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Discrete TF

Discrete

Implements a discrete-time transfer function H(z) = B(z)/A(z) using the Direct Form II Transposed structure. Coefficients are specified as space-separated values in descending powers of z.

Mathematical Model

H(z) = \frac{b_0 + b_1 z^{-1} + \dots + b_m z^{-m}}{1 + a_1 z^{-1} + \dots + a_n z^{-n}}

Coefficients are given in descending powers of z. Example: numerator 1 0.5 means z + 0.5.

Inputs & Outputs

Direction	ID	Label	Type	Status
→ In	`in`	In	number	Required
→ In	`reset`	Reset	number	Optional
← Out	`out`	Out	number	Output

Parameters

Parameters	Label	Type	Default
`numerator`	Numerator B(z)	polynomial	`1`
`denominator`	Denominator A(z)	polynomial	`1 -0.5`
`sampleTime`	Sample Time	number	`0.01`
`initialCondition`	Initial Condition	number	`0`

Usage Examples

Transfer Function	Numerator	Denominator
First-order LP: 0.5/(z - 0.5)	`0 0.5`	`1 -0.5`
Moving average: (1 + z⁻¹)/2	`0.5 0.5`	`1`
Unit delay: z⁻¹	`0 1`	`1 0`

Remarks & Best Practices

Causality: Numerator order should not exceed denominator order for proper real-time implementation
Initial transients: Filter states start at zero; first few output samples reflect start-up transient behaviour
Sample time: Must match or be a multiple of the simulation's base sample time
Coefficient format: Coefficients are space-separated in descending powers of z; trailing zeros in the numerator are significant
Direct Form II Transposed: Numerically robust implementation with fewer delay states than Direct Form I

Related Components

TransferFunction: Continuous-time transfer function G(s)
UnitDelay: Simple one-sample delay (z⁻¹)