Need help with z-transform question.

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The question is to find the z-transform of $$ x(n) = 3ncdot u(n-2)$$

So far I have seen a question asking to find z-transformation of $x(n)=3^n u(n-2)$ and I know the solution. Howver for the sequence $ x(n) = 3ncdot u(n-2)$ , I am having a hardtime finding the z-transform. Is this a typo? If not, please provide a solution.

asked Aug 21 at 13:03

R SMITH

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up vote
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The question is to find the z-transform of $$ x(n) = 3ncdot u(n-2)$$

asked Aug 21 at 13:03

R SMITH

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up vote
-2
down vote

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The question is to find the z-transform of $$ x(n) = 3ncdot u(n-2)$$

asked Aug 21 at 13:03

R SMITH

The question is to find the z-transform of $$ x(n) = 3ncdot u(n-2)$$

asked Aug 21 at 13:03

R SMITH

asked Aug 21 at 13:03

R SMITH

asked Aug 21 at 13:03

R SMITH

asked Aug 21 at 13:03

R SMITH

add a commentÂ |Â

1 Answer
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Let us do it step-by-step:

z-transform of $u(n)$:
$$u(n)to frac11-z^-1$$

Then for $u(n-2)$ we use time-shifting property:

$$u(n-2)to z^-2,frac11-z^-1=fracz^-21-z^-1$$

Now it's time to multiply $n$ and use differentiation in z-domain property:

$$nu(n-2)to -zfracddzleft(fracz^-21-z^-1right)$$

And of course there is a $3$ to be multiplied:

$$3nu(n-2)to -3zfracddzleft(fracz^-21-z^-1right)$$

and by simplifying the right-hand-side we get:

$$mathcalZ(3nu(n-2))=3,frac2z^-2-z^-3(1-z^-1)^2$$

edited Aug 21 at 13:55

answered Aug 21 at 13:46

Alla Tarighati

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1 Answer
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active

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1 Answer
1

active

oldest

votes

up vote
0
down vote

Let us do it step-by-step:

z-transform of $u(n)$:
$$u(n)to frac11-z^-1$$

Then for $u(n-2)$ we use time-shifting property:

$$u(n-2)to z^-2,frac11-z^-1=fracz^-21-z^-1$$

Now it's time to multiply $n$ and use differentiation in z-domain property:

$$nu(n-2)to -zfracddzleft(fracz^-21-z^-1right)$$

And of course there is a $3$ to be multiplied:

$$3nu(n-2)to -3zfracddzleft(fracz^-21-z^-1right)$$

and by simplifying the right-hand-side we get:

$$mathcalZ(3nu(n-2))=3,frac2z^-2-z^-3(1-z^-1)^2$$

edited Aug 21 at 13:55

answered Aug 21 at 13:46

Alla Tarighati

2623

add a commentÂ |Â

up vote
0
down vote

Let us do it step-by-step:

z-transform of $u(n)$:
$$u(n)to frac11-z^-1$$

Then for $u(n-2)$ we use time-shifting property:

$$u(n-2)to z^-2,frac11-z^-1=fracz^-21-z^-1$$

Now it's time to multiply $n$ and use differentiation in z-domain property:

$$nu(n-2)to -zfracddzleft(fracz^-21-z^-1right)$$

And of course there is a $3$ to be multiplied:

$$3nu(n-2)to -3zfracddzleft(fracz^-21-z^-1right)$$

and by simplifying the right-hand-side we get:

$$mathcalZ(3nu(n-2))=3,frac2z^-2-z^-3(1-z^-1)^2$$

edited Aug 21 at 13:55

answered Aug 21 at 13:46

Alla Tarighati

2623

add a commentÂ |Â

up vote
0
down vote

Let us do it step-by-step:

z-transform of $u(n)$:
$$u(n)to frac11-z^-1$$

Then for $u(n-2)$ we use time-shifting property:

$$u(n-2)to z^-2,frac11-z^-1=fracz^-21-z^-1$$

Now it's time to multiply $n$ and use differentiation in z-domain property:

$$nu(n-2)to -zfracddzleft(fracz^-21-z^-1right)$$

And of course there is a $3$ to be multiplied:

$$3nu(n-2)to -3zfracddzleft(fracz^-21-z^-1right)$$

and by simplifying the right-hand-side we get:

$$mathcalZ(3nu(n-2))=3,frac2z^-2-z^-3(1-z^-1)^2$$

edited Aug 21 at 13:55

answered Aug 21 at 13:46

Alla Tarighati

2623

Let us do it step-by-step:

z-transform of $u(n)$:
$$u(n)to frac11-z^-1$$

Then for $u(n-2)$ we use time-shifting property:

$$u(n-2)to z^-2,frac11-z^-1=fracz^-21-z^-1$$

Now it's time to multiply $n$ and use differentiation in z-domain property:

$$nu(n-2)to -zfracddzleft(fracz^-21-z^-1right)$$

And of course there is a $3$ to be multiplied:

$$3nu(n-2)to -3zfracddzleft(fracz^-21-z^-1right)$$

and by simplifying the right-hand-side we get:

$$mathcalZ(3nu(n-2))=3,frac2z^-2-z^-3(1-z^-1)^2$$

edited Aug 21 at 13:55

answered Aug 21 at 13:46

Alla Tarighati

2623

edited Aug 21 at 13:55

answered Aug 21 at 13:46

Alla Tarighati

2623

answered Aug 21 at 13:46

Alla Tarighati

2623

answered Aug 21 at 13:46

Alla Tarighati

2623

add a commentÂ |Â

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