Biomedical Engineering Reference
In-Depth Information
FIgURE 7.16:
Three strategies for contending with bandwidth limitations of wireless implantable neu-
ral recording systems.
substantial bandwidth and power savings. These pulses have better noise immunity than conven-
tional analog signals in transmission and also eliminates the need for a traditional ADC. The latest
version using a delta-sigma modulation style to produce timing events resulted in 52 µW of power
dissipation with 8-bit resolution [
60
]. Given a band-limited continuous signal
y
(
t
), we create an
alternate representation
∑
∑
−
ˆ
(
)
=
(
)
(
−
)
=
(
)
y
t
h
t
∗
w
δ
t
t
w
h
t
t
(7.1)
k
k
k
k
k
k
where |
y
(
t
) -
ŷ
(
t
)|<
ε
for all time,
w
k
are appropriate weights, and
h
(
t
) is the sinc function. Sampling
times
t
i
are given by:
f
(
t
k
) =
k
θ
, where
t
k
+
1
t
∫
∫
y
(
t
)
d
t
=
θ
and
f
(
t
)
=
y
(
τ
)
d
τ
(7.2)
t
t
k
0
Previously, simple linear low-pass filters were used as crude reconstruction filters from IF
outputs, computing something similar to rate coding from the spike train, and the performance
was poor. Pulse times are determined by the local area under the signal input
x
(
t
), and they can be
used for perfect reconstruction. Let us assume that
x
(
t
) is band-limited to
Ω
s
and the maximum
interspike interval
T
max
satisfies
T
max
< π /
Ω
s
. From mathematical frame theory, it is known that any
