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Frequency Response: Waterfalls
Index
Waterfall plots are used by driver and loudspeaker designers for driver selection, to identify resonances or reflections, and to view driver and waveguide behavior.

The Waterfall feature is accessed via the "3DPlot" menu.  Waterfalls are calculated from an impulse response while measuring. 

What does a Waterfall mean?
A waterfall is an attempt to illustrate on a 3-D graph how the energy decays or is radiated over a range of frequencies.  OmniMic includes three different styles of waterfall processes, selectable via the "Waterfall Type" menu.  

A "Cumulative Spectral Decay", or "CSD" waterfall shows a series of time slices approximately indicating the contribution to the total response that is made after the time instant shown in the axis going into the screen.  When a loudspeaker is driven with an electrical impulse, the pressure it creates should ideally also represent a pressure impulse.  But loudspeaker drivers aren't ideal so they also generate resonances -- pressure waves that decay more slowly at various frequencies.  The effects of echoes can hide the resonances in a CSD waterfall, but at higher frequencies the echoes can be removed by "Windowing" the calculation to only include the part of the Impulse Response that occurs before the first reflection (from a surface such as a wall or furniture) reaches the OmniMic.  Careful choice of positioning within the Impulse Response is critical, because the effects of any reflections included within the selected portion will contaminate all regions of the graph up to that point on the time axis.  Below some frequency determined by where the Impulse Response is clicked and how far along on the time (depth) axis a trace exists, meaningful calculation cannot be done.  The graph curve is chopped off at those points on the waterfall display. 

The CSD waterfall calculation process introduces some spurious side effects, so the graph should be viewed in general terms.  Exact values along the curves of waterfalls are not usually reliable, rather, the positions and sizes of decaying forward-approaching ridges on the graph indicate frequency and relative intensities of resonances. 

CSD waterfall curves can now be shown with different degrees of smoothing, and can also be used with long time lengths (to 150 milliseconds) for viewing effects of room reflections.


"Toneburst Energy Storage" (TES) shows the effect that would occur if the loudspeaker were driven by short tonebursts of energy one at a time, concentrated near each test frequency.  The speaker output would ideally end after the toneburst ended, but real world devices will continue to ring as the energy stored within dies out.  This is similar to a test devised by Linkwitz  using special hardware, but OmniMic can calculate it from impulse responses.  The number of applied toneburst cycles can be selected using a control at the bottom right.   Like the CSD waterfall, the impulse response can be windowed to remove effects of reflections.

The gray area shows the energy that is expected if there were no storage or hangover.   The light-blue area near the floor of the plot represents the stored (delayed) energy at the indicated frequency caused by the driver.

The CSD and Toneburst Energy Storage waterfall plots are useful identifying moderate to high Q resonances in a driver's frequency response.  The audibility of the features easily identified in these waterfall plots is somewhat controversial, with some research (see Toole) indicating that the higher Q resonances seen in waterfall displays are significantly less audible than low-Q resonances that do not stand out in CSD or TES waterfall displays.  In any event, it should be remembered that waterfall data (and also frequency response data) are simply alternate presentations of information contained within impulse responses.


"Wavelet Spectrogram" shows a combined time/frequency representation of the impulse response.  The Wavelet Spectrogram in OmniMic uses a very fast algorithm that allows the display to occur in real time.  In all time/frequency displays there is a mathematical "uncertainty principle" which limits the degree of time resolution that can be obtained for a given frequency resolution, and vice versa.  In other words, the more detailed the time character of the display, the less detailed will be the frequency character.  The Wavelet Spectrogram shows the optimized presentation, giving as much combined resolution as possible.  The horizontal axis is time, the vertical axis is frequency, and color shows the relative intensity (in dB).  You can select the octave resolution, in a control below the plot, to determine the desired resolution trade off.  An ideal wavelet spectrogram (flat response, no resonances or reflections) will look like a vertical tapered horn, like this:

The time resolution is more detailed at higher frequencies than at lower frequencies (because there are more "Hz" in an octave at high frequencies than at lower frequencies).  

A typical loudspeaker will show a less clear graph, with smearing at various frequencies and additional color features appearing at later times where reflection or diffraction occur.

If you spread the time axis out to full length, you can also use the Wavelet Spectrogram for viewing room reflections and the frequency ranges over which they predominate.


Features of the Waterfall Displays
  • For CSD and TES type waterfalls, the top of the screen reference line is set by the largest feature over the selected frequency range.  Both types also allow selection of an "EQ flat" function that adjusts gain at each frequency, as if an ideal equalizer were applied.  Time is shown on the "depth" axis. You can click at the end of a line trace on the labeled axes (time for CSD, frequency for Toneburst) to highlight the single line in a waterfall plot for easier reading.
  • For CSD and TES, the position where you click within the Impulse Response graph below determines the length of the waterfall calculation, starting from 0ms..
  • For the Wavelet Spectrograms, the red color indicates the highest decibel level in the frequency range.  The "EQ flat" button can be used so that red instead indicates the highest level at each frequency (in effect, what would be obtained if the speaker could be equalized flat without affecting its phase).  Impulse response windowing will not have an effect on Wavelet Spectrogram displays.
  • The three dimensions (intensity, frequency, and time) of the graph can be adjusted as desired for display using scaling controls similar to those on the other OmniMic graphs.
  • As with the rest of the OmniMic graphs, there are buttons provided for both taking Snapshots of graphs or for sending copies of the screen display to a printer.
  • Often selection of the Log format display of the Impulse Response graph below will allow for easier location of strong reflections.
  • To return to the normal Frequency Response page of OmniMic, click on the "Return to FR" menu button.