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iztrans

Inverse Z-transform

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Syntax

iztrans(F)
iztrans(F,transVar)
iztrans(F,var,transVar)

Description

example

iztrans(F)returns theInverse Z-TransformofF. By default, the independent variable iszand the transformation variable isn. IfFdoes not containz,iztransuses the functionsymvar.

example

iztrans(F,transVar)uses the transformation variabletransVarinstead ofn.

example

iztrans(F,var,transVar)uses the independent variablevarand transformation variabletransVarinstead ofzandnrespectively.

Examples

Inverse Z-Transform of Symbolic Expression

Compute the inverse Z-transform of2*z/(z-2)^2. By default, the inverse transform is in terms ofn.

syms z F = 2*z/(z-2)^2; iztrans(F)
ans = 2^n + 2^n*(n - 1)

Specify Independent Variable and Transformation Variable

Compute the inverse Z-transform of1/(a*z). By default, the independent and transformation variables arezandn, respectively.

syms z a F = 1/(a*z); iztrans(F)
ans = kroneckerDelta(n - 1, 0)/a

指定transformation variable asm. If you specify only one variable, that variable is the transformation variable. The independent variable is stillz.

syms m iztrans(F,m)
ans = kroneckerDelta(m - 1, 0)/a

Specify both the independent and transformation variables asaandmin the second and third arguments, respectively.

iztrans(F,a,m)
ans = kroneckerDelta(m - 1, 0)/z

Inverse Z-Transforms Involving Kronecker Delta Function

Compute the inverse Z-transforms of these expressions. The results involve the Kronecker Delta function.

syms n z iztrans(1/z,z,n)
ans = kroneckerDelta(n - 1, 0)
f = (z^3 + 3*z^2)/z^5; iztrans(f,z,n)
ans = kroneckerDelta(n - 2, 0) + 3*kroneckerDelta(n - 3, 0)

Inverse Z-Transform of Array Inputs

Find the inverse Z-transform of the matrixM. Specify the independent and transformation variables for each matrix entry by using matrices of the same size. When the arguments are nonscalars,iztransacts on them element-wise.

syms a b c d w x y z M = [exp(x) 1; sin(y) i*z]; vars = [w x; y z]; transVars = [a b; c d]; iztrans(M,vars,transVars)
ans = [ exp(x)*kroneckerDelta(a, 0), kroneckerDelta(b, 0)] [ iztrans(sin(y), y, c), iztrans(z, z, d)*1i]

Ifiztransis called with both scalar and nonscalar arguments, then it expands the scalars to match the nonscalars by using scalar expansion. Nonscalar arguments must be the same size.

syms w x y z a b c d iztrans(x,vars,transVars)
ans = [ x*kroneckerDelta(a, 0), iztrans(x, x, b)] [ x*kroneckerDelta(c, 0), x*kroneckerDelta(d, 0)]

Inverse Z-Transform of Symbolic Function

Compute the Inverse Z-transform of symbolic functions. When the first argument contains symbolic functions, then the second argument must be a scalar.

syms f1(x) f2(x) a b f1(x) = exp(x); f2(x) = x; iztrans([f1, f2],x,[a, b])
ans = [ iztrans(exp(x), x, a), iztrans(x, x, b)]

If Inverse Z-Transform Cannot Be Found

Ifiztranscannot compute the inverse transform, it returns an unevaluated call.

syms F(z) n F(z) = exp(z); f = iztrans(F,z,n)
f = iztrans(exp(z), z, n)

Return the original expression by usingztrans.

ztrans(f,n,z)
ans = exp(z)

Input Arguments

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Input, specified as a symbolic expression, function, vector, or matrix.

Independent variable, specified as a symbolic variable, expression, vector, or matrix. This variable is often called the "complex frequency variable." If you do not specify the variable, theniztransusesz. IfFdoes not containz, theniztransuses the functionsymvar.

Transformation variable, specified as a symbolic variable, expression, vector, or matrix. It is often called the"time variable" or "space variable." By default,iztransusesn. Ifnis the independent variable ofF, theniztransusesk.

More About

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Inverse Z-Transform

WhereRis a positive number, such that the functionF=F(z)is analytic on and outside the circle|z| =R, the inverse Z-transform is

f ( n ) = 1 2 π i ∮ | z | = R F ( z ) z n − 1 d z , n = 0 , 1 , 2...

Tips

  • If any argument is an array, theniztransacts element-wise on all elements of the array.

  • If the first argument contains a symbolic function, then the second argument must be a scalar.

  • To compute the direct Z-transform, useztrans.

Version History

Introduced before R2006a

See Also

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