diff --git a/src/math_channel.cpp b/src/math_channel.cpp
new file mode 100644
index 0000000..11e3c13
--- /dev/null
+++ b/src/math_channel.cpp
@@ -0,0 +1,233 @@
+// SPDX-License-Identifier: MIT
+// SPDX-FileCopyrightText: 2026 Martino Ferrari
+
+#include "math_channel.hpp"
+
+#include <algorithm>
+#include <cmath>
+
+namespace udpscope {
+namespace {
+
+constexpr double kPi = 3.14159265358979323846;
+
+/// A biquad's coefficients for one node, from the RBJ audio-EQ cookbook. `q` is 1/sqrt(2)
+/// (Butterworth) for the plain low/high pass, and the node's own for the band pass -- which is
+/// built here as the constant-0-dB-peak form, because a derived trace wants the band itself and
+/// not whatever gain its width happened to produce.
+void biquad(MathOp op, double fc, double q, double dt, double& b0, double& b1, double& b2,
+            double& a1, double& a2) {
+  // Two Nyquist guards and a floor: a cutoff at or above Nyquist has no meaning to give, and one
+  // at zero would give coefficients of zero -- a trace that is flat because the filter is broken
+  // rather than because the signal is.
+  const double nyquist = 0.5 / std::max(dt, 1e-12);
+  fc = std::clamp(fc, nyquist * 1e-6, nyquist * 0.99);
+  q = std::clamp(q, 1e-3, 100.0);
+  const double w0 = 2.0 * kPi * fc * dt;
+  const double cos_w0 = std::cos(w0);
+  const double alpha = std::sin(w0) / (2.0 * q);
+  const double a0 = 1.0 + alpha;
+  switch (op) {
+    case MathOp::LowPass:
+      b0 = (1.0 - cos_w0) * 0.5;
+      b1 = 1.0 - cos_w0;
+      b2 = b0;
+      break;
+    case MathOp::HighPass:
+      b0 = (1.0 + cos_w0) * 0.5;
+      b1 = -(1.0 + cos_w0);
+      b2 = b0;
+      break;
+    default:  // BandPass
+      b0 = alpha;
+      b1 = 0.0;
+      b2 = -alpha;
+      break;
+  }
+  a1 = -2.0 * cos_w0;
+  a2 = 1.0 - alpha;
+  b0 /= a0;
+  b1 /= a0;
+  b2 /= a0;
+  a1 /= a0;
+  a2 /= a0;
+}
+
+/// One biquad step, transposed direct form II -- the form whose state words are the two things
+/// that actually need carrying between samples.
+double biquad_step(double x, double b0, double b1, double b2, double a1, double a2, double& z1,
+                   double& z2) {
+  const double y = b0 * x + z1;
+  z1 = b1 * x - a1 * y + z2;
+  z2 = b2 * x - a2 * y;
+  return y;
+}
+
+}  // namespace
+
+const char* math_op_name(MathOp op) {
+  switch (op) {
+    case MathOp::Source: return "channel";
+    case MathOp::Gain: return "gain + offset";
+    case MathOp::Abs: return "abs";
+    case MathOp::Sqrt: return "sqrt";
+    case MathOp::Clamp: return "clamp";
+    case MathOp::LowPass: return "low pass";
+    case MathOp::HighPass: return "high pass";
+    case MathOp::BandPass: return "band pass";
+    case MathOp::Sum: return "sum";
+    case MathOp::Sub: return "difference";
+    case MathOp::Mul: return "product";
+    case MathOp::Div: return "ratio";
+  }
+  return "?";
+}
+
+int math_op_count() { return 12; }
+
+MathOp math_op_at(int index) {
+  switch (index) {
+    case 0: return MathOp::Source;
+    case 1: return MathOp::Gain;
+    case 2: return MathOp::Abs;
+    case 3: return MathOp::Sqrt;
+    case 4: return MathOp::Clamp;
+    case 5: return MathOp::LowPass;
+    case 6: return MathOp::HighPass;
+    case 7: return MathOp::BandPass;
+    case 8: return MathOp::Sum;
+    case 9: return MathOp::Sub;
+    case 10: return MathOp::Mul;
+    default: return MathOp::Div;
+  }
+}
+
+int math_op_arity(MathOp op) {
+  switch (op) {
+    case MathOp::Source: return 0;
+    case MathOp::Sum:
+    case MathOp::Sub:
+    case MathOp::Mul:
+    case MathOp::Div: return 2;
+    default: return 1;
+  }
+}
+
+bool math_op_uses_gain(MathOp op) { return op == MathOp::Gain; }
+bool math_op_uses_filter(MathOp op) {
+  return op == MathOp::LowPass || op == MathOp::HighPass || op == MathOp::BandPass;
+}
+bool math_op_uses_clamp(MathOp op) { return op == MathOp::Clamp; }
+
+void math_prepare(const MathChannel& channel, MathRuntime& rt, double dt) {
+  const std::size_t n = channel.nodes.size();
+  rt.value.assign(n, 0.0);
+  rt.b0.assign(n, 1.0);
+  rt.b1.assign(n, 0.0);
+  rt.b2.assign(n, 0.0);
+  rt.a1.assign(n, 0.0);
+  rt.a2.assign(n, 0.0);
+  // A rate change *keeps* the filter state: the state words are in the signal's units, not in
+  // time, so a decimation change moves the cutoffs (which is why the coefficients are rebuilt)
+  // without making the trace jump. A node that is new gets zeros, which is a filter starting from
+  // rest -- the only honest starting point there is.
+  rt.z1.resize(n, 0.0);
+  rt.z2.resize(n, 0.0);
+  rt.dt = dt;
+  rt.ready = true;
+  for (std::size_t i = 0; i < n; ++i) {
+    const MathNode& node = channel.nodes[i];
+    if (!math_op_uses_filter(node.op)) continue;
+    biquad(node.op, node.fc, node.q, dt, rt.b0[i], rt.b1[i], rt.b2[i], rt.a1[i], rt.a2[i]);
+  }
+}
+
+double math_step(const MathChannel& channel, MathRuntime& rt,
+                 const std::function<double(const std::string&)>& source) {
+  const std::size_t n = channel.nodes.size();
+  if (n == 0 || rt.value.size() != n) return std::nan("");
+  const auto at = [&](int index) -> double {
+    if (index < 0 || static_cast<std::size_t>(index) >= n) return std::nan("");
+    return rt.value[static_cast<std::size_t>(index)];
+  };
+  for (std::size_t i = 0; i < n; ++i) {
+    const MathNode& node = channel.nodes[i];
+    double x = 0.0;
+    switch (node.op) {
+      case MathOp::Source:
+        x = source(node.source);
+        break;
+      case MathOp::Gain:
+        x = at(node.in_a) * node.gain + node.offset;
+        break;
+      case MathOp::Abs:
+        x = std::fabs(at(node.in_a));
+        break;
+      case MathOp::Sqrt:
+        // Of the magnitude: the square root of a negative sample has no real answer, and a derived
+        // trace that turns into NaN for half a cycle is not a useful one.
+        x = std::sqrt(std::fabs(at(node.in_a)));
+        break;
+      case MathOp::Clamp:
+        x = std::clamp(at(node.in_a), std::min(node.lo, node.hi), std::max(node.lo, node.hi));
+        break;
+      case MathOp::LowPass:
+      case MathOp::HighPass:
+      case MathOp::BandPass:
+        x = biquad_step(at(node.in_a), rt.b0[i], rt.b1[i], rt.b2[i], rt.a1[i], rt.a2[i], rt.z1[i],
+                        rt.z2[i]);
+        break;
+      case MathOp::Sum:
+        x = at(node.in_a) + at(node.in_b);
+        break;
+      case MathOp::Sub:
+        x = at(node.in_a) - at(node.in_b);
+        break;
+      case MathOp::Mul:
+        x = at(node.in_a) * at(node.in_b);
+        break;
+      case MathOp::Div: {
+        const double d = at(node.in_b);
+        // A scope trace must not go to infinity or NaN: a division by zero reads as zero, which is
+        // visibly wrong on the plot instead of invisibly wrong in the number.
+        x = std::fabs(d) > 0.0 ? at(node.in_a) / d : 0.0;
+        break;
+      }
+    }
+    rt.value[i] = x;
+  }
+  const int out = channel.output;
+  if (out < 0 || static_cast<std::size_t>(out) >= n) return std::nan("");
+  return rt.value[static_cast<std::size_t>(out)];
+}
+
+bool math_channel_valid(const MathChannel& channel, std::string* why) {
+  const std::size_t n = channel.nodes.size();
+  const auto fail = [&](const std::string& text) {
+    if (why != nullptr) *why = text;
+    return false;
+  };
+  if (n == 0) return fail("empty graph");
+  for (std::size_t i = 0; i < n; ++i) {
+    const MathNode& node = channel.nodes[i];
+    if (node.op == MathOp::Source && node.source.empty()) {
+      return fail("node " + std::to_string(i + 1) + ": no channel chosen");
+    }
+    const int arity = math_op_arity(node.op);
+    const int ins[2] = {node.in_a, node.in_b};
+    for (int k = 0; k < arity; ++k) {
+      // Only nodes *before* this one: the evaluator walks the list in order, so a forward or
+      // self reference is not a cycle to detect, it is a node reading a value that is not there.
+      if (ins[k] < 0 || ins[k] >= static_cast<int>(i)) {
+        return fail("node " + std::to_string(i + 1) + ": input " + std::to_string(k + 1) +
+                    " is not connected");
+      }
+    }
+  }
+  if (channel.output < 0 || static_cast<std::size_t>(channel.output) >= n) {
+    return fail("no output chosen");
+  }
+  return true;
+}
+
+}  // namespace udpscope
diff --git a/src/math_channel.hpp b/src/math_channel.hpp
new file mode 100644
index 0000000..f5d2e0d
--- /dev/null
+++ b/src/math_channel.hpp
@@ -0,0 +1,95 @@
+// SPDX-License-Identifier: MIT
+// SPDX-FileCopyrightText: 2026 Martino Ferrari
+#pragma once
+
+#include <functional>
+#include <string>
+#include <vector>
+
+namespace udpscope {
+
+/// A math channel's operations. `Source` reads another channel by name; `Sum`/`Sub`/`Mul`/`Div`
+/// combine two node values; the rest take one. `Sqrt` and `Clamp` are here because a scope's
+/// derived traces want them constantly (an envelope, a rectified-and-squared RMS input, a
+/// bounded control signal) and they cost the same to carry as the ones that were asked for.
+enum class MathOp {
+  Source,
+  Gain,      ///< y = x * gain + offset
+  Abs,
+  Sqrt,
+  Clamp,     ///< y = min(max(x, lo), hi)
+  LowPass,   ///< biquad, corner `fc` Hz
+  HighPass,
+  BandPass,  ///< `fc` Hz centre, `q` wide
+  Sum,       ///< a + b
+  Sub,       ///< a - b
+  Mul,       ///< a * b
+  Div,       ///< a / b, zero when b is 0 (a scope trace must not go to inf/NAN)
+};
+
+const char* math_op_name(MathOp op);
+int math_op_count();
+MathOp math_op_at(int index);
+/// Inputs the op takes: 0 for `Source`, 1 for the unary ones, 2 for the arithmetic.
+int math_op_arity(MathOp op);
+/// Which of the per-node parameters an op actually reads, so a dialog can show only those rows --
+/// an option that does nothing for an op is left out rather than stored and ignored.
+bool math_op_uses_gain(MathOp op);
+bool math_op_uses_filter(MathOp op);
+bool math_op_uses_clamp(MathOp op);
+
+/// One node of a math channel's graph. Node indices are positions in `MathChannel::nodes`, and a
+/// node may only read ones before it: the evaluator walks the list in order, which is what makes a
+/// cycle impossible by construction rather than by a check.
+struct MathNode {
+  MathOp op = MathOp::Source;
+  std::string source;   ///< `Source`: the channel to read, by name.
+  int in_a = -1;        ///< other ops: node indices, -1 while unconnected.
+  int in_b = -1;
+  double gain = 1.0;
+  double offset = 0.0;
+  double fc = 100.0;    ///< LP/HP corner, BP centre, Hz.
+  double q = 0.707;     ///< BP quality factor.
+  double lo = -1.0;     ///< `Clamp` bounds.
+  double hi = 1.0;
+  double x = 0.0;       ///< the editor's box position, logical pixels.
+  double y = 0.0;
+};
+
+/// A derived channel: a graph of nodes and which node is the answer.
+struct MathChannel {
+  std::string name;     ///< user-facing; also how another graph names it as a `Source`.
+  std::string unit;     ///< optional. When empty, the first `Source` node's unit is used.
+  bool enabled = false;
+  std::vector<MathNode> nodes;
+  int output = -1;      ///< the node whose value is the channel's.
+};
+
+/// The per-channel runtime: the filter memory and the per-node scratch. Kept apart from the
+/// `MathChannel` because it is *state* (one sample of history per biquad) while the channel is
+/// *configuration* -- so the pane can edit one while the producer streams through the other.
+struct MathRuntime {
+  std::vector<double> value;  ///< one per node, this sample.
+  /// Biquad coefficients per node (transposed direct form II), and its two state words.
+  std::vector<double> b0, b1, b2, a1, a2, z1, z2;
+  /// The rate the coefficients were built for; a change rebuilds them.
+  double dt = 0.0;
+  bool ready = false;
+};
+
+/// Fills `rt`'s size and the biquad coefficients for `dt` seconds per sample. Call it whenever the
+/// graph or the stored rate changes -- cheap, and it is what keeps the filters' cutoffs honest
+/// across a decimation change, where `dt` is not what it was when the user typed a frequency.
+void math_prepare(const MathChannel& channel, MathRuntime& rt, double dt);
+
+/// One sample through the graph. `source(name)` returns that channel's current value, and NAN when
+/// it is not acquired -- which propagates to the output, so a math channel whose source is disabled
+/// reads as "no data" rather than as whatever the last good sample was.
+double math_step(const MathChannel& channel, MathRuntime& rt,
+                 const std::function<double(const std::string&)>& source);
+
+/// Whether the graph is complete enough to produce a value: an output node that exists, and every
+/// input it needs connected to a node that exists (with `Source` nodes naming something).
+bool math_channel_valid(const MathChannel& channel, std::string* why = nullptr);
+
+}  // namespace udpscope
diff --git a/src/measure.cpp b/src/measure.cpp
new file mode 100644
index 0000000..ee78119
--- /dev/null
+++ b/src/measure.cpp
@@ -0,0 +1,228 @@
+// SPDX-License-Identifier: MIT
+// SPDX-FileCopyrightText: 2026 Martino Ferrari
+
+#include "measure.hpp"
+
+#include <algorithm>
+#include <cmath>
+
+namespace udpscope {
+
+MeasureStats measure_stats(const std::vector<double>& time, const std::vector<double>& value) {
+  MeasureStats s;
+  const std::size_t n = std::min(time.size(), value.size());
+  for (std::size_t i = 0; i < n; ++i) {
+    const double v = value[i];
+    if (!std::isfinite(v)) continue;
+    if (!s.valid) {
+      s.lo = s.hi = v;
+      s.at_lo = s.at_hi = time[i];
+      s.valid = true;
+    } else {
+      if (v < s.lo) {
+        s.lo = v;
+        s.at_lo = time[i];
+      }
+      if (v > s.hi) {
+        s.hi = v;
+        s.at_hi = time[i];
+      }
+    }
+    s.sum += v;
+    ++s.count;
+  }
+  return s;
+}
+
+
+const char* measure_type_name(MeasureType type) {
+  switch (type) {
+    case MeasureType::Average: return "average";
+    case MeasureType::Min: return "min";
+    case MeasureType::Max: return "max";
+    case MeasureType::PeakToPeak: return "peak to peak";
+    case MeasureType::Amplitude: return "amplitude";
+    case MeasureType::Top: return "top";
+    case MeasureType::Bottom: return "bottom";
+    case MeasureType::PulseDuration: return "pulse duration";
+    case MeasureType::Period: return "period";
+    case MeasureType::Frequency: return "frequency";
+  }
+  return "?";
+}
+
+int measure_type_count() { return 10; }
+
+MeasureType measure_type_at(int index) {
+  switch (index) {
+    case 0: return MeasureType::Average;
+    case 1: return MeasureType::Top;
+    case 2: return MeasureType::Bottom;
+    case 3: return MeasureType::Max;
+    case 4: return MeasureType::Min;
+    case 5: return MeasureType::PeakToPeak;
+    case 6: return MeasureType::Amplitude;
+    case 7: return MeasureType::PulseDuration;
+    case 8: return MeasureType::Frequency;
+    default: return MeasureType::Period;
+  }
+}
+
+bool measure_uses_threshold(MeasureType type) {
+  return type == MeasureType::Top || type == MeasureType::Bottom ||
+         type == MeasureType::PulseDuration;
+}
+
+bool measure_uses_side(MeasureType type) { return type == MeasureType::PulseDuration; }
+
+bool measure_can_show_on_plot(MeasureType) { return true; }
+
+MeasureResult compute_measure(const std::vector<double>& time, const std::vector<double>& value,
+                              MeasureType type, const MeasureOptions& options,
+                              const MeasureStats* stats) {
+  MeasureResult out;
+  const std::size_t n = std::min(time.size(), value.size());
+  if (n == 0) return out;
+
+  // A threshold as a share of the window's own range, which is what makes one percentage
+  // travel across signals: a threshold in volts would have to be typed for each. The bounds
+  // come from the caller when it has them (several measurements on one signal), because the
+  // scan is O(visible samples) and this runs per frame while a live window scrolls.
+  const MeasureStats b = stats != nullptr ? *stats : measure_stats(time, value);
+  if (!b.valid) return out;
+
+  // A threshold as a share of the window's own range. A flat window has no range at all, so
+  // the level is the signal's one value -- every sample is on neither side of it (nothing is
+  // strictly above or below), and the crossing types then find no edge, which is the honest
+  // answer for a signal that never moves.
+  const double pct = std::clamp(options.threshold_pct, 0.0, 100.0) / 100.0;
+  const double level = b.lo + pct * (b.hi - b.lo);
+
+  switch (type) {
+    case MeasureType::Average: {
+      if (b.count == 0) return out;
+      out.primary = b.sum / static_cast<double>(b.count);
+      // A mean is a level like any other, so it can be shown as one ruler.
+      out.marks.push_back({true, out.primary});
+      out.valid = true;
+      return out;
+    }
+    case MeasureType::Min:
+    case MeasureType::Max: {
+      // A ruler at the extreme, and a marker at the time it happened: "the minimum" is a level
+      // and a place. The place comes from the shared scan, which takes the *first* sample to
+      // reach the extreme -- the one a reader's eye lands on when the extreme is a plateau.
+      const bool want_max = type == MeasureType::Max;
+      out.primary = want_max ? b.hi : b.lo;
+      out.marks.push_back({true, out.primary});
+      out.marks.push_back({false, want_max ? b.at_hi : b.at_lo});
+      out.valid = true;
+      return out;
+    }
+    case MeasureType::PeakToPeak:
+    case MeasureType::Amplitude: {
+      // Both come straight out of the window's own extremes, which every type already needs:
+      // the two rulers are the same pair, and the numbers differ by a factor of two.
+      out.primary = type == MeasureType::PeakToPeak ? b.hi - b.lo : 0.5 * (b.hi - b.lo);
+      // A ruler at each extreme: the *span* is the measurement, and two levels are how a
+      // plot states a span without a band between them.
+      out.marks.push_back({true, b.lo});
+      out.marks.push_back({true, b.hi});
+      out.valid = true;
+      return out;
+    }
+    case MeasureType::Top:
+    case MeasureType::Bottom: {
+      const bool want_high = type == MeasureType::Top;
+      double sum = 0.0;
+      std::size_t used = 0;
+      for (std::size_t i = 0; i < n; ++i) {
+        if (!std::isfinite(value[i])) continue;
+        if ((value[i] > level) != want_high) continue;
+        sum += value[i];
+        ++used;
+      }
+      if (used == 0) return out;
+      out.primary = sum / static_cast<double>(used);
+      out.marks.push_back({true, out.primary});
+      out.valid = true;
+      return out;
+    }
+    case MeasureType::PulseDuration:
+    case MeasureType::Period:
+    case MeasureType::Frequency: {
+      // No options here on purpose: a period is the spacing of *rising* crossings of the
+      // *mid* level -- one edge per cycle -- and a threshold or a side to choose from would
+      // only let the user make the count wrong (a threshold near either extreme counts noise
+      // as crossings; counting both edges halves the period).
+      const double period_level = b.lo + 0.5 * (b.hi - b.lo);
+      // Every strict side change is an edge. "Strict" is what keeps a signal that merely
+      // touches the level from counting each sample as a crossing: a sample equal to the
+      // level is on neither side, so the walk holds the last decided side until one is.
+      struct Edge {
+        double t;
+        bool rising;
+      };
+      std::vector<Edge> edges;
+      bool have_side = false;
+      bool side = false;
+      for (std::size_t i = 0; i < n; ++i) {
+        const double v = value[i];
+        if (!std::isfinite(v) || v == period_level) continue;
+        const bool cur = v > period_level;
+        if (have_side && cur != side) edges.push_back({time[i], cur});
+        side = cur;
+        have_side = true;
+      }
+      if (edges.size() < 2) return out;
+      // The pulse is the `above` side: its widths run from the edge that enters it to the
+      // edge that leaves it, and a period is the spacing of the edges that enter it -- one
+      // per cycle, whatever else the waveform does in between.
+      std::vector<double> starts;
+      std::vector<double> widths;
+      for (std::size_t i = 0; i + 1 < edges.size(); ++i) {
+        if (edges[i].rising != options.above) continue;
+        starts.push_back(edges[i].t);
+        if (edges[i + 1].rising == options.above) continue;
+        widths.push_back(edges[i + 1].t - edges[i].t);
+      }
+      if (type == MeasureType::PulseDuration) {
+        if (widths.empty()) return out;
+        double sum = 0.0;
+        for (const double w : widths) sum += w;
+        out.primary = sum / static_cast<double>(widths.size());
+        // Duty as width/period, not as pulse-time over the window: a window that starts or
+        // ends mid-pulse holds partial cycles, and counting only the complete ones against
+        // the whole span would report a duty that depends on where the window happened to
+        // begin. The period is the spacing of the pulse's own enter-edges.
+        double period = 0.0;
+        if (starts.size() >= 2) {
+          period = (starts.back() - starts.front()) / static_cast<double>(starts.size() - 1);
+        }
+        // The duty needs a period, which needs two pulses; a window holding one reports the
+        // width alone rather than a duty computed against a span that is not a cycle.
+        out.secondary = period > 0.0 ? out.primary / period : 0.0;
+        out.has_secondary = period > 0.0;
+        if (!starts.empty()) {
+          out.marks.push_back({false, starts.front()});
+          out.marks.push_back({false, starts.front() + out.primary});
+        }
+        out.valid = true;
+        return out;
+      }
+      if (starts.size() < 2) return out;
+      const double span = starts.back() - starts.front();
+      const double period = span / static_cast<double>(starts.size() - 1);
+      if (!(period > 0.0)) return out;
+      out.primary = type == MeasureType::Period ? period : 1.0 / period;
+      out.marks.push_back({false, starts.front()});
+      out.marks.push_back({false, starts.front() + period});
+      out.valid = true;
+      return out;
+    }
+  }
+  return out;
+}
+
+
+}  // namespace udpscope
diff --git a/src/measure.hpp b/src/measure.hpp
new file mode 100644
index 0000000..fd5ba7c
--- /dev/null
+++ b/src/measure.hpp
@@ -0,0 +1,121 @@
+// SPDX-License-Identifier: MIT
+// SPDX-FileCopyrightText: 2026 Martino Ferrari
+#pragma once
+
+#include <string>
+#include <vector>
+
+namespace udpscope {
+
+/// What a measurement computes over the visible window of one signal.
+enum class MeasureType {
+  Average,        ///< the mean of every visible sample
+  Min,            ///< the smallest visible value
+  Max,            ///< the largest visible value
+  /// The largest swing in the window: `max - min`, the two extremes the eye would measure
+  /// with a ruler across the waveform.
+  PeakToPeak,
+  /// Half the peak-to-peak swing, `(max - min) / 2` -- the amplitude of a symmetric waveform
+  /// about its own mean, which is the figure a datasheet quotes and a signal generator is set
+  /// to. Deliberately not `max(|value|)`: that is a *distance from zero*, which for a signal
+  /// riding on an offset is a different and less useful number.
+  Amplitude,
+  Top,            ///< the signal's high level (the mean of the samples above the threshold)
+  Bottom,         ///< the signal's low level (the mean of the samples below it)
+  PulseDuration,  ///< how long the signal spends on one side of the threshold
+  Period,         ///< the time between two successive crossings of the threshold
+  Frequency,      ///< 1 / period
+};
+
+/// Type-specific behaviour. Every field is meaningful only for the types named below; the
+/// others ignore it (an option that does nothing for a type is left out of the dialog
+/// rather than stored and ignored).
+struct MeasureOptions {
+  /// `Top`/`Bottom`/`PulseDuration`/`Period`/`Frequency`: where the split is, as a share of
+  /// the window's own min..max. The middle by default, which is what a symmetric waveform
+  /// wants; a 3.3 V logic signal with ringing wants it nearer the top.
+  double threshold_pct = 50.0;
+  /// `PulseDuration`: which side of the threshold is "the pulse". `Period`/`Frequency`
+  /// use it as the edge direction, so one cycle is counted once.
+  bool above = true;
+  /// Draw the value on the plot: a ruler at a level (top/bottom), both rulers at the
+  /// extremes (min/max), the pulse's two edges as vertical markers (pulse duration). The
+  /// markers are readouts -- they follow the window, and the user cannot drag them.
+  bool show_on_plot = false;
+};
+
+/// One entry in the measurements pane, and everything needed to recompute it: the signal by
+/// *name* (a CONFIG renumbers channels, so an index would start measuring another signal)
+/// and the type with its options.
+struct Measure {
+  std::string signal;
+  MeasureType type = MeasureType::Average;
+  MeasureOptions options;
+};
+
+/// One thing to draw on the plot for a measurement: a *level* (a horizontal ruler) or a
+/// *time* (a vertical marker). A result carries up to two, and they need not be the same kind
+/// -- `min` is a ruler at the value and a marker where the value occurred.
+struct MeasureMarkSpec {
+  bool level = false;
+  double value = 0.0;
+};
+
+/// What a measurement computed. `valid` is what the pane shows as `--` when a type has
+/// nothing to measure in the window (a period on a flat signal, a pulse that never crosses).
+struct MeasureResult {
+  double primary = 0.0;    ///< the value the pane prints
+  double secondary = 0.0;  ///< pulse duration also reports the duty; unused otherwise
+  bool has_secondary = false;
+  std::vector<MeasureMarkSpec> marks;  ///< what to draw, empty when the type draws nothing
+  bool valid = false;
+};
+
+/// The window's own extremes, which every threshold-relative type scales from and which
+/// several types report directly. Public so a caller holding *several* measurements on one
+/// signal can pay for the scan once: it is O(visible samples) and a live view at 1 MS/s makes
+/// that the difference between a frame budget and a stall.
+struct MeasureStats {
+  double lo = 0.0;
+  double hi = 0.0;
+  /// The sum and count of the finite samples: the mean, and the mean over a level, are both
+  /// derived from them, so the window is read once for every type that is not an edge count.
+  double sum = 0.0;
+  std::size_t count = 0;
+  /// The time of the *first* sample to reach each extreme -- "min" is a level and a place, and
+  /// finding the place is why this is not just the two numbers.
+  double at_lo = 0.0;
+  double at_hi = 0.0;
+  bool valid = false;
+};
+
+/// One pass over a window: both extremes with their first positions, and the sum and count.
+MeasureStats measure_stats(const std::vector<double>& time, const std::vector<double>& value);
+
+/// The engine: the visible samples of one signal, in stream seconds and in the signal's own
+/// units. Both arrays are the same length and in time order; the function reads nothing else,
+/// which is what makes it testable and what keeps the answer independent of the plot.
+///
+/// `stats` is `measure_stats(time, value)` when the caller already has it -- several measurements
+/// on one signal share one scan -- and null to compute it here. It must describe these arrays.
+MeasureResult compute_measure(const std::vector<double>& time, const std::vector<double>& value,
+                              MeasureType type, const MeasureOptions& options,
+                              const MeasureStats* stats = nullptr);
+
+/// A measurement type's name, as the pane's row and the dialog's dropdown spell it.
+const char* measure_type_name(MeasureType type);
+/// The number of entries the dialog's dropdown holds; the index is `MeasureType`.
+int measure_type_count();
+MeasureType measure_type_at(int index);
+/// Whether a type uses the threshold (see `MeasureOptions`), so the dialog can show the
+/// field only then. Deliberately not the case for `Period`/`Frequency`: a period is the
+/// spacing of the crossings of the *mid* level, one rising edge per cycle, and offering a
+/// threshold there only invites a setting that makes the count wrong.
+bool measure_uses_threshold(MeasureType type);
+/// Whether a type uses the `above` side (only `PulseDuration`, where it says which half of
+/// the waveform is the pulse).
+bool measure_uses_side(MeasureType type);
+/// Whether a type draws its result on the plot when asked.
+bool measure_can_show_on_plot(MeasureType type);
+
+}  // namespace udpscope