Energy Time Curves
These can be very useful although also more difficult to interpret. They are a steady-state measurements taken at different times, then averaged for either the entire frequency range or a band of frequencies. Why would this be important? Well, like the reverberation times, we would like the energy of all frequencies to decay uniformly. One of the problems with energy time curves is that they can be difficult to interpret. Each curve is a very fast snapshot of what energy was present at that exact moment in time. Because there may be comb filtering interferences, it can occasionally be deceiving but in general, it is best to interpret the energy time curves by ignoring any dips in energy that then rise again after the dip. The following graph shows energy time curves for the full range and the band from 4kHz to 8kHz. Notice that they track each other nicely. This is what is expected and ideal.

A subset of energy time curves is the cumulative decay plot. This is taken across the entire frequency range and is a snapshot at that particular time. The first snapshot occurs at 0ms, each subsequent snapshots at various intervals depending on what we are looking for. Ideally the 0ms reading should be flat (it will have significant fluctuations due to comb filtering but it should be flat overall). If it isn't flat, this generally indicates problems with the equipment since the direct wave response has no room interaction. Cumulative decay plots can be a great tool for troubleshooting. I was once sent a set of graphs that showed the cumulative decay at 0ms (meaning the direct wave) with a strong roll-off in the high frequencies. The decay in the high end was not as rapid as everywhere else, however. The overall (meaning integrated over a longer time) frequency response was pretty flat. I called the user and asked him if he had a treble control. He replied that he did. I asked if it was turned all the way down. He responded that it was, yes. It turned out that his room was very reflective due to a lot of glass. The glass was leaking bass energy while reflecting and thus compounding the high frequency energy. He compensated for this 'brightness' by turning the treble/tweeter control all the way down.


Below is a different graph where the initial 0ms response is close to flat and in-room energy falls off rapidly at the high frequencies.

Waterfall Plots
Eye candy? People have actually said this to me - waterfall plots are simply eye candy. I firmly disagree. Waterfall plots do look great but they are very useful. In a simple 3-D snapshot, we can see if the energy is decaying uniformly. This is basically just a different way of looking at the cumulative decay plot. I like it because if I see one particular frequency carried out much longer than all others, I've identified some sort of resonance, usually caused by the room. How long it is carried out has a lot to do with how significant that resonance is. The graph below shows a prominent resonance centered around 80 Hz.

Psycho-Acoustical Response Curve
This is a highly debated -- and some might say controversial -- subject but in our tests, it has proven extremely useful. Some acousticians will say that the steady-state response is all that you need. For trained acousticians who may deal with this on a regular basis, this could well be the case. The basic premise of a psycho-acoustical response curve is that it mimics in a 2-D graph what the human ear perceives relative to frequency response. Thus if there is a resonant mode, it will be displayed as a peak at that frequency. The human ear has longer integration times at lower than at higher frequencies. Thus the gate time for the psycho-acoustical response curve is longer for low frequencies than high frequencies. Here is a psycho-acoustical response curve of the waterfall plot seen above.

We use the psycho-acoustical response curve to set up our analog-domain room equalizer PARC. It is very easy to interpret and our results have worked out incredibly well, simply by using the psycho-acoustical curve as our benchmark and bringing its response as close to flat as is possible.


Special Note Regarding the Graphs
All measurements were taken using the Rives Audio Professional Test Kit. The analysis and display software is ETF from Acoustisoft. We have found this software and hardware to be the most cost-effective method of obtaining state-of-the-art measurements.


Rives Audio at HE 2004, May 20-23rd, New York
Rives Audio will be at the HE show. Please bring your questions. We will be more than happy to discuss general questions regarding room acoustics with you.


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