The wavelet reading¶
A PSD says which frequencies a record contains and nothing about when they occur. For a stationary run that is all there is to know. For anything else, such as a rattle that comes and goes, a shock's ring-down, or a resonance a sweep passes through, the timing is what matters, and the spectrum has averaged it away. The wavelet reading shows it: time across, frequency up a logarithmic axis, and amplitude as color. In 3-D, amplitude is the height of the surface above the floor.
Where it lives¶
Wavelet is on a time history's plot bar with the record's other readings, and at most one of them is on at a time. It opens in 3-D, because a scalogram is a function of two variables and a surface shows that directly; the 3D button switches it to the flat picture shown above. In a report, the transient and shock templates include the same figure, drawn from the same computation. For a shock it is used in place of a PSD, because a density's level depends on how much quiet time before and after the event the recording holds.
From a script, the same reading is one call:
The panel¶
The scalogram shows one record at a time, because it is dense and two side by side are hard to read. The record is chosen the same way as everywhere else, in the project tree. Pick a record in the object's grid and the scalogram is of that record; select the whole object and it opens on the first record, with the tree's selection moved to that record so it always says what the picture shows. The panel holds the settings the tree cannot:
- From and To set the frequency range. The default covers everything the record can carry: from the frequency where the longest wavelets still fit inside the record up to just under Nyquist (0.98 of it). The amplitude stays accurate to a fraction of a percent right up to the top.
- Per octave sets how many lines are computed per octave. The axis is logarithmic because a wavelet's bandwidth is a constant fraction of its frequency. The default of twelve draws a ridge that looks continuous without computing rows that cannot be told apart.
- Cycles sets the trade between time and frequency resolution. The transform slides a wave packet along the record, and Cycles is how many cycles fit under its window. Few cycles resolve when something happens and blur its frequency; many cycles resolve the frequency and blur the timing. The default of six is the usual choice and close to the lowest value for which the transform is valid. The box takes 3 to 30.
Below the settings, the derived rows (Cone at bottom, Resolves and Lines) show what the settings imply before the transform runs. The most important of these is the cone, described below.
What the picture can and cannot show¶
Four limits apply, and each one can be seen in the picture itself.
The cone of influence. A low-frequency wavelet is long, and near the ends of the record it runs off the edge, so what it reads there is where the record was cut, not the test article. The affected span is shaded in the flat picture and walled off in 3-D, and it is widest at the bottom of the frequency axis. It is marked because it looks exactly like data. A range whose bottom rows are entirely inside the cone shows only the edges of the recording; the panel warns when the cone covers a third of the record or more at the lowest frequency, and says so plainly when it covers all of it.
Amplitude is in the record's own units. A 2 g tone reads 2 wherever it sits on the frequency axis, so the color bar carries the channel's units and a value can be read off the picture. (The other convention in the literature, unit energy, draws the same tone four times taller at 50 Hz than at 800 Hz; Visual Dynamics does not use it.)
A ridge that ripples usually means the record itself ripples. Two tones within one wavelet's bandwidth of each other add up to an amplitude-modulated signal, exactly as they would through any filter that wide, and the ripple is at their difference frequency. Raising Cycles narrows the band and separates tones that are far enough apart. Tones a hertz apart at hundreds of hertz cannot be separated by any window short of one that removes the time axis, and their beat is part of the measurement. A single steady tone draws perfectly smooth, which shows that the transform adds no ripple of its own.
A long record is drawn at a picture's width. The transform is computed
for every sample, but the picture holds time to 4096 columns, each
showing the largest magnitude in its slice of the record. Because it is
a peak-hold, a burst only a few samples wide still shows up as a
column; taking every nth sample instead could skip the samples it is
in. A record shorter than that is drawn sample for sample, with
nothing held. This is what lets a five-minute record at 16 kHz open in
a few seconds. The scripting plot_scalogram draws the same way, and a
report figure holds time the same way to the width of a document and
says so in its note.
When to use it¶
- A sweep: each tone's path is a ridge, and crossings, dwells and the resonances it passes through are easy to see (the sine workflow starts with it).
- A transient or a shock: what rang, and for how long after the event. The transient and shock reports include the figure for this reason.
- A record that fails kurtosis: the kurtosis bars say a channel has peaks its spectrum did not predict, and the scalogram shows when they happened and at what frequency, which is usually enough to find the source of the rattle.
- Not a stationary random run: everything about it is in the PSD, and the scalogram will draw a texture with nothing to find in it.