Results

Figure 8 plots the $K=5$ weighted principal components identified for the angle-dependent component of the horn radiativity. Each component is weighted by its corresponding singular value, thus visually indicating its importance. Also plotted using the same line type are the zero-lines for each principal component. Note in particular that the first (largest) principal component is entirely positive.

Figure 8: First 5 principal components weighted by their corresponding singular values. Each angle-dependent impulse response is modeled as a linear combination of these angle-independent impulse-response components.

Figure 9 shows the complete horn impulse-response model ( $\mbox{${\bm \alpha}$}$$+$   $\mbox{${\bm \gamma}$}$$\cdot$   diag$(z^{-\tau_i})$ ), overlaid with the original raw data ${\mathbf{h}}$ . We see that both the fixed base-leakage and the angle-dependent horn-output response are closely followed by the fitted model.

Figure 9: Overlay of measured (solid) and modeled (dotted) impulse-responses at multiples of 15 degrees.

Figure 10 shows the estimated impulse response of the base-leakage component $\underline{a}(n)$ , and Fig.11 shows the modeled angle-dependent horn-output components $\mbox{${\bm \gamma}$}$ delayed out to their natural arrival times.

Figure 10: Modeled base-leakage impulse-response (angle-independent).

Figure 11: Modeled horn-output impulse-responses at multiples of 15 degrees.

Figure 12 shows the average power response of the horn outputs. Also overlaid in that figure is the average response smoothed according to Bark frequency resolution [16]. This equalizer then becomes $H_0(z)$ in Fig.. The filters $H_{0L}(z)$ and $H_{0R}(z)$ in Fig. 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 in Fig..

Figure 12: Average angle-dependent amplitude response overlaid with Bark-smoothed response to be used as a fixed equalization applied to the source.

Figure 13 shows a spectrogram view of the angle-dependent amplitude responses of the horn with $H_0(z)$ (Bark-smoothed curve in Fig.12) divided out. This angle-dependent, differential equalization is used to design the filters $H_{0L}(z)$ and $H_{0R}(z)$ in Fig.. Note that below 12 Barks or so, the angle-dependence is primarily to decrease amplitude as the horn points away from the listener, with high frequencies decreasing somewhat faster with angle than low frequencies.

Figure 13: Angle-dependent amplitude response divided by Bark-smoothed average response to be used as the basis for design of time-varying, angle-dependent equalization to be applied after $H_0(z)$ .