By Laplace transforming, the transfer function is
The impulse response of the synaptic ballistic filter is h(t) = —-[e-bt - e-at] 4.1-4
The total area under the h( t ) curve can be shown to be 1/ab. Thus if H(s) is multiplied by ab, the area under h(t) = 1, regardless of a and b. Thus, for time-domain simulation purposes, one can write the ODEs for constant-area psps:
In the special case where a = b, the transfer function will be a 2
The impulse response of this filter is sometimes called the alpha response; it is:
A Simnon program to generate linear psps is given:
continuous system LinSynBF " v. 3/10/99 A Linear ballistic filter STATE x1 x2 DER dx1 dx2 TIME t dx1 = -a*x1 + Vs dx2 = -b*x2 + x1*a*b " ab factor causes all h(t) to
" have same area under curve.
Vs1 = IF t > dt THEN 0 ELSE Vso " Makes three input impulses.
dt t2 t3
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