My question is straightforward: How do I convert a continuous function into a discrete-valued function?

The function I want to convert is the JacobiAmplitude function:

[Phi][t_] = With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; Plot[[Phi][t], {t, 0, 50}]

I am using RSolve to solve a second-order difference equation and want to add a discrete-time version of the JacobiAmplitude function to the model as a forcing term.

I'd like to put a discrete-time JacobiAmplitude function, [Phi][n], into the following difference equation:

RSolve[{y[n + 2] - y[n + 1] + 0.99*y[n] == [Phi][n], {y[0] == 0, y[1] == 1, [Phi][0] == 0}}, y[n], n]; ListPlot[Transpose@Table[{y[n]} /. First[%], {n, 0, 350}], Joined -> True, PlotRange -> All]

I'd immensely appreciate any assistance.

Thanks.