DiscreteTransferFunction Block

Implements a discrete-time transfer function H(z) = B(z)/A(z) using Direct Form II transposed

# DiscreteTransferFunction Block

Description

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) = B(z) / A(z)

B(z) = b₀ + b₁·z⁻¹ + b₂·z⁻² + ... + bₘ·z⁻ᵐ
A(z) = 1 + a₁·z⁻¹ + a₂·z⁻² + ... + aₙ·z⁻ⁿ

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

Parameters

numerator

Space-separated numerator coefficients in descending powers of z. Example: 1 0.5 represents z + 0.5.

denominator

Space-separated denominator coefficients in descending powers of z. Example: 1 -0.5 represents z - 0.5.

sampleTime

Discrete sample time (seconds).

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

• 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

See Also

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