Scale & Offset

Shipping

scale_offset

Linear transform y = a·x + b with configurable order

Signature

Inputs

signalSignalrequired

Outputs

resultSignal

Parameters

Key	Type	Default	Notes
`scale`	float	1.0
`offset`	float	0.0
`order`	enum	scale_then_offset	one of: scale_then_offset, offset_then_scale

Description

Scale & Offset applies an affine (linear) transform to its input signal: it multiplies by a constant gain scale ( $a$ ) and adds a constant bias offset ( $b$ ). The order parameter selects whether the offset is applied after scaling ( $y = a x + b$ ) or before scaling ( $y = a (x + b)$ ), which are genuinely different transforms whenever $b \neq = 0$ .

The node operates sample-by-sample on the values of a Signal, preserving its timestamps and sample rate. It is purely memoryless — there is no state carried across samples or graph ticks — so the same input always produces the same output regardless of history.

Because scale and offset are treated as exact constants, uncertainty propagates by the linear rule: multiplying by $a$ scales the standard deviation by $∣ a ∣$ , and adding $b$ leaves it unchanged. Thus $σ_{y} = ∣ a ∣ σ_{x}$ in both orderings. Physical units flow through unchanged; scale is dimensionless and offset is interpreted in the signal's own unit, so no rescaling of the unit label occurs.

This node is the canonical primitive for linear calibration, unit-preserving gain staging, and sign inversion (via a negative scale).

Mathematics

y = a x + b (scale_then_offset)

y = a (x + b) (offset_then_scale)

σ_{y} = ∣ a ∣ σ_{x}

Examples

Two-point sensor calibration

A thermocouple front-end outputs raw millivolts that map linearly to temperature. Using the standard order $y = a x + b$ , set scale to the slope and offset to the intercept obtained from a two-point fit:

scale  = 24.98   # °C per mV
offset = -1.35   # °C
order  = scale_then_offset

Every input sample $x$ (mV) becomes $y = 24.98 x - 1.35$ (°C), with the input's uncertainty scaled by $24.98$ .

Bias removal before gain

To subtract a known DC pedestal before amplifying, choose offset_then_scale with a negative offset: $y = a (x + b)$ . With scale = 10 and offset = -0.5, a signal is first shifted down by $0.5$ then multiplied by $10$ , unlike the reversed order which would yield $10 x - 0.5$ .

Applications

Linear calibration of sensor readings (thermocouples, load cells, pressure transducers) from raw counts or volts to engineering units.
Gain staging and level trimming in signal chains, including sign inversion with a negative scale.
Unit-consistent normalization, e.g. converting a 0–5 V ADC range to a 0–100% or physical span before downstream processing.
Removing a known DC bias or applying a fixed setpoint offset in control and instrumentation pipelines.

Neat

The two `order` options are not redundant: $a x + b$ and $a(x + b)$ coincide only when $b = 0$; otherwise they differ by a factor of $a$ applied to the offset.

A negative `scale` acts as an exact sign inversion while still scaling uncertainty by $|a|$, so the standard deviation stays positive even as the mean flips.

Known issues

Setting `scale = 0` collapses the signal to a constant (`offset` or $a\cdot b = 0$) and forces $\sigma_y = 0$, discarding all input variability and uncertainty — this is mathematically correct but easy to trigger by accident.