Ernst Niggli edited res_fitfunction.md  over 9 years ago

Commit id: 254b6fa06aaf360b02f8b4093bef8ff06948d64a

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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: \[  f(A, d, \tau_{d}, \tau_{r}, \mu, t, \sigma) = g \ast G  \]