Impulse Response Reconstruction
In a ray tracing simulation (with the Ray Acoustics interface), an impulse response (IR) can be reconstructed by recombining the information carried by rays and detected at the receiver. The information carried by the rays consists of the ray power (with a given frequency band resolution) and the travel time. The aim of the reconstructed IR is to have the correct energetic signature, energy decay characteristics, and spectral characteristics. A reconstructed IR, from a ray tracing simulation, will never match a measured IR if compared sample per sample. This is simply not possible since information like the phase content is missing when frequency bands are used; ray tracing is not a full wave method.
The ray tracing simulation consists of propagating rays (ray index n) in frequency bands (band index c and center frequency fc). In each frequency band c, the ray power Qn (of ray n) decreases at ray wall interactions (absorption) and due to volumetric attenuation. Wall absorption, scattering, and volumetric attenuation characteristics is defined with a given n’th octave band resolution.
The ray arrives at the receiver at time tn with an intensity/pressure amplitude contribution, given by
where Vrec is the volume of the receiver, d is the distance traveled in the receiver by the ray, prms is the RMS pressure, ρ is the density, and c is the speed of sound. The arrival time tn is computed as the time instance where the ray has traveled half the distance d/2 in the receiver volume (this leads to a good accuracy in time).
To reconstruct the IR the filter kernels (of the nth octave filter bank) are convolved with the impulse signal (it is assumed that rays carry an impulse or Dirac impulse when emitted from the source). The filter kernel of band c is wc(t). The built-in filters are so-called brick-wall with Kaiser window filters, defined in octaves, 1/3 octaves, or 1/6 octaves (see Impulse Response Plot). The fc = 1 kHz octave filter kernel in time and frequency domain is depicted inFigure 8-8.
Figure 8-8: The 1 kHz brick-wall with Kaiser window filter kernel in time and frequency domain.
An often seen expression for the IR reconstruction is given using amplitude summation
where Nref,n is the number of reflections undergone by ray n, before arriving at the receiver. The first factor in the sum ensures that rays that follow the same path (such as direct sound and early reflections) are summed up correctly (in phase), while rays that have undergone many reflections get a pseudo random phase applied (see Ref. 6 and Ref. 7).
An issue with the above summation approach is that the level of the IR is not correct in absolute terms. For example, the level of the reconstructed signals at a small and large receiver, placed at the same location, will not be identical. To remedy this, the convolution/filtering of each ray is still done on the amplitude but the summation has to be done energetically. This gives instead
where the superscript p stands for power summed signal. This ensures a consistent energy content and energy conservation of the reconstructed IR signal.