Correlation Detection of Early Reflections pt. 2

We hope you were hooked by part 1 of this classic paper. Above we see the ETC (energy time curve) for a sound entering a well in a random well depth diffuser, and you may notice that the energy sustains for some time. The waterfall chart from last issue showed us that this unwanted effect occurred across a fairly wide bandwidth.

By the end of this newsletter, you should know which type of diffuser is best to use in a high-end audio room, and should understand the drawbacks of using too many of the wrong type.

From a presentation by Arthur M Noxon, PE, at the 11th AES Conference in 1992. Enjoy this excerpt in classic technical paper style, and look for the conclusion in our next issue. Read the full PDF on our website.

Incoherent Reflections

Zero correlation occurs when the reflected signal bears little to no resemblance to the direct signal. This can occur when the reflected signal has no amplitude because it was absorbed. Incident sound onto 2″ of medium density fiberglass does not reflect 1/3 octave noise at 3K. Figure 4a shows the ETC of this absorbed “reflection”. The correlation test in Figure 4b shows “zero” because the silent reflection bears no resemblance to time wise signature of the direct signal.

There is zero correlation if the reflecting signal is not really reflected at all but instead is an independent sound. A whistle tone at 1K was played while the direct 1/3 octave noise at 3K was tested. The tone bears no resemblance to the direct signal and Figure 5 shows zero correlation.

Mixed Reflections

A series of correlation tests were run on each of three types of reflecting surfaces. The signal used was 1/3 octave bandwidth noise on 1/3 octave centers between 125 Hz and 3 KHz. The correlation between the direct signal and the reflection was made for flat wall bounces, for the absorption/reflection diffuser and for the multi-depth trough diffuser. For the higher frequencies the correlation of all three reflectors is strong with the time window being spread out according to the degree of multi-reflections for each.

The test set up for this sequence (Fig. 1) uses an incident angle of 45° and picks up the reflection also about 45°. There are two data collecting runs. The first one (Figs. 6-12) ranges in 1/3 octave increments from 125 Hz to 500 Hz using 1/3 octave pink noise. The analyzer steps 0.2 ms, just over 100 times to draw out the correlation curve. The correlation time window is just over 20 ms and is time delayed sufficient to catch the leading edge of the reflecting wavefront.

Because narrow band noise is used, the correlation signature will appear as a sine wave of the frequency that is the center frequency of the 1/3 octave noise. The amplitude of the correlation measurement depends on the amplitude of the received signal and how similar it is to the direct signal. The absorption/reflection diffuser should provide some attenuation of the correlation signal due to reduced reflecting signal strength. The random well depth diffuser has no absorption and any loss in correlation amplitude can be related to either an off axis concentration of reflected sound (lobe beaming) or a signal correlation problem.

The 125 Hz through 500 Hz survey shows the absorption/reflection diffuser to mimic the bare wall bounce faithfully except for a full bandwidth amplitude reduction due to absorption. The random well depth diffuser has a thinning of correlation in the 200 Hz 1/3 octave band (Fig. 8c) and again at 500 Hz (Fig. 12c). The 200 Hz incoherent reflection is attributable to wood panel resonance and the 500 Hz problem belongs to the 1/4 wavelength resonance of the deepest wells.

A higher frequency series (Figs. 13-15) shows the same test except the step in 50 ms, four times faster than before. The full test window now is 5 ms. The wave form appears to be longer but only because the time scale is shorter. The weak correlation for random well depth diffusers still exists at 1000 Hz (Fig. 13) but by the 2K octave and above both diffusing systems have full and adequate correlation except that the random depth wells have additional multiple reflections (Fig. 15) that stretch out over the 5 ms window. shown in test results.

The ETC for the random depth well diffuser was taken with the mic in the bottom of one of the deep wells for frequencies between 200 Hz and 20kHz. The only indication of possible resonance effects is (Fig. 16) the rapid drop of initial reflections followed by a resurgence of energy discharge between 4 and 7 ms after the initial reflection. The waterfall (Fig. 17) was taken to try to identify the resonance. It ranges from 50 to 500 Hz over a time period of almost 100 ms. By using the heavy time averaging window of 40 ms, the structural resonance effects below 250 and the 1/4 wavelength at 375 Hz become evident.

There seems to be low correlation when the reflected signal is involved with resonance even though the energy of the reflection is high. The resonant discharge produces a tone that has its own time wise identity, not a simple time delayed and coherent reflection of the direct signal.