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Consider the discrete-time LTI system characterized by the following difference equation with input and initial conditions specified: y[n] - 2 y[n-1] – 3 y[n-2] = x[n] , with y[0] = -1 and y[1] = 0, x[n] = (-1/2)n u[n-2]. ? Write a MATLAB program to simulate this difference equation. You may try the commands ‘filter’ or ‘filtic’ or create a loop to compute the values recursively. ? Printout and plot the values of the input signal, x[n] and the output signal, y[n] over the range 1 ? n ? 10. ? Solve this difference equation by hand using the classical method. ? Verify that the values of the output signal, y[n] produced by MATLAB are the same as those calculated by hand for the values of n = 2, 3, 4.
