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Absolute Value

Math

The Absolute Value block computes the magnitude (absolute value) of the input signal. The output is always non-negative regardless of input sign. This is used for magnitude calculations, error metrics, and signal rectification in control systems and signal processing applications.

Mathematical Model

y(t) = |u(t)| = \begin{cases} u(t), & \text{if } u(t) \ge 0 \\ -u(t), & \text{if } u(t) < 0 \end{cases}

Inputs & Outputs

Direction	ID	Label	Type	Status
→ In	`in`	Input	number	Required
← Out	`out`	Output	number	Output

Usage Examples

Sine wave input produces rectified output with doubled frequency component.

Remarks & Best Practices

Output always ≥ 0 regardless of input sign
Non-differentiable at u = 0 (infinite slope)
Zero computational overhead
Often cascaded with filters for magnitude tracking
Commonly combined with Product or SquareRoot for norm calculations

Related Components

Product: Multiplication (useful for magnitude-squared)
SquareRoot: n-th root (for RMS from magnitude-squared)
Saturation: Output limiting