Derive the lpe model for a band pass soft limiter and

Question

Derive the LPE model for a band pass soft limiter and simulate the band pass and LPE models with the same input as in Problem and compare the results.

Problem
Derive the complex lowpass equivalent (CPE) model for the cubic nonlinearity of the form

y(t) = x(t) - 0.25x³(t)

For a two-tone input of equal amplitudes at f₁ = 13 Hz and f₂ = 15 Hz, find the first-zone output for the band pass case analytically and compute the power levels of the various output components. Simulate the band pass and the LPE models and compare the simulated power levels with the computed power levels. Do this for at least three different sampling rates and compare the results.