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Please clarify your question. I understand that you want to know what this function does?? A simple manipulation shows that
y = 8*x - 7*x(n-1)
if y is an output sequence and x is an input sequence, then this equation (model) is just a simple autoregressive model. Or you can think of it as the difference between weighted input sequence at present time, x and one-step delayed input sequence, x(n-1).