Using the z transform method, solve the difference equation $Y[n] - 4y[n-1]+ 4y[n-2] = x[n]- x[n-1] \\ \text {When } \space y(-1) = y(-2) = 0$

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written 9.1 years ago by

teamques10 ★ 70k

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Mumbai University > EXTC > Sem 4 > Signals and Systems

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Year : MAY 2015

signals and systems

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written 9.1 years ago by

teamques10 ★ 70k

The given difference equation is

$y[n] – 4y[n – 1] + 4y[n – 2] = x[n] – x[n – 1]$

Taking the unilateral Z-transform of above equation, $Y(z) – 4[z^{-1} Y(z) + y(-1)] + 4[z^{-2} Y(z) + y(-1)z^{-1} + y(-2)] = X(z) – [z^{-1} X(z) + x(-1)] ---------- 1 $ …

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