note # 10
The Waterfall Plot
application note describes how to use the Sample Champion Waterfall
This module computes and plots (see the figure above) a 3D Cumulative
Spectral Decay of an Impulse Response. This is a well-known
way to present and analyze an Impulse Response
and to detect loudspeaker and box resonances. One of the first
articles about this method is the following:
J.M., Loudspeaker evaluation using digital techniques.
Presented at the Audio Eng. Soc. 50th Convention, London,
4th March, 1975.
How is the plot generated?
of all, an Impulse Response must be measured or loaded in Sample
Champion. The anechoical part of the Impulse Response must be
selected by using "Selection A" (in case of 2 channels
measurements, the second channel must be selected with "Selection
B" or vice versa, depending on the options set in the Settings|FFT
2 - Impulse Response selection
Now the plugin can be opened (from the "New Measurement" Window);
the dialog in figure 1 will appear (without any plotting).
Press F5 to transfer the time data from the main program to
the plugin and plot the result of the FFT of the selected data.
This spectrum is computed with the parameters (FFT Size and
Weighting Window) set in the plugin. The selected Weighting
Window (Half-Right Blackman-Harris, Half-Right Hamming or Rectangular)
is modified with an initial short Half-Left Blackman-Harris
Window, long as specified in the "Attack" field (values
between 0 and 0.4 msec).
The Y scale of the FFT plot can now be set automatically by
pressing the "Y Autoscale" button inside the plugin.
The spectrum plot obtained in this way is the first slice of
the waterfall. It can be shown in logarithmic or linear scales
and it is also possible to select the desired frequency range.
next slices are computed by pressing the "Waterfall"
button. For every successive slice, the plugin shifts to the
right the beginning of the selection (by the number of points
indicated in the "Dpoints" value), computes the FFT
and plots the obtained spectrum.
The FFT size can be chosen between 256 and 16384 points (using
zero padding). Since
the lower resolution limit depends (for every measurement method)
on the weighting window length and type, the plugin automatically
excludes from the plot all unreliable results concerning low
frequencies. This is performed by computing the lower frequency
limit for every slice and its corresponding window length.
plugin allows choosing different color schemes.
Figure 3 shows a plot where colors vary between red and blue
4 shows a plot where colors vary between red and blue with frequency.
5 and 6 show color schemes similar to those in figures 3 and
4, but with thin lines.
Figure 7 shows the plot with a classic color scheme.
8 shows a frequency zoom of the plot.
9 shows the plot with a linear frequency axis.
10 shows the plot with a white background color.
pictures can be saved as BITMAP images.
information about this and other Loudspeakers Measurements can
be found in the following paper:
J., Loudspeakers: What measurements can tell us...
and what they can't tell us!, AES Preprint 4608, 103rd
AES Convention, New York, September 1997
author of this paper kindly offers an on-line version of this
paper (in three parts) on the Stereophile website. You can read
it at the following links:
PDF file (1468K) Shift-click
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