Biomedical Engineering Reference
In-Depth Information
To understand the implication of the inhibi-
tory coupling for noise shaping, a sinusoidal
input at frequency
f
0
=
1 kHz was applied to all
the neurons and the population firing rates are
analyzed in frequency domain using a short-time
Fourier transform.
Figure 2.6
c shows a compari-
son of the power spectrum for a single neuron, a
neuron in a population of a coupled and an
uncoupled network, respectively. The spectrum
for a single neuron shows that it is unable to
track the input signal since its bandwidth (1 kHz)
is much larger than the firing rate of the neuron,
whereas for the uncoupled/coupled neurons in
a population case, the input signal can be easily
seen. For the uncoupled case, the noise floor,
however, is flat, whereas for the coupled case, the
noise floor from the signal band is shifted in the
higher-frequency range, as shown in
Figure 2.6
c.
The shaping of the in-band noise floor enhances
the SNR ratio of the network for a large network,
and the improvement is directly proportional to
the number of neurons
[30]
.
(a)
(b)
10
0
10
0
Out-of-noise band
Noise floor
Uncoupled
Noise floor
10
-
2
10
-
2
Coupled
In-band noise shaping
10
-
4
10
-
3
Single neuron
In-band noise shaping
10
1
10
2
10
3
10
1
10
2
10
3
f (Hz)
(c)
FIGURE 2.6
Illustration showing the noise-shaping principle in a population of integrate-and-fire neurons
[30]
and in
electric fish [
14, 34
]: (a) spiking patterns generated when no inhibitory coupling exist, (b) spiking patterns generated when
inhibitory coupling exists between the neurons that make the firing more uniform compared to the uncoupled case,
(c) comparison in the spectral domain that clearly shows the connection between inhibitory coupling and noise shaping,
and (d) noise shaping observed in electric fish. Adapted from Refs.
14 and 34
.
(d)
Frequency (Hz)
