To examine the performance of the neural model with a linearly increasing input frequency, an IPFM SGL model is used as a linear VFC. The IPFM SGL is given a linearly increasing analog input, Vfa = Kr * t (no noise or offset is used at first). Figure 4.4-4 illustrates the performance of the band detector with harmonic suppression. The input frequency is swept up linearly. Parameters used are listed in the program above. Trace 1 = input spikes from IPFM VFC, 2 = y2 = excitatory input spikes with delay D2, 3 = y3 = inhibitory input spikes with delay D1, 4 = y3 = N3 output spikes, 5 = v3 (RPFM output neuron state). Note that the output fires over a narrow range of input frequencies. Also note that the v3 peaks in the output range of frequencies.

This more detailed simulation of a band detector with harmonic suppression illustrates that this frequency-selective behavior indeed exists for a neural model that includes the sum of two ballistic epsps minus a ballistic ipsp as the drive for an RPFM SGL "T-neuron." The interested reader will find it instructive to introduce random noise into the IPFM VFC input voltage, Vin, causing a noisy instantaneous frequency, rk , of the input pulse train. This BDHS cannot detect single rks lying in the passband because of the "memory" of the RPFM SGL low-pass filter.

FIGURE 4.4-4 Results of simulating the BDHS using Simnon program, BDsuprl.T. The input frequency is increased linearly. Traces: 1, swept-frequency input spikes; 2, y2 (exitatory input spikes with delay, D2); 3, y3 (inhibitory input spikes with delay D1); 4, y3 (N3 output spikes); 5, = 0.355 (N3 firing threshold); 6, v3 (N3 state). Vertical scale, arbitrary; horizontal scale, ms. Note that the BDHS system fires over a narrow range of the input neuron instantaneous spike frequency.

FIGURE 4.4-4 Results of simulating the BDHS using Simnon program, BDsuprl.T. The input frequency is increased linearly. Traces: 1, swept-frequency input spikes; 2, y2 (exitatory input spikes with delay, D2); 3, y3 (inhibitory input spikes with delay D1); 4, y3 (N3 output spikes); 5, = 0.355 (N3 firing threshold); 6, v3 (N3 state). Vertical scale, arbitrary; horizontal scale, ms. Note that the BDHS system fires over a narrow range of the input neuron instantaneous spike frequency.

Where might BDs or BDHSs be found in nature? An obvious application might be in frequency analysis in the auditory system. Another might be in the central processing of electrosensory signals used for guidance in weakly electric fish (Heiligenberg, 1991) (see Section 2.5).

This section has examined the results of modeling two theoretical neural operations with signal-processing implications; the T-neuron and the band detector. Modeling was carried out using the locus approach and the RPFM spike generator algorithm. psps were modeled using the so-called alpha function so that a presynaptic spike produced a psp of the form: q(t) = K t exp(-at). Postsynaptic potentials were simply summed to form the spike generator potential that was the input to the RPFM SGL of the output neuron.

It is interesting to note that simulation with the more realistic neural models with synaptic ballistic potentials and RPFM SGL showed that the T-neuron did indeed act as an AND gate with a memory. The band detector with harmonic suppression behaved as a band-pass filter for an input pulse train with slowly changing frequency. Reiss's (1964) original T-neuron and band detector only used AND logic, delays, and one-shot multivibrator elements giving gating dwells in their representations. Reiss's systems were closer to logic than neurons.

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