MATLAB: 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

Best Answer

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)

Related Solutions

MATLAB: Z-transform of unit step function

I don't have the Symbolic Toolbox but I think that the provided answer is correct. If

 x[n] = 0.5^n * u[n]
 => x[n] = {…,0,0,0.5^0 * 0, 0.5^1 * 1, 0.5^2 * 1,…}

then the z-transform is

 sum(n=-Inf:+Inf)(0.5^n)*(z^-n)
    = sum(n=0:+Inf)(0.5^n)*(z^-n)  % ignore all n<0
    = 0.5 + sum(n=1:+Inf)(0.5^n)*(z^-n)
    = 0.5 + sum(n=1::+Inf)(0.5/z)^n
    = 0.5 + (0.5/z)/(1-(0.5/z))    % assuming abs(0.5/z)<1
    = 0.5 + 0.5/(z-0.5)
    = 1/2 + (1/2)/(z-1/2)
    = 1/(2*z - 1) + 1/2

MATLAB: Is it correct? (dirac delta function)

no it should be 2*(n==0)

However there is another sense in which dirac(x) should be infinite when x is 0 instead being 1.

Best Answer

Related Solutions

MATLAB: Z-transform of unit step function

MATLAB: Is it correct? (dirac delta function)

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