Let y[n] = x[n] ∗ h[n], where ∗ denotes convolution and x[n] and h[n] are two discrete time sequences. Given that the z-transform of y[n] is Y(z) = 2 + 3z-1 + z-2, the z-transform of p[n] = x[n] ∗ h[n − 2] is

2 + 3z + z−2

3z + z−2

2z2 + 3z + 1

2z−2 + 3z−3 + z−4

Let y[n] = x[n] ∗ h[n], where ∗ denotes convolution and x[n] and h[n] are two discrete time sequences. Given that the z-transform of y[n] is Y(z) = 2 + 3z-1 + z-2, the z-transform of p[n] = x[n] ∗ h[n − 2] is Correct Answer 2z−2 + 3z−3 + z−4

y = x*h

Y(z) = 2 + 3z^-1 + z^-2

p = x*h

Apply z – transform on both sides

p(z) = X(z) H(z) z^-2 → (1)

y = x*h

Apply Z- transform on both sides

Y(z) = X(z).H(z) → (2)

From (1) and (2)

P(z) = (2 + 3z^-1 + z^-2)z^-2 = 2z^-2 + 3z^-3 + z^-4

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Feb 20, 2025

Let y[n] = x[n] ∗ h[n], where ∗ denotes convolution and x[n] and h[n] are two discrete time sequences. Given that the z-transform of y[n] is Y(z) = 2 + 3z-1 + z-2, the z-transform of p[n] = x[n] ∗ h[n − 2] is

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