A Silicon Model of 
Amplitude Modulation Detection 
in the Auditory Brainstem 
Andr6 van Schaik, Eric Fragniire, Eric Vittoz 
MANTRA Center for Neuromimetic Systems 
Swiss Federal Institute of Technology 
CH- 1015 Lausanne 
email: Andre.van_Schaik@ di.epfl.ch 
Abstract 
Detection of the periodicity of amplitude modulation is a major step in 
the determination of the pitch of a sound. In this article we will 
present a silicon model that uses synchronicity of spiking neurons to 
extract the fundamental frequency of a sound. It is based on the 
observation that the so called 'Choppers' in the mammalian Cochlear 
Nucleus synchronize well for certain rates of amplitude modulation, 
depending on the cell's intrinsic chopping frequency. Our silicon 
model uses three different circuits, i.e., an artificial cochlea, an Inner 
Hair Cell circuit, and a spiking neuron circuit. 
1. INTRODUCTION 
Over the last few years, we have developed and implemented several analog VLSI 
building blocks that allow us to model parts of the auditory pathway [1], [2], [3]. This 
paper presents one experiment using these building blocks to create a model for the 
detection of the fundsmental frequency of a harmonic complex. The estimation of this 
fundamental frequency by the model shows some important similarities with psycho- 
acoustic experiments in pitch estimation in humans [4]. A good model of pitch 
estimation will give us valuable insights in the way the brain processes sounds. 
Furthermore, a practical application to spcach recognition can be expected, either by 
using the pitch estimate as an element in the acoustic vector fed to the recognizer, or by 
normalizing the acoustic vector to the pitch. 
742 A. van Schaik, E. Fragnidre and E. Vittoz 
Although the model doesn't yield a complete model of pitch estimation, and explains 
probably only one of a few different mechanisms the brain uses for pitch estimation, it 
can give us a better understanding of the physiological background of psycho-acoastic 
restfits. An electronic model can be especially helpful, when the parameters of the model 
can be easily controlled, and when the model will operate in real time. 
2. THE MODEL 
The model was originally developed by Hewitt and Mealdis [4], and was based on the 
observation that Chopper cells in the Cochlear Nucleus synchronize when the stimulus 
is modulated in amplitude within a particular modulation frequency range [5]. 
CoeMear medumicd Codder nudeud 
Ilieri Inner !lr ehopper 
edl/AN 
Inferior cdliculue 
eoinddmee 
J Lg chopping Low BMF 
/Low BMF 
flair edl tumid Spikin neuron 
Fig. 1. Diagram of the AM detection model. BMF=Best Modulation Frequency. 
The diagram shown in figure 1 shows the elements of the model. The cochlea filters the 
incoming sound signal. Since the width of the pass-band of a cochlear band-pass filter is 
proportional to its cut-off frequency, the filters will not be able to resolve the individual 
harmonics of a high frequency carrier (>3kHz) amplitude modulated at a low rate 
(<500Hz). The outputs of the cochlear filters that have their cut-off frequency slightly 
above the carrier frequency of the signal will therefore still be modulated in amplitude at 
the original modulation frequency. This modulation component will therefore 
synchronize a certain group of Chopper cells. The synchronization of this group of 
Chopper cells can be detected using a coincidence detecting neuron, and signals the 
presence of a particular amplitude modulation frequency. This model is biologically 
plausible, because it is known that the choppers synchronize to a particular amplitude 
modulation frequency and that they project their output towards the Inferior Colliculus 
(amongst others). Furthermore, neurons that can function as coincidence detectors are 
shown to be present in the Inferior Colliculus and the rate of firing of these neurons is a 
A Silicon Model of Amplitucle Modulation Detection 743 
band-pass function of the amplitude modulation rate. It is not known to date however if 
the choppers actually project to these coincidence detecter neurons. 
The actual mechanism that synchronizes the chopper cells will be discussed with the 
measurements in section 4. In the next section, we will first present the circuits that 
allowed us to build the VLSI implementation of this model. 
3. THE CIRCUITS 
All of the circuits used in our model have already been presented in more detail 
elsewhere, but we will preseat them briefly for completeness. Our silicon cochlea has 
been presented in detail at NIPS'95 [1], and more details about the Inner Hair Cell 
circuit and the spiking neuron circuit can be found in [2]. 
3.1 THE SILICON COCHLEA 
The silicon cochlea consists of a cascade of second order low-pass filters. Each filter 
section is biased using Compatible Lateral Bipolar Transistors (CI.BTs) which control 
the cut-off frequency and the quality factor of each section. A single resistive line is 
used to bias all CI.BTs. Because of the exponential relation between the Base-F. mitter 
Voltage and the Collector current of the CI.BTs, the linear voltage gradient introduced 
by the resistive line will yield a filter cascade with an extmoentially decreasing cut-off 
frequency of the filters. The output voltage of each filter Vo,,t then represents the 
displacement of a basilar membrane section. In order to obts_in a representation of the 
basilar membrane velocity, we take the difference between Vo,,t and the voltage on the 
internal node of the second order filter. 
We have integrated this silicon cochlea using 104 filter stages, and the output of every 
second stage is connected to an output pin. 
3.2 THE INNER HAIR CELL MODEL 
The inner hair cell circuit is used to half-wave rectify the basilar membrane velocity 
signal and to perfoam some form of temporal adaptation, as can be seen in figure 2b. 
The differential pair at the input is used to conv the input voltage into a current with 
a compressive relation between input amplitude and the actual amplitude of the current. 
Fig. 2. a) The Inner Hair Cell circuit, b) measured output current. 
We have integrated a small chip containing 4 independent inner hair cells. 
744 A. van Schaik, E. Fragnibre and E. ttoz 
3.3 THE SPIKING NEURON MODEL 
The spiking neuron circuit is given in figure 3. The membrane of a biological neuron is 
modeled by a capacitance, Cmem, and the membrane leakage current is controlled by the 
gate voltage, Vl, of an NMOS transist. In the absence of any input x=0), the 
membrane voltage will be drawn to its resting potential (controlled by Vr), by this 
leakage current. Excitatc inputs simply add charge to the membrane capacitance, 
whereas inhibitcl'y inputs are simply modeled by a negative Ix. ff an excitatory current 
larger than the leakage current of the membrane is injected, the membrane potential will 
increase from its resting potential. This membrane potential, Vmm, is cxnpared with a 
controllable threshold voltage Vth, USing a basic transconductance amplifier driving a 
high impedance load. If Vm exceeds Vth, an actlea potential will be generated. 
V+ 
I 
Fig. 3. The Spiking Neuron circuit 
The generation of the action potential happens in a similar way as in the biological 
neurea, where an increased sodi-m conductance creates the upswing of the spike, and a 
delayed increase of the potassium conductance creates the downswing. In the circuit this 
is modeled as follows. If Vmm rises above Vt, the output voltage of the ccnparator 
will rise to the positive power supply. The output of the following inverter will thus go 
low, thereby allowing the "sodhm current" INa to pull up the membrane potential. At the 
same time however, a second inverter will allow the capacitance Cx to be charged at a 
speed which can be controlled by the current Ii,. As soon as the voltage on Cx is high 
enough to allow conduction of the NMOS to which it is ceanected, the "potasshm 
current" Ix will be able to discharge the membrane capacitance. 
If Vmem now drops below Vt-, the output of the first inverter will become high, cutting 
off the current INa. Furthermore, the second inverter will then allow Cx to be discharged 
by the current I:ow. If I:ow is small, the voltage on C: will decrease only slowly, and, 
as long as this voltage stays high enough to allow Ix to discharge the membrane, it will 
be impossible to stimulate the neuron if !x is smaller than I:. Therefore I:ow, can be 
said to control the 'refractory period' of the neuron. 
We have integrated a chip, confining a group of 32 neurons, each having the same bias 
voltages and currents. The component mismatch and the noise ensure that we actually 
have 32 similar, but not completely equal neurons. 
4. TEST RESULTS 
Most neuro-physiological data camping low frequency amplitude modulation of high 
frequency carriers exists for carriers at about 5kHz and a modulaflea depth of about 
50%. We therefore used a 5 kHz sinusoid in our tests and a 50% modulation depth at 
frequencies below 550Hz. 
A Silicon Model of Amplitude Modulation Detection 745 
150 
100 
,5O 
0 
0 10  0 40 0 
150 
lOO 
5O 
o 
Fig. 4. PSTH of the chopper chip for 2 different sound intensifies 
First step in the elaborafiou of the model is to test if the group of spiking neurous ou a 
single chip is capable of performing like a group of similar Choppers. Neurous in the 
auditory brainstem are often characterized with a Post Stimulus Time Histogram 
(PSTIO, which is a histogram of spikes in response to repeated stimulation with a pure 
tone of short duration. If the choppers on the chip are really similar, the PSTH of this 
group of choppers will be very similar to the PSTH of a single chopper. In figure 4 the 
PSTH of the circuit is shown. It is the result of the snmmed response of the 32 neurons 
on chip to 20 repeated stimulations with a 5kHz tone burst. This figure shows that the 
response of the Choppers yields a PSTH typical of chopping neurons, and that the 
chopping frequency, keeping all other parameters constant, increases with increasing 
sound intensity. The chopping rate for an input signal of given intensity can be 
controlled by setting the refractory period of the spiking neurous, and can thus be used 
to create the different groups of choppers shown in figure 1. The chopping rate of the 
choppers in figure 4 is about 300Hz for a 29dB input signal. 
0.5 
5 
refractory charging spike 
period period width 
10 lime(ms) 
:':-:-?.. -..;.. 'ii Envelope 
Membrane 
potential 
Stimulation 
threshold 
Fig. 5. Spike generafirm for a Chopper cell. 
To understand why the Choppers will synchrouize fo a certain amplitude modulation 
frequency, oue has to look at the signal envelope, which contains temporal informatiou 
on a time scale that can influence the spiking neurons. The 5kHz carrier itseft will not 
contain any temporal information that influences the spiking neuron in an important 
way. Consider the case when the modulation frequency is similar to the chopping 
frequency (figure 5). If a Chopper then spikes during the rising flank of the envelope, it 
will come out of its refractory period just before the next rising flank of the envelope. If 
the driven chopping frequency is a bit too low, the Chopper will couae out of its 
refractory period a bit later, therefore it receives a higher average stimulatiou and it 
spikes a little higher on the rising flank of the envelope. This in turn increases the 
chopping frequency and thus provides a form of negative feedback on the chopping 
frequency. This therefore makes spiking on a certain point on the rising flank of the 
envelope a stable situation. With the same reasoning one can show that spiking on the 
falling flank is therefore an unstable situation. Furthermore, it is not possible to stabilize 
a cell driven above its maximnm chopping rate, ne is it possible to stabilize a cell that 
fires mee than once per modulation period. Since a group of similar choppers will 
746 A. van Schaik, E. Fragnibre and E. ttoz 
stabilize at about the same point on the rising flank, their spikes will thus coincide when 
the modulation frequency allows them to. 
150 
100 
5O 
0 
0 lOO 2oo 3oo 400 5o0 6oo 
mmhlnlbn rale (!) 
0 w 
modulnlion tale (H) 
Fig. 6. AM sensitivity of the coincidence detecting neuron. 
Another free parameter of the model is the threshold of the coincidence detecting 
neuron. If this parameter is set so that at least 60% of the choppers must spike within 
lms to be considered a coincidence, we obt_oin the output of figure 6. We can see that 
this yields the expected band-pass Modulation Transfer Function (MTF), and that the 
best modulation frequency for the 29dB input signal corrds to the intrinsic 
chopping rate of the group of neurons. Figure 6 also shows that the best modulation 
frequency (BMI, just as the chopping rate, increases with increasing sound intensity, 
but that the maximnm nnmber of spikes per second actually decreases. This second 
effect is caused by the fact that the stabilizing effect of the positive flank of the signal 
envelope only influences the time during which the neuron is being charged, which 
becomes a smaller part of the total spiking period at higher intensities. The negative 
feedback thus has less influence on the total chopping period and therefore synchronizes 
the choppers less. 
0 100 200 (x) 400  
moduhtlon ral., (Hz) 
:) , I ( .t. , / . 
modulalion rid. (Hz) 
Fig. 7. AM sensitivity of the coincidence detecting neuron. 
When the coincidence threshold is lowered to 50%, we can see in figure 7a that the 
maximum nnmber of spikes goes up, because this threshold is more easily reached. 
Furthermore, a second pass-band shows up at double the BMF. This is because the 
choppers fire only every second amplitude modulation period, and part of the group of 
choppers will synchronize during the odd periods, whereas others during the even 
periods. The division of the group of choppers will typically be close to, but hardly ever 
exactly 50-50, so that either during the odd or during the even modulation period the 
50% coincidence threshold is exceeded. The  threshold of figure 6 will only rarely 
be exceeded, explaining the weak second peak seen around 500Hz in this figure. 
A Silicon Model of Amplitude Modulation Detection 747 
Figure 7b. shows the MTF fo low intensity signals with a 50% coincidence threshold. 
At low intensities the effect of an additional non-linearity, the stimulation threshold, 
shows up. Whenever the instantaneous value of the envelope is lower than the 
stimulation threshold, the spiking neuron will not be stimulated because its input current 
will be lower than the cell's leakage current. At these low intensities the activity during 
the valleys of the modulation envelope will thus not be enough to sfmulate the Choppers 
(see figure 5). Fo stimuli with a lower modulation frequency than the gronp's chopping 
frequency, the Choppers win come out of their refractory period in such a valley. These 
choppers therefore will have to wait fc the envelope amplitude to increase above a 
certain value, before they receive anew a stimulation. This waiting period nullifies the 
effect of the variation of the refractory period of the Choppers, and thus synchronizes the 
Choppers for low modulation frequencies. A second effect of this waiting period is that 
in this case the firing rate of the Choppers matches the modulation frequency. When the 
modulation frequency becomes higher than the maximum chopping frequency, the 
Choppers will fire only every second period, but will still be synchronized, as can be 
seen between 300Hz and 500Hz in figure 7b. 
5. CONCLUSIONS 
In this article we have shown that it is possible to use our building blocks to build a 
multi-chip system that models part of the auditory pathway. Furthermore, the fact that 
the spiking neuron chip can be easily biased to function as a group of similar Choppers, 
combined with the relative simplicity of the spike generation mechanism of a single 
neuron on chip, allowed us to gain insight in the process by which chopping neurons in 
the mammalian Cochlear Nucleus synchronize to a particular range of amplitude 
modulation frequencies. 
References 
[1] 
[2] 
[3] 
[4] 
[5] 
A. van Schaik, E. Fragnire, & E. Vittoz, "Improved silicon ea using 
compatible lateral bipolar transistors," Advances in Neural Information Processing 
Systems 8, M1T Press, Cambridge, 1996. 
A. van Schaik, E. Fragnire, & E. Vittoz, "An analoge elecuonic model of venual 
cochlear nucleus neurons," Proc. Fifth Int. Conf. on Microelectronics for Neural 
Networks and Fuzzy Systems, I-I. Computer Society Press, Los Alamitos, 1996, 
pp. 52-59. 
A. van Schaik and R. Mealdis, "The electronic ear; towards a blueprint," 
Neurobiology, NATO ASI series, Plenum Press, New York, 1996. 
M.J. I-Iewitt and R. Mealdis, "A computer model of amplitude-modulation sensitivity 
of single units in the inferior colliculus," J. Acoust. Soc. Am., 95, 1994, pp. 1-15. 
M.J. Itewitt, R. Mealdis, & T.M. Shackleton, "A cnputer model of a cochlear- 
nucleus stellate cell: responses to amplitude-modulated and pure tone stimuli," J. 
Acoust. Soc. Am., 91, 1992, pp. 2096-2109. 
PART VI 
SPEECH HANDWRITING AND SIGNAL 
PROCESSING 
