(a) Find the responses for systems described by the following difference equations with th...

(a) Find the responses for systems described by the following difference equations with the initial conditions given:

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(i)

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(ii) y[n] = 0.7y[n – 1] = u[n], y[–1] = –3

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(iii) y[n] – 0.7y[n – 1] = e–n u[n],y[–1] = 0

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(iv) y[n] + 1.7y[n – 1] + 0.72y[n – 2] = u[n], y[–1] = 0, y[–2] = 1

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(v) y[n] – 0.7y[n – 1] = cos(n)u[n], y[–1] = –1

(b) Verify that your response satisfies the initial conditions and the difference equation.

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(c) Use MATLAB to verify your solutions in Parts (a) and (b) by finding y(n) for n = 0, 1, 2, and 3.