Clip / Saturation

Shipping

clip

Amplitude limiting: hard clip, soft clip, or wrap

Signature

Inputs

signalSignalrequired

Outputs

resultSignal

Parameters

Key	Type	Default	Notes
`mode`	enum	clip	one of: clip, soft_clip, wrap
`min_value`	float	-1.0
`max_value`	float	1.0
`softness`	float	0.5

Description

Clip / Saturation constrains the amplitude of a signal to the interval $[min_value, max_value]$ , emulating the bounded output range of physical systems (converters, amplifiers, actuators). It operates element-wise, preserving signal length, sample rate, and the input's physical unit — the output carries the same dimension as the input.

Three mode behaviors are available. `clip` (hard saturation) replaces any sample above max_value with max_value and any below min_value with min_value. `soft_clip` applies a smooth tanh-shaped knee near the limits so the transition into saturation is continuous in its derivative; the softness parameter in $[0, 1]$ controls how gradually the knee engages. `wrap` performs modulo wrapping: values leaving the range re-enter from the opposite bound, mimicking phase accumulators and counter overflow.

The node is stateless — each sample maps through a memoryless nonlinearity with no dependence on neighbors or history. Because saturation is nonlinear, uncertainty does not propagate linearly: samples pinned to a bound have their sensitivity to the input collapse toward zero, so any attached $σ$ is attenuated in the clipped region and preserved where the signal passes through unaltered.

Units attached to the signal flow through unchanged; min_value and max_value are interpreted in the same unit as the incoming signal.

Mathematics

clip (x) = min (max (x, x_{m i n}), x_{m a x})

soft (x) = \frac{x _{m a x} + x _{m i n}}{2} + \frac{x _{m a x} - x _{m i n}}{2} tanh (\frac{2 x - ( x _{m a x} + x _{m i n} )}{( x _{m a x} - x _{m i n} ) ( 1 - s )})

wrap (x) = x_{m i n} + ((x - x_{m i n}) mod (x_{m a x} - x_{m i n}))

Examples

Hard saturation of a converter output

Model a DAC that saturates at $\pm 1 V$ . With mode = clip, min_value = -1.0, max_value = 1.0, a sine of amplitude $1.5$ is flattened at both rails, producing the characteristic clipped plateaus. Everything within $[- 1, 1]$ passes through untouched.

Soft-clip guitar-style saturation

Set mode = soft_clip, softness = 0.7 to round the knee. Instead of the abrupt corner of hard clipping, the signal eases into the limits along a tanh curve, adding smooth harmonic content rather than the harsh high-order harmonics of a hard corner.

mode      = soft_clip
min_value = -1.0
max_value =  1.0
softness  =  0.7

Applications

Modeling saturation and rail limits in amplifiers, DAC/ADC front-ends, and sensor conditioning circuits.
Actuator constraint enforcement in control-loop simulations, where commanded effort must not exceed physical travel or torque limits.
Audio waveshaping and overdrive/distortion effects using hard or soft (tanh) clipping.
Phase and counter wrapping in oscillator and modular-arithmetic pipelines via the `wrap` mode.

Neat

In `soft_clip` mode as `softness` approaches 0 the knee sharpens toward the hard-clip corner, while values near 1 spread the nonlinearity across the entire range — hard clip is effectively the limiting case.

Because saturation zeroes the local slope of the transfer curve at a pinned rail, `clip` acts as a nonlinear uncertainty limiter: it can suppress $\sigma$ growth on samples driven into the bounds.

Known issues

In `wrap` mode a degenerate range where `max_value` equals `min_value` yields a zero-width interval, making the modulo undefined (division by zero) at the boundary.

Hard `clip` introduces a slope discontinuity at each limit; downstream derivative or FFT stages will see spectral artifacts (added harmonics) from the sharp corners.