A very simple way to simulate the timbre of flutter echoes in spatial audio

A Very Simple Way to Simulate the Timbre of Flutter Echoes in Spatial AudioThe "strange" timbre of flutter echoes is often not included in spatial audio, auralisations and room simulations for video games etc., perhaps due to lack of knowledge, but also because a detailed simulation will be very heavy. In common room acoustic modelling only a relatively small number of reflections are used, and the later part of the decay is treated simply as diffuse reverberation. For rooms likely to give a flutter echo, this will not be sufficient. First we must distinguish between room resonances and flutter echoes, even if both are the result of repetition between parallel walls. Room resonances between two surfaces appear in the lower frequency range, and the signal must be longer than the period of the room resonance. For shorter sounds, like handclaps, which often also do not include the frequency range of the bass-room-resonances, the resulting flutter-timbre is of much higher frequency, giving the typical "snarry" sound of a flutter echo. This flutter-timbre will of course also appear for longer sounds, like speech, but then the effect is more masked.The paper will show that typical measurements of flutter echoes in rooms of common size with absorbent ceiling and two reflecting, parallel walls show a gradually narrowing of the broadband noise of, for instance a handclap a sharp "tail" around 2 kHz. Why does this happen?The paper will show that a spherical sound field gradually converts into a plane wave between the two surfaces, due to diffraction from the edges of the reflecting surfaces. I general, the sound pressure level of a spherical wave is reduced by 6 dB pr. doubling of distance, while a plane wave is affected only by air absorption (and possibly of absorption at the surfaces). The transformation from spherical to plane waves can be explained inspecting Fresnel zones etc., including the fact that the distance from the mirror source to the corresponding reflecting surfaces grow very fast. Seen from the mirror source, the dimension of the reflecting surfaces will soon be very small. This gives that the transition from spherical to plane is frequency dependent. Earlier investigations states that for a plane wave between two surfaces S [m2] with distance l [m], the wave is dampened only by the absorption coefficients alpha at each surface and the air absorption, m. (frequency dependent). The frequency content of flutter can be looked upon as the "sum" of three reverberation "asymptotes" for the reverberation time versus frequency, f. c is the velocity of sound.1. Low Frequency damping due to finite surface areas: T_1=(0.041 x 2fS)/c2. Damping due to absorption on the surfaces: T_2=(0.041*l)/alpha3. Damping in the air (dissipation): T_3=0.041/m The total reverberation time, TFL, can be written as:1/T_FL =1/T_1 +1/T_2 +1/T_3These three "asymptotes" work together to get the total maximum reverberation for a mid/high frequency band, and how the different parameters influence on the position of the "peak" and, to a certain degree, how narrow this "tail" will be, (the "Q-factor" of the combined filter).Kuhl's equation gives a good explanation of what is happening, and we can see how the "tonal" characteristic of the flutter changes with different geometry and minor changes in surface absorption, but the method uses reverberation time only as a parameter, the equation for the effect of non-infinite surfaces is empirical, and the results do not give as sharp "tail"/"Flutter Band Tonality" as measured in actual rooms.Diffraction can be calculated more in detail using Edge Diffraction Toolbox by Peter Svensson for MatLab, but this would be too cumbersome for "almost real time" purposes.For practical use in room simulations and electro-acoustic music, it is found that a very simple way to simulate flutter echoes is to make repetitive repetitions between the two actual dimensions and make a gradual bandpass filtering to about 2 kHz. This has been implemented in Max/Pd and as a plug in.We started out stating that flutter echoes had nothing to do with room resonances, but since the fluttering is filtering, the final "target" of the flutter tail actually will be the nth harmonic of the room resonance, (where n might be typically in the order of 50-150). A more detailed simulation for which of these resonances that "win" could be interesting, but for a "real time" simulation, 2 kHz clearly gives the timbre of flutter.