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Ernst Niggli edited res_fitfunction.md
over 9 years ago
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The transient consists of four phases: zero level before the onset of the transient, an exponential increase with time constant \(\tau_r\) starging when \(t=\mu-2\tau_r\), a plateau phase of duration \(d\) starting at \(t=\mu\) and an exponential decay with time constant \(\tau_d\) starting at \(t=\mu+d\)
For the optimizer to obtain good performance when
fitting fitting, the function used for fitting should be continously differentiable. With this in mind, the transient function is convolved with a gaussian \(G(\sigma)\) to yield the actual fitting function:
\[
f(A, d, \tau_{d}, \tau_{r}, \mu, t, \sigma) = g \ast G
\]