I have a(adsbygoogle = window.adsbygoogle || []).push({}); differenceequationwhich is given as:

ΔP = e^P [1]

where we can re-write ΔP as: Δ P = P_2 - P_1, where the subscripts indicate two distinct discrete time indices.

What I would like to do:is to convert this into a continuous time expression and solve it, if possible.

In order to help give some insight, I will solve a similar type of problem where I know the solution.

ΔP = c_1 [2]

Note here, that in all cases we are running the recursive algorithm at afixed data rate. Therefore, I can rewrite equation [1] as:

Δ P = P_2 - P_1 = c_2 ⋅ Δ t

where c_1 = c_2 ⋅ Δ t

This allows me to divide both sides by [equation] \Delta t [/equation]:

ΔP /Δt = c_2

And in the limit:

dP/dt = c_2

which then becomes:

P(t) - P(0) = c_2⋅(t - t_0)

And so the result is that this recursive equation [2] gives us a linear ramp if we were to implement it. What I am trying to do for equation [1] is figure out what this expression will look like.

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# Difference Equation

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