4.32 Find the inverse z transforms of the following by using...

4.32 Find the inverse z transforms of the following by using the partial-fraction method: (a) (X(z) = frac{(z - 1)^2}{z^2 - 0.1z - 0.56}) (b) (X(z) = frac{4z^3}{(2z + 1)(2z^2 - 2z + 1)})

Transcript

00:01 So here in the first part of the question, we have to find out the inverse z transform of the function which is represented as x of z that is equals to z minus 1 to its whole square, which is divided by z square minus 0 .1 of z minus 0 .56.

00:15 So this is given to us.

00:17 Let's say this is the first equation.

00:19 So here we have to partially transaction of the denominator considering here.

00:23 So z raised to the power 2 minus 0 .1 of z minus 0 .56 we are considering here.

00:28 Simplifying the term, that from here is equals to z raised to the power 2 minus 0 .8 of z plus 0 .7 of z minus 0 .56.

00:38 So this from here is z minus z minus 0 .8 plus 0 .7 multiplied by z minus 0 .8.

00:45 So simplifying the term, we get the two roots that is z plus 0 .7 multiplied by z plus z minus 0 .8.

00:52 So from the equation one, this is our equation one.

00:56 So from equation one, we can say that the value of x of z become equals to z minus 1 to its whole square, which is divided by the z square minus 0 .1 of z minus 0 .56.

01:09 So the value of x of z which is divided by z become equals to z minus 1 to its whole square, which is divided by z multiplied by the z minus 0 .8 multiplied by the z plus 0 .7.

01:20 So simplifying the term, we get the value of equation in the terms of x of z divided by z that is equals to z minus 1 to its whole square, which is divided by z multiplied by the z minus 0 .8 multiplied by the z plus 0 .7.

01:35 So this from here is equals to a divided by z plus b divided by z minus 0 .8 plus c divided by the z plus 0 .7...

Question

4.32 Find the inverse z transforms of the following by using the partial-fraction method: (a) (X(z) = frac{(z - 1)^2}{z^2 - 0.1z - 0.56}) (b) (X(z) = frac{4z^3}{(2z + 1)(2z^2 - 2z + 1)})

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