A Synthesis Scenario

Let $N_s$ denote the number of virtual acoustic sources and let $N$ be the number of speakers. Then in PBAP, the $j$ th speaker signal is given by a sum of delayed source signals:

$$s_j(n) = \sum_{i=1}^{N_s} x_i(n-D_{ij}), \quad j=1,2,\ldots,N$$ (4)

where $x_i(n)$ is the $i$ th source signal, and $D_{ij}$ is the time-delay, in samples, from virtual source $i$ to speaker $j$ . The signal $x_i(n-D_{ij})$ is obtained as the output of a fractional-delay filter driven by $x_i(n)$ . The same delay line can be used for source $i$ to all $N$ speakers, using ``taps'' to interpolate (Smith et al., 2002).