Results, Cont'd

Complete horn impulse-response model ( $\mbox{${\bm \alpha}$}$$+$   $\mbox{${\bm \gamma}$}$$\cdot$   diag$(z^{-\tau_i})$), overlaid with the original raw data ${\mathbf{h}}$:

Overlay of measured (solid) and modeled (dotted) impulse-responses at multiples of 15 degrees

We see that both the fixed base-leakage and the angle-dependent horn-output response are closely followed by the fitted model.

Estimated impulse response of the base-leakage component $\underline{a}(n)$:

Modeled base-leakage impulse-response (angle-independent)

Modeled angle-dependent horn-output components $\mbox{${\bm \gamma}$}$ delayed out to their natural arrival times:

Modeled horn-output impulse-responses at multiples of 15 degrees

Average power response of the horn outputs. Also overlaid in that figure is the average response smoothed according to Bark frequency resolution. This equalizer then becomes the shared filter $H_0(z)$ in the simulation.

Filters $H_{0L}(z)$ and $H_{0R}(z)$ in the simulation are obtained by dividing the Bark-smoothed frequency-response at each angle by $H_0(z)$ and designing a low-order recursive filter to provide that equalization dynamically as a function of horn angle. The impulse-response arrival times $\tau_i$ determine where in the delay lines the filter-outputs are to be summed.

Average angle-dependent amplitude response overlaid with Bark-smoothed response to be used as a fixed equalization applied to the source