Biomedical Engineering Reference
In-Depth Information
is lopsided towards a complex frontend (accurate sample-and-hold that uses large chip areas and
consumes a lot of power) versus a very easy backend (lowpass filtering). Here we require exactly the
opposite, that is, a sampling scheme that is implemented in a simple frontend circuit eventually
with a more difficult reconstruction in the backend. Our group at Florida has recently proposed the
integrate-and-fire (IF) representation, which accomplishes these goals. The signal is integrated up
to a threshold and a pulse is fired when the voltage crosses a threshold. Hence, the time between
the pulses is proportional to the integral of the voltage, providing an aperiodic sampling scheme.
Provided that there are sufficient pulses on an interval, one can show that this scheme obeys the
definition of sampling (a one to one mapping with a unique inverse). What is interesting is that
the IF representation is very easy to build in hardware and is immune to noise in the chip on dur-
ing transmission because of the pulse nature of the representation. As long as delays are constants,
they do not affect the accuracy of the representation. The quantization noise is associated with how
precise is the pulse timing, so data rates will not increase with precision as in conventional A/Ds.
Moreover, this representation naturally improves the fidelity of the high-amplitude portions of the
signals (where there are more spikes), so in many applications (as in spike trains) considerably lower
data rates are necessary to represent the signals when compared with Nyquist samplers. The power-
size-bandwidth specification of this sampler seems better than conventional Nyquist samplers.
The availability of the IF representation also opens the door to blend analog and signal pro-
cessing in a much more interesting way. Figure
7.16
shows our present thinking on three approaches
to decrease data rates through processing at the frontend.
Strategy 1 is sends out the data directly after the IF representation. The data rates depend
on the input structure and the threshold. By selecting higher thresholds the data rates decrease, but
aliasing starts cropping up in the low amplitude portions of the signal.
Strategy 2 does signal compression in the pulse domain before sending the data out. The idea
is to use the time between the pulses and their polarity to recognize the events of importance that
in our case will be neural spikes. The objective is to decrease the data rates and only send out events
that are of interest.
The third strategy is to ultimately do the processing on the chip by creating signal process-
ing algorithms that work with point processes. The output will be directly connected to an external
device for brain control.
Integrate and Fire Representation.
The voltage output of the amplifier is first converted into
current and, by integrating this current, the amplitude information is encoded into an asynchronous
digital pulse train. This IF module efficiently encodes the analog information as an asynchronous
train of pulses [
59
]. The principle is to encode amplitude in the time difference between events.
The advantage is that a single event represents a high-resolution amplitude measurement, with
