`SchmittTrigger`#

Description#

The Schmitt trigger (Otto Schmitt, 1934) is a hysteresis comparator: a circuit whose output changes only when the input crosses the opposite threshold from the one that last triggered it. This double-threshold behavior gives the trigger its noise immunity - a noisy input that briefly dips back across a single threshold cannot rapidly toggle the output.

\[\begin{split} \text{output}[t] = \begin{cases} 1.0 & \text{if } x[t] > \text{upper} \\\\ 0.0 & \text{if } x[t] < \text{lower} \\\\ \text{output}[t-1] & \text{otherwise} \end{cases} \end{split}\]

The window [lower, upper] is the dead band. Inside it the output is latched: whichever value (1.0 or 0.0) the trigger last committed to is held until the input crosses out the other side.

Until the first input crosses either threshold the output holds the initial latch seed. The default is 0.0 (the low state), so a signal that starts inside the dead band reads low rather than NaN. Pass initial=1.0 to start high, or initial=nan to leave the output undefined until the first crossing.

Parameters#

lower: lower threshold. Must be strictly less than upper. The output latches to 0.0 when the input falls below this value.
upper: upper threshold. The output latches to 1.0 when the input rises above this value.
initial: the latch value held before the first threshold crossing. Must be 0.0 (low), 1.0 (high), or nan (undefined until the first crossing). Defaults to 0.0.

Implementation Details#

O(1) per step. One scalar of state (the latched output). The constructor rejects lower >= upper, non-finite thresholds, and an initial that is not 0.0, 1.0, or nan; reset() restores the latched state to initial.

Examples#

Usage example#

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from screamer import SchmittTrigger

# A noisy sine wave that repeatedly crosses zero.
t = np.linspace(0, 4 * np.pi, 400)
x = np.sin(t) + 0.25 * np.random.default_rng(0).standard_normal(400)

# A naive zero-cross comparator would chatter on the noise. The
# Schmitt trigger requires the signal to swing past +/- 0.3 before
# toggling, so it produces a clean square wave.
trig = SchmittTrigger(lower=-0.3, upper=0.3)
y = trig(x)

fig = make_subplots(rows=2, cols=1, shared_xaxes=True,
                    row_heights=[0.6, 0.4], vertical_spacing=0.05)
fig.add_trace(go.Scatter(y=x, mode='lines', name='input'),     row=1, col=1)
fig.add_hline(y=+0.3, line_dash='dash', line_color='gray', row=1, col=1)
fig.add_hline(y=-0.3, line_dash='dash', line_color='gray', row=1, col=1)
fig.add_trace(go.Scatter(y=y, mode='lines', name='trigger',
                         line=dict(color='red')),             row=2, col=1)
fig.update_layout(
    title="Schmitt trigger on a noisy sine wave (lower=-0.3, upper=+0.3)",
    xaxis2_title="Sample", yaxis=dict(title="Input"),
    yaxis2=dict(title="Trigger", range=[-0.2, 1.2]),
    margin=dict(l=20, r=20, t=60, b=20),
    legend=dict(orientation="h", yanchor="bottom", y=1.02,
                xanchor="right", x=1),
)
fig.show()

Reference#

A simple debouncer pattern from analog electronics. The exact same logic appears in microcontroller GPIO input filtering, regime-classification rules in algorithmic trading (e.g. "go long above +x, flat between -x and +x, short below -x"), and any signal-flow stage that needs to convert a continuous signal into a sticky binary state.

SchmittTrigger#