Martino Ferrari
e83ad86b8f
A bench scope separates Vtop/Vbase from Vmax/Vmin because a band-limited edge overshoots and rings: the mock's `square` at 30 harmonics reaches ±1.179 where its plateau is ±1. On the rippled square the old readings were a property of the edges rather than of the waveform -- `top` 0.986496, `amplitude` 1.179350 -- and `amplitude` reported the overshoot. `top`, `bottom` and `amplitude` are now the flat levels and their delta. A flat level is a density question -- the plateau holds most of the samples and the ringing a few percent -- so `measure_scan_buckets()` folds a 64-bin histogram of the whole buckets' midpoints while it has the list in hand (one observation per bucket, each bin carrying its buckets' exact sum and finite count), and `measure_flat_levels()` takes, either side of the split, the densest bin holding at least half the densest one's buckets -- the outermost of those, which is what makes a waveform with no plateau read its peak -- and the exact mean of the samples of the buckets within 5 % of the window's peak-to-peak of it. 5 % is deliberately under the ~9 %-of-swing Gibbs overshoot. `amplitude` is `top - bottom` (a scope's Vamplitude), not the half-swing it was. Measured, fast mock, 2 s window, harmonics 0 -> 30: top 1.000000 -> 0.999983, bottom -1.000000 -> -0.999983, amplitude 2.000000 -> 1.999966, while `peak to peak` keeps the extremes (2.000000 -> 2.358701). On the 1 Hz sine top is 0.957988 (it was 0.636620, the half-wave mean; a sine has no plateau, so the densest band is at its peak) with sd 0.0014 over a scrolling window, and `peak to peak` is still exactly 2. No raw pass and no new fetch: the histogram is the same fetched bucket list read a second time, gated on a pane that holds one of the three types. `raw` is unchanged (0.1% clean, 2.1% with the --noise 0.1 interferer, against 0.1%/2.1% before) for 0.44 -> 0.50 ms and 0.52 -> 0.65 ms a pass. A window the pyramid cannot summarize -- an hf-filtered walk, or one shorter than a bucket -- keeps the old readings: the mean of each side of the split, and the window's peak to peak for amplitude. Docs: the flat-level invariant (and the two 2/pi assertions it replaces), the probe readings, the manual's measurements page and the README.
123 lines
7.8 KiB
Plaintext
123 lines
7.8 KiB
Plaintext
<page xmlns="http://projectmallard.org/1.0/"
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type="topic" style="task"
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id="measurements">
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<info>
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<link type="guide" xref="index#analysis"/>
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<link type="seealso" xref="cursors"/>
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<desc>A measurement is a statistic of the visible window of one signal, with optional
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on-plot marks and a per-measurement statistics line.</desc>
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<credit type="author copyright">
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<name>Martino Ferrari</name>
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</credit>
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</info>
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<title>Measurements</title>
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<p>A measurement is a statistic of the <em>visible window</em> of one signal, recomputed as
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that window moves. The pane lists them with their values; each can also draw its result on
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the plot.</p>
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<section id="reach">
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<title>How to reach it</title>
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<steps>
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<item>
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<p>Press the measurements button in the toolbar, or <key>m</key>.</p>
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</item>
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<item>
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<p>The pane's <gui>+</gui> adds one; clicking a row opens the dialog where the signal,
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the type, the threshold share and the on-plot marks are set, with <gui>Save</gui> and
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<gui>Delete</gui>.</p>
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</item>
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</steps>
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</section>
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<section id="knowing">
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<title>Worth knowing</title>
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<list>
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<item><p>The types are average, top, bottom, min, max, peak to peak, amplitude, pulse
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duration, period and frequency. <gui>top</gui> and <gui>bottom</gui> are the waveform's
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<em>flat</em> high and low levels: the level the signal dwells at, taken from the densest
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band of the window on each side of the split. A band-limited edge overshoots and rings —
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a nominal 2 V square reaches about ±1.18 at its edges — and a ripple or an overshoot is
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therefore <em>not</em> what these read. <gui>amplitude</gui> is the delta between those two
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levels, and <gui>peak to peak</gui> is the swing between the extremes (so on a rippled
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square <gui>amplitude</gui> reads 2 V where <gui>peak to peak</gui> reads 2.36 V).</p></item>
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<item><p><gui>top</gui> and <gui>bottom</gui> also read <em>near the peak</em> on a
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waveform that has no flat part, which is the honest reading rather than a failure: a unit
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sine has no plateau, so the densest band is at its peak and these read about ±0.96 — not
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the 0.64 a mean over each half would give, and not ±1 either. Only a level the signal
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actually dwells at is a level.</p></item>
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<item><p>The <em>split</em> says which side a level is read from, so any share between the
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two levels reads the same number; it is not a boundary the value depends on. The one case
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where it is read directly is a window the scope cannot summarize by level — a window
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shorter than a level's own resolution, or one read through <gui>hf</gui> — where
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<gui>top</gui>/<gui>bottom</gui> fall back to the mean of each side of the split and
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<gui>amplitude</gui> to the window's peak to peak.</p></item>
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<item><p>The on-plot marks come in two kinds and the mix is the reading: a <em>level</em>
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mark is a ruler at a value, a <em>time</em> mark is a marker at a position. An average
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draws one level mark; a max draws a level mark <em>and</em> a time mark at the first
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sample that reached it; <gui>peak to peak</gui> draws a ruler at each extreme and
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<gui>amplitude</gui> a ruler at each of its two flat levels — the pair is the span, so
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the two rulers <em>are</em> the measurement.</p></item>
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<item><p>Marks cannot be dragged. A measurement mark says what the measurement measured,
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so it is created unselectable — as is the trigger marker.</p></item>
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<item><p>A pass is throttled to a cadence rather than run every frame, so a ruler over a
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live view is <em>stepped</em>. The number and the ruler come from the same pass, so they
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always agree.</p></item>
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<item><p>An invalid pass keeps its <em>level</em> marks and drops its <em>time</em>
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marks. A level is a property of the signal and outlives the window; a position inside
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the window does not. That is what stops the rulers blinking off at a mode change.</p></item>
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<item><p>A crossing is counted with <em>hysteresis</em>, not on a bare level: the
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thresholds are a tenth of the window's peak to peak either side of the share, and an
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edge is counted only once the signal has passed the far one. Period, frequency and pulse
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duration all depend on it. The mid level is exactly where a waveform moves fastest, so
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any interferer faster than the fundamental recrosses a single level several times per
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real crossing — a 5 Hz sine with a 500 Hz tone at a tenth of the amplitude reads 39 Hz
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without the band and 5 Hz with it. The band holds to an interferer a third of the
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waveform's own size.</p></item>
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<item><p>The band is clamped to stay inside the data, which is what keeps a threshold set
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near an extreme usable: a fixed band there would sit above every sample and the
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measurement would read nothing. A share near an extreme still leaves the band little
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room, so it rejects less — which is one reason period and frequency offer no share to
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set.</p></item>
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<item><p>A window with too few crossings reads <code>invalid</code> / <code>--</code>
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rather than a plausible invented number. Frequency over a window holding one edge is the
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usual case.</p></item>
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<item><p><gui>frequency</gui> is reported in Hz and <gui>period</gui>/<gui>pulse
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duration</gui> in seconds; every other type carries the channel's own unit. A value is
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written with a <em>metric prefix</em> so its digits sit in <code>1..999</code> —
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<code>636.62 mV</code>, not <code>0.64 V</code> — including when the stream declares no
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unit at all, which is always the case for a math channel: there the prefix goes tight
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against the number (<code>636.62m</code>), since two decimals of an unprefixed small
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value is <code>0.00</code>.</p></item>
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<item><p>Cost is bounded by reading the summary pyramid the producer already maintains,
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not the raw window: a bucket's sum is a sum, so the mean, the extremes and a level's own
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mean are exact. <gui>top</gui>, <gui>bottom</gui> and <gui>amplitude</gui> read the
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<em>density</em> of the window out of that same summary — which is what tells a flat level
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from a ripple — so those three cost a second read of the summary and never of a sample.</p></item>
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<item><p><gui>Statistics</gui> adds a second line to every measurement showing
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<code>n</code>, the mean, the standard deviation and the range. Each observation is one
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<em>recompute</em> of the pane, so <code>n</code> counts windows measured, not samples —
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a mean frequency over many windows is what that claims to be. <gui>Reset</gui> clears
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every accumulator and starts fresh. A change of display window, a CONFIG or a
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measurement edit also resets; a pause, a resume, a zoom, a pan and the toggle itself do
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not, so turning the line off to read the plot and back on again keeps the history.</p></item>
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</list>
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</section>
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<section id="example">
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<title>Example</title>
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<p>On a 1 Hz ±1 sine: <code>average=0</code>, <code>top=0.957988</code>,
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<code>bottom=-0.957988</code> (the flat levels, near the peaks — a sine has no plateau),
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<code>max=1</code>, <code>min=-1</code>,
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<code>peak to peak=2</code>, <code>amplitude=1.915983</code>, <code>pulse duration=0.5 s</code>
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(duty 0.5), <code>period=1 s</code>, <code>frequency=1 Hz</code>. On the same stream's
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band-limited <code>square</code>, whose edges ring out to ±1.179: <code>top=0.999983</code>,
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<code>bottom=-0.999983</code>, <code>amplitude=1.999966</code> against
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<code>peak to peak=2.358701</code> — the levels are the plateau's and the extremes are the
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edges'. Over a 2 M-sample window those passes read about 0.1% of the samples.</p>
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</section>
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</page>
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