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ztrans

Z-transform

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Syntax

ztrans(f)
ztrans(f,transVar)
ztrans(f,var,transVar)

Description

example

ztrans(f)finds theZ-Transformoff. By default, the independent variable isnand the transformation variable isz. Iffdoes not containn,ztransusessymvar.

example

ztrans(f,transVar)uses the transformation variabletransVarinstead ofz.

example

ztrans(f,var,transVar)uses the independent variablevarand transformation variabletransVarinstead ofnandz, respectively.

Examples

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Compute the Z-transform ofsin(n). By default, the transform is in terms ofz.

syms n f = sin(n); ztrans(f)
ans = (z*sin(1))/(z^2 - 2*cos(1)*z + 1)

Compute the Z-transform ofexp(m+n). By default, the independent variable isnand the transformation variable isz.

syms m n f = exp(m+n); ztrans(f)
ans = (z*exp(m))/(z - exp(1))

Specify the transformation variable asy. If you specify only one variable, that variable is the transformation variable. The independent variable is stilln.

syms y ztrans(f,y)
ans = (y*exp(m))/(y - exp(1))

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

ztrans(f,m,y)
ans = (y*exp(n))/(y - exp(1))

Compute the Z-transform of the Heaviside function and the binomial coefficient.

syms n z ztrans(heaviside(n-3),n,z)
ans = (1/(z - 1) + 1/2)/z^3
ztrans(nchoosek(n,2))
ans = z/(z - 1)^3

Find the 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,ztransacts 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]; ztrans(M,vars,transVars)
ans = [ (a*exp(x))/(a - 1), b/(b - 1)] [ (c*sin(1))/(c^2 - 2*cos(1)*c + 1), (d*1i)/(d - 1)^2]

Ifztransis 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 ztrans(x,vars,transVars)
ans = [ (a*x)/(a - 1), b/(b - 1)^2] [ (c*x)/(c - 1), (d*x)/(d - 1)]

Compute the 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; ztrans([f1 f2],x,[a b])
ans = [ a/(a - exp(1)), b/(b - 1)^2]

Ifztranscannot transform the input then it returns an unevaluated call.

syms f(n) f(n) = 1/n; F = ztrans(f,n,z)
F = ztrans(1/n, n, z)

Return the original expression by usingiztrans.

iztrans(F,z,n)
ans = 1/n

Input Arguments

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

Independent variable, specified as a symbolic variable. This variable is often called the "discrete time variable". If you do not specify the variable, thenztransusesn. Iffdoes not containn, thenztransuses the functionsymvar.

Transformation variable, specified as a symbolic variable, expression, vector, or matrix. This variable is often called the "complex frequency variable." By default,ztransusesz. Ifzis the independent variable off, thenztransusesw.

More About

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Z-Transform

The Z-transformF=F(z)of the expressionf=f(n)with respect to the variablenat the pointzis

F ( z ) = ∑ n = 0 ∞ f ( n ) z n .

Tips

  • If any argument is an array, thenztransacts 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 inverse Z-transform, useiztrans.

版本历史

之前介绍过的R2006a

See Also

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Topics