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.