Question

Given two sequences, $x_1(n) = 5\delta(n) - 2\delta(n - 2)$ and $x_2(n) = 3\delta(n - 3)$, a. determine the z-transform of convolution of the two sequences using the convolution property of z-transform $X(z) = X_1(z)X_2(z)$; b. determine convolution by the inverse z-transform from the result in (a) $x(n) = Z^{-1}(X_1(z)X_2(z)).$

          Given two sequences,
$x_1(n) = 5\delta(n) - 2\delta(n - 2)$ and
$x_2(n) = 3\delta(n - 3)$, 
a. determine the z-transform of convolution of the two sequences using
the convolution property of z-transform
$X(z) = X_1(z)X_2(z)$;
b. determine convolution by the inverse z-transform from the result
in (a)
$x(n) = Z^{-1}(X_1(z)X_2(z)).$

Given two sequences,
x1(n) = 5δ(n) - 2δ(n - 2) and
x2(n) = 3δ(n - 3),
a. determine the z-transform of convolution of the two sequences using
the convolution property of z-transform
X(z) = X1(z)X2(z);
b. determine convolution by the inverse z-transform from the result
in (a)
x(n) = Z^-1(X1(z)X2(z)).

Added by Mariano B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Gopal Sharma

Step 1

Given x[n] = 58n - 28n - 2 and x[n] = 38n - 3, we can find their respective z-transforms. For x1[n] = 58n - 28n - 2, the z-transform is given by: X1(z) = Z{x1[n]} = 58Z{n} - 28Z{n} - 2Z{1} = 58 * (z / (z - 1)^2) - 28 * (z / (z - 1)^2) - 2 * (z / (z - 1)) Show more…

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Given two sequences, x[n] = 58n - 28n - 2 and x[n] = 38n - 3 a. Determine the z-transform of the convolution of the two sequences using the convolution property of the z-transform: X(z) = X1(z) * X2(z); b. Determine the convolution by the inverse z-transform from the result in (a): x[n] = Z^-1{X(z) * X2(z)}.