_ZTransform

it.grypho.scala.leonardo.transform._ZTransform
case class _ZTransform(x: _Expression, n: _Variable, z: _Variable) extends _Functional

AST node for the z-transform: ztrans(x, n, z) in the grammar.

Computes the one-sided (unilateral) transform X(z) = sum(k >= 0) x[k]*z^-k via the rule table in zTransformOf. The summation binder n is excluded from children per the _Functional convention; z names the output variable and appears free in the result.

One-sided rather than bilateral by design, matching laplace, which is itself unilateral. A bilateral transform would have to carry a region of convergence on every result — without one the same X(z) inverts to a causal or an anti-causal signal, so the inverse would have to guess — and that is deferred as future work.

eval applies zTransformOf and guards against the fixpoint (stays symbolic when the rule table cannot reduce the expression), the convention shared with _Laplace.

Value parameters

n

the discrete index variable (binder -- excluded from children)

x

the sequence expression to transform, in terms of the index n

z

the complex frequency variable (free in the result)

Attributes

Graph
Supertypes
trait Serializable
trait Product
trait Equals
class _Functional
trait _Expression
class Object
trait Matchable
class Any
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Members list

Value members

Concrete methods

override def children: List[_Expression]

Sub-expressions subject to recursive structural traversal. Binder positions (e.g. the differentiation variable) are excluded.

Sub-expressions subject to recursive structural traversal. Binder positions (e.g. the differentiation variable) are excluded.

Attributes

Definition Classes
override def eval(env: Environment): Either[_Expression, _Value]

Reduces this expression in the given environment.

Reduces this expression in the given environment.

Value parameters

env

variable bindings and display precision

Attributes

Returns

Right(v) when all free variables resolved to concrete values; Left(e) when reduction is partial or impossible

Definition Classes
override def rebuild(c: List[_Expression]): _Expression

Reconstructs the same node shape with replacement sub-expressions.

Reconstructs the same node shape with replacement sub-expressions.

Value parameters

newChildren

replacements in the same order and count as children

Attributes

Definition Classes
override def toString: String

Returns a string representation of the object.

Returns a string representation of the object.

The default representation is platform dependent.

Attributes

Returns

a string representation of the object.

Definition Classes
Any

Inherited methods

def productElementNames: Iterator[String]

Attributes

Inherited from:
Product
def productIterator: Iterator[Any]

Attributes

Inherited from:
Product

Inherited fields

lazy val freeVars: Set[String]

Cached set of free variable names; O(1) after the first access.

Cached set of free variable names; O(1) after the first access.

Attributes

Inherited from:
_Expression