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:
 
    ϕ[t_] = With[{k = 1.01}, JacobiAmplitude[k t, k^-3]]; 

    Plot[ϕ[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, ϕ[n], into the following difference equation:
                                        
    RSolve[
     {y[n + 2] - y[n + 1] + 0.99*y[n] == ϕ[n], {y[0] == 0, y[1] == 1, ϕ[0] == 0}}, 
     y[n], n
    ];

    ListPlot[
      Transpose@Table[{y[n]} /. First[%],
      {n, 0, 350}], 
      Joined -> True, PlotRange -> All
    ]

I'd immensely appreciate any assistance.