Showing Time Delays in Inverse Z Tranform Results

Hello,

I need some help.

Say we have the next function:

F(z) = z / (z - 0.5)

The inverse Z function to this function will result as:

f(k) = 0.5^(k)

And Matlab agrees with me:

>> syms z k

>> F = z / (z - 0.5);

>> f = iztrans(F, k);

>> f = vpa(f, 2)

f =

0.5^k

If we'll divide F(z) by z we'll have the next function:

F(z) = 1 / (z - 0.5)

Therefore, we'll expect to have a time delay in the inverse Z transform function:

f(k) = 0.5^(k - 1)

However, this time Matlab won't cooperate:

>> F = 1 / (z - 0.5);
>> f = iztrans(F, k);
>> f = vpa(f, 2)

f =

2.0*0.5^k - 2.0*kroneckerDelta(k, 0)

The result we get is (of course) correct, but very messy and not very nice to look at, this is a big problem with more complex inverse Z tranforms, the way I'd like to see the result is in the same way f(k) is shown. How can I do that?

Also, the unit step function is for some reason shown as such in Matlab after a Z transform:

1 - kroneckerDelta(k, 0)

This is also a big part of the unreadable mess I get when using Matlab for inverse Z tranforms, is there anything I can do?

Thank-you,

NoamVH.