Fast and wideband Identification of Systems: Fast 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 Jäneda, 17. juuni, 2013

Wavelets, chirplets, chirplet transform Wavelets (Haar, ) – 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. 3 Jäneda, 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. a)b)c) d) 4 Jäneda, 17. juuni, 2013

Rectangular pulses T 2/  of max value 1/T 2/T Waveforms for excitation signals 5 Jäneda, 17. juuni, 2013

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 Jäneda, 17. juuni, 2013

Sinc & Gaussian pulses sinc(ωt) = max 2T TGTG 0.5max 0 1/2T time lin f 1/T G max 0.5max 0 sin(ωt)/(ωt) Gaussian G(t) = A 0 exp(-0.5(t/  ) 2 ) 7 Jäneda, 17. juuni, 2013

Using of linear chirp excitation BW = 10 kHz to 1 MHz lin f 0 1 MHz linear response lin magn log f 1 MHz1 MHz 10 kHz = 1 / 100  s log response time T pulse = 100  s = t obs amplitude 8 Response from a transplanted muscle 0 Jäneda, 17. juuni, 2013

Exponential chirp and its amplitude spectrum: we can change the amplitude spectrum without modifying amplitudes 9 Jäneda, 17. juuni, 2013

Binary chirp and its amplitude spectrum

Signal processing of sine wave signals Jäneda, 17. juuni, 2013

Signal processing of chirp signals Jäneda, 17. juuni, 2013

Signal processing of chirp signals using quadrature correlation with windowed reference Jäneda, 17. juuni, 2013

Random initial phases Optimised initial phases Jäneda, 17. juuni, 2013 Multisine signals (11 frequencies: 1f, 2f, 4f, f) Random initial phases Optimised initial phases

(a) (b) A sum of four sine waves with frequencies 1f 1, 3f 1, 5f 1, 7f 1 ; A i =1 RMS i = Φ i = 90 0 CF= 2.83 Φ i = optimized CF= 1.45 Jäneda, 17. juuni, 2013 Multisine signals (4 frequencies: 1f, 3f, 5f, 7f)

CF = corresponds to a single sine wave Optimal crest factors (CF) of multisine signals Jäneda, 17. juuni, 2013

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

Jäneda, 17. juuni, 2013 QUADRA TM FAMILY IMPEDANCE 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 Jäneda, 17. juuni, 2013 QUADRA TM FAMILY IMPEDANCE SPECTROSCOPY DEVICES: Application Areas

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

Hetkeseis: 2013 SOOVITUD  1 ms – 1 s mõõteaken  Mõõtesignaal – arbitrary (n Mpunkti)  I/O vähemalt 200 Msps, 50 oomi, DC  Sidekanal: USB 3.0 või Gbit Ethernet  Virtex 6 / bit ADC & 16 bit DAC  Vähemalt 64 kilopunktiline FFT (x2)  Sünkro sisse ja välja TEGELIK Ca 1 ms mõõteaken (ei ole täpne) Arbitrary 64 k punkti I/O ca 65 Msps, 50 oomi, AC Sidekanal: Gigabit Ethernet ca 110 Mbps Virtex 6, ML605 kit + FMC kpunkti FFT mõlemas kanalis Sünkro 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 ! Jäneda, 17. juuni, 2013

Thank you for listening !!! Jäneda, 17. juuni, 2013