Compressive Sensing system for recording of ECoG signals in-vivo

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The spectra of the input signal have been depicted in Cadence, (see Fig. 6.2.1.2) and it can beobserved that most of the information in frequency is approximately in the range between 300Hz and 12 kHz. In this way, the values for R and C has to verify Eq.17 for a frequency polewhich has been chosen f p = 100 Hz. The main parameters of the simulation are shown in Table6.2.1.1:ParameterPole frequency (f p )Sampling frequency (f s )Integration period (Δt)Signal BandwidthRCSpecification100 Hz33 kHz32μs12 kHz1.59 GΩ1 pFTable 6.2.1.1. Main parameters for the simulation of the Passive Integrator-based multipath channel.Figure 6.2.1.2. Input signal Spectra.As it has been commented previously, the mixing has to be included within the integrator,hence, it can be implemented by considering a switch which in controlled by the random binarysequence which comes from the random generator. In this way, when the actual value of therandom sequence is ‘1’, the switch is close and so the value which is being registered in theelectrode passes across the resistor and accumulates in the integrator capacitor. The56
considered switch is almost ideal, that is, the close circuit resistance is 1 Ω and the open circuitresistance is 1 TΩ. The control voltages have been chosen as underfor closingthe switch, and overto close it. In this way the uncertain range of control voltageis minimize, but anyway the random binary sequence does not distort. The mixer-integrator hasbeen sketched in Fig.6.2.1.1. A complete multipath acquisition array has been implemented inCadence by considering N = 128 and M = 64. The resulting compressed signal has beencompared in Fig.6.2.1.3 with the one which has resulted in Matlab implementation.As the reconstructed signal is robust in both of the models, the differences regarding thesamples of the compressed signal have to be caused by non-idealities during the sampling andintegrating phases. The compressed signal coming from Cadence is slightly different to the onewhich has been calculated in Matlab, so the reconstruction signal for both of the models iscompared in Fig.6.2.1.4 for LASSO reconstruction method and in Fig.6.2.1.5 for BPDM. InLASSO-based reconstruction (see Eq.15) and in BPDN-based reconstruction(see Eq.14). Both of the values have been chosen as those which have led a better SNRbetween the original signal and the reconstructed one. Hereafter reconstructed signals areincluded for each topology, a comparison between all of them is introduced at 6.2.5 and SNRcomparison is included in 6.2.6.Figure 6.2.1.3. Compressed signals comparison.It is clear that this topology cannot be used for CS purposes on-chip, because in order toincrease the signal swing it is necessary to increase the RC ratio, and so, it becomes a noimplementable design due to area constraints.57
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August, 31 th , 2012Compressive Sen
Page 5: The present project has been submit
Page 9: AbstractThe project “Compressive
Page 13: RiassuntoIl progetto “Compressive
Page 17 and 18: IndexAcknowledgments 7Abstract 9Gan
Page 19 and 20: E.2. Signal Digital Conversion 84Gl
Page 21 and 22: Figure 6.2.1.2. Input signal Spectr
Page 23: Index of TablesTable 2.1.1. Summary
Page 26 and 27: Figure 1.1. Energy a power costs fo
Page 29 and 30: 2. State of the art2.1 Neural Signa
Page 31 and 32: patterns in response to visual targ
Page 33 and 34: 2.4. Compressive Sensing2.4.1. Comp
Page 35 and 36: 2.4.2. Sparsifying basesSparsifying
Page 37 and 38: It is worth mentioning that compres
Page 39 and 40: y specially considering the integra
Page 41 and 42: Figure 4.1.1.1. LSFR parallel (top)
Page 43 and 44: 4.1.3. Serial Implementation with t
Page 45: 4.1.4. Randomness CheckingIn order
Page 48 and 49: een designed independently as it is
Page 50 and 51: time, which has been approximated a
Page 52 and 53: Figure 5.2.2. Original and reconstr
Page 54 and 55: 6. Analog Path Design6.1. Design Di
Page 58 and 59: Figure 6.2.1.4. LASSO reconstructio
Page 60 and 61: Figure 6.2.2.3. Compressed signals
Page 62 and 63: In this way, the pole frequency is
Page 64 and 65: A can be floating when the mixing s
Page 66 and 67: Figure 6.2.4.4. BPDN method reconst
Page 68 and 69: Figure 6.2.5.3. BPDN method reconst
Page 71 and 72: 7. Conclusions7.1. RemarksAs it is
Page 73: AppendixAppendix AConvexOptimizatio
Page 76 and 77: The total power cost for the digita
Page 78 and 79: Figure B.2.2.1. Block diagram for a
Page 80 and 81: 80Figure B.2.3.2. Binary-weighted S
Page 82 and 83: The main model is shown in Fig.C.1.
Page 84 and 85: Appendix EE.1. AmplificationThe sma
Page 87 and 88: GlossaryADC: Analog-to-Digital Conv
Page 89 and 90: References[1] D. Gangopadhyay et al
Page 91: [35] M.F. Duarte et. al., Recovery
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Compressive Sensing system for recording of ECoG signals in-vivo

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