2T

TG

0.5max

0

1/2T

time

lin f1/TG

max

0.5max

0

sin(ωt)/(ωt)

Gaussian G(t) = A0exp(-0.5(t/)2)


Using of linear chirp excitation

BW = 10kHz to 1MHz

)2/)/(2sin()( 2tTBttch

lin f0 1 MHz

linear response

log f

1 MHz10kHz = 1/ 100s

log response

time

Tpulse = 100s = tobs

8

Response from a transplanted muscle

0


Exponential chirp and its amplitude spectrum: we can change the amplitude spectrum without modifying amplitudes

9

1

1u

10u

100u

1m

10m

100m

Frequency10k10m 100m 1 10 100 1k


Binary chirp and its amplitude spectrum

Excitation generator

Phase shifter ( 90°)

Multiplyer X

Multiplyer X

Low pass filter LPF

Low pass filter LPF

Vector calculator

I / V

ReZ(ω)

Z(ω)

Φ(ω)

ImZ(ω)

Vexc

. I

. V

Measurement setup

. I m (VZ)

sine wave reference – sin(ωt) – determines Re axis

cosine wave reference – cos(ωt) – determines Im axes

0°

90°

. Re (VZ)

Buffer

Zx

Signal processing of sine wave signals


reference

(a)

Impedance vector

calculator

Z(ω)

(ω)

Chirp generator

generator

Ż Cross-

correlator

Iz

FFT

Vch[(ω(t)]

reference

Z(ω)

FFT

Impedance vector

calculator

(ω)

(b)

Chirp generator

generator

Ż FFT

Vch[(ω(t)] Iz

Signal processing of chirp signals


Signal processing of chirp signals using quadrature correlation with windowed reference


1

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1m0 200u 400u 600u 800u

1

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1m0 200u 400u 600u 800u

Random initial phases

Optimised initial phases


Multisine signals (11 frequencies: 1f, 2f, 4f, ... 1024f)

0.3

0

0.05

0.1

0.15

0.2

0.25

10M1k 10k 100k 1M

Random initial phases

Optimised initial phases

(a) (b)

A sum of four sine waves with frequencies 1f1, 3f1, 5f1, 7f1 ; Ai =1 RMSi = 0.707

Φi = 900

CF= 2.83

Φi = optimized

CF= 1.45


Multisine signals (4 frequencies: 1f, 3f, 5f, 7f)

CF = 1.414 corresponds to a single sine wave

Optimal crest factors (CF) of multisine signals



Multifrequency excation as a sequence of binary pulses (binary multifrequency signal)

|Ż (f )|

(f )

DFT or FFT analysis Timing t 1 to t 2 Frequency f 1 to f 2

. response Vz

Generator of binary excitation I exc

Z

Z (ω) and Φ(ω) or ReŻ (ω) and ImŻ (ω)

Ż

. . Z = Vz / Iexc


QUADRATM FAMILYIMPEDANCE SPECTROSCOPY DEVICES: Fast and Wideband

Frequency range covered simultaneously: selectable, maximally from 1 kHz to 400 kHz during 1 ms. Number of frequency components in the covered range: selectable from 4 to 16.

Target applications in biology and medicine include:• Single cell and multi-cell studies• Biomaterial studies and bioengineering• Processes in microfluidics, continuous and droplet flow• Reconstructive surgery, tissue and organ transplantation• Monitoring and diagnosing of ischemic phenomena• Cardiovascular monitoring and diagnosing• Many other applications in medical monitoring and diagnosing


QUADRATM FAMILYIMPEDANCE SPECTROSCOPY DEVICES: Application Areas

DEVICE NSLAVE( N ≤ 8 )

PC

DEVICE 1MASTER

USB N

USB 1

DEVICE 2SLAVE

USB 2

CLOCKSYNCKEY

DATA POWER

CLOCKSYNCKEY

DATA POWER

OBJECT

Algne plaan (AD 2010):Vähemalt 8 mõõtekanalit;Vähemalt 4 mõõtesagedust, mis genereeritakse vajadusel igas kanalis;1 ms mõõteaken impedantsi tulemuste jaoks;Mõõtesageduste vahemik: 1 kHz – 1MHz;Impedantsi mõõtevahemik 1 Ω – 1 kΩ;Piiratud vooluga vooluallikas, max 400uA;Sidekanal: USB 3.0 või Ethernet (optiline);Altium NanoBoard 3000XN – with fixed Xilinx® Spartan™-3AN device; (XC3S1400AN-4FGG676C)Vähemalt 1024 punktiline FFT

Paljukanaliline DDS

moodul

Paljukanalilinesignaaliprotsessor

jakommunikatsiooni

moodul

A/D muundur2,048 Msps

4 kVisolatsioon

Sisend

võimendi

G=2-2000

I kanal

V kanal

A/D muundur2,048 Msps

I info

V/I

konv

erte

r

Sünkronisatsioonja

seaded,testvektorid?

Sisend

võimendi

G=2-2000

Ühine sünkro

Üks mõõtekanalitest

Hetkeseis: 2013SOOVITUD

1 ms – 1 s mõõteakenMõõtesignaal – arbitrary (n Mpunkti)I/O vähemalt 200 Msps, 50 oomi, DCSidekanal: USB 3.0 või Gbit EthernetVirtex 6 / 7 + 16 bit ADC & 16 bit DACVähemalt 64 kilopunktiline FFT (x2)Sünkro sisse ja välja

TEGELIKCa 1 ms mõõteaken (ei ole täpne)Arbitrary 64 k punkti I/O ca 65 Msps, 50 oomi, ACSidekanal: Gigabit Ethernet ca 110 MbpsVirtex 6, ML605 kit + FMC15064 kpunkti FFT mõlemas kanalisSünkro puudub

EK-V6-ML605-D

AES-FMC-4DSP150

+ üksjagu koodi

Tuleb teha:Uus analoog plaat FMC150 asemel järgmise poolaasta plaanis.Olemasolevat lahendust tuleb igakülgselt kontrollida ja hinnata:

o Miks suurematel kiirustel ebastabiilne?o Miks 1 ms mõõteaken on muutlik?o Kas n*64 k punkti arb oleks reaalne, i.e.

mõõteaken sammuga 1ms, 10ms, kuni 10s ?

o Kas DAC’id õnnestuks 400 (800) Msps kiirusega käima panna, hoides ADC 200 Msps kiirusel?

o Miks Gbit Ethernet vaevalt 100 Mbit kiirusega käib (võiks 500 Mbit)?

o Sünkro küsimused?Lahenduse optimeerimine!(sisseehitatud) testimine !Uute signaalitöötlusmeetodite arendamine ja võrdlus optimeeritud FFT’ga !


Thank you for listening !!!


fast and wideband identification of systems: fast and wideband identification of systems: broadband...

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