DiscreteDerivative Block

Discrete-time derivative. Computes the rate of change: (u[n] - u[n-1]) / Ts.

# DiscreteDerivative Block

Description

Computes the discrete-time derivative (backward difference) of the input signal. Outputs zero on the first sample.

Mathematical Model

y[n] = (u[n] - u[n-1]) / T
y[0] = 0

where y[n] is the current output, u[n] the current input, and T the sample time.

Parameters

sampleTime

Discrete sample period (seconds).

Remarks

• Noise amplification: Differentiation amplifies high-frequency noise; pre-filter noisy signals with Smooth or a low-pass filter
• First sample: Output is zero on the first simulation step (no prior input value available)
• Sample time: Smaller sample times increase derivative gain; the output is scaled by 1/T
• Backward difference: This is the standard backward Euler differentiator — causal and computationally efficient
• For continuous design: Use the Derivative block (with built-in filtering) for smoother continuous differentiation

See Also

• Derivative: Continuous-time derivative
• DiscreteIntegrator: Discrete-time integrator (inverse operation)