can any one tell me how to find z transform of unit step??

i have tried but ans isn't correct... like a=heaviside(n) ztrans(a) ans =

1/(z - 1) + 1/2

why 1/2 ???? plz help me out

Answer 1

[Star Strider]

The Heaviside function is defined.

From the documentation:

• heaviside(x) returns the value 0 for x < 0, 1 for x > 0, and 1/2 for x = 0.

So these commands:

syms z 
zth0 = ztrans(heaviside(sym(0)))
zth1 = ztrans(heaviside(sym(1)))

return:

zt0 =

z/(2*(z - 1))

zt1 =

z/(z - 1)

(in R2014b)

[Ced]

I was too slow ^^. See here as well: http://compgroups.net/comp.soft-sys.matlab/step-discrete-function-u-k/398174

[Asia khan]

what if i want to calculate ztransform of u(n-2)??

[Star Strider]

For:

syms n
zunm2 = ztrans(heaviside(n-2))

the result:

zunm2 =

(1/(z - 1) + 1/2)/z^2

[Asia khan]

Thank you... but still that isn't for the answer of u(n-2) that must be (z/(z-1) + 1/2)/z^2 that was the confusion actually.....

[Star Strider]

My pleasure!

[yasmeen abu alsaud]

what if i have heaviside(-n-1)? how can i use sym(1) in this case?

[Star Strider]

Do the experiment —

syms n
zunm2 = ztrans(heaviside(-n-1))

zunm2 = 

0

the heaviside funciton does not exist for .

.

[yasmeen abu alsaud]

when i calculate it manually the answer is different than 0, how can i always get the same result using matlab and table( or using formula)?

[Star Strider]

The MATLAB calculation is correct, for the reason I stated.

[Paul]

@yasmeen abu alsaud

What is your manual result? You may want to search this forum for other questions about finding the z-transform of a left-sided sequence, or post a new Question if you can't find what you're looking for.

Answer 2

[Azzi Abdelmalek]

That depends on how the function heaviside is defined. In Matlab heaviside is defined as

f[n]=0 if n<0
f(0)=1/2
f(n)=1 if n>0

In your case, your function is maybe defined as

f(n)=0 if n<0
f(n)=1 if n>=0

what you need to do is

syms n 
a=heaviside(n)+0.5*kroneckerDelta(n)
out=ztrans(a)

[Asia khan]

Thank you...

[Asia khan]

what is kronecker delta ???? iztrans(1/z) ans= kroneckerDelta(n - 1, 0) will you explain that ??

[Ced]

The kronecker delta in this form is a function which has

kroneckerDelta(n) = 1 for n = 0
kroneckerDelta(n) = 0 for all other n

Since the problem is that heaviside is 0.5 at n = 0 instead of 1, Azzi Abdelmalek adds 0.5*kroneckerDelta(n), which is only nonzero at n = 0, and therefore "fixes" heaviside.