Inverse filtering-based approaches

corresponding to the length of the smoothing window. The smoothing window Wsm(i) is given by

The integer m(k) can be considered as a bandwidth function by which a fractional octave or any other nonuniform frequency smoothing scheme can be implemented.

The variable b determines the roll-off rate of the smoothing window. As a special case when b = 1, the window reduces to a rectangular window.

3.4 Inverse filtering-based approaches

3.4.1 HRTF-based Inverse Filtering for single listener with upmixing (upmixingHIF1) method

The upmixingHIF1 method is developed to deal with the single listener mode with two-channel input contents. The block diagram of the upmixingHIF1 method is shown in Fig. 9, where two-channel input signals are extended to four channels by the upmixing algorithm and next inverse filtered to produce the outputs. For the design of the inverse filters, the acoustical plants H(z) are the frequency response functions between the input to the loudspeaker and the output to the microphone mounted in KEMAR’s (Knowles Electronics Manikin for Acoustic Research) [32] ears, as formulated in Eq. (6). The matching model matrices and the calculated inverse filters were presented as Eqs. (7) and (8). In addition, some listeners reported that the sound image width is slightly compromised in applying inverse filtering in an informal listening test. To reconcile the problem, the weighted (0.45) and delayed (4 ms) four-channel inputs are mixed into the respective channels. It is noted that this processing will also be applied in all the inverse-filtering-based methods.

3.4.2 HRTF-based Inverse Filtering for single listener (HIF1) method

The structure of the HIF1 method shown in the block diagram of Fig 10 is the same as that of the upmixingHIF1 method except that it does not require upmix processing. Given the 5.1-channel inputs and four loudspeakers, the center channel has to be attenuated before mixing into the front-left and front-right channels. Next, front two channels and rear two channels are fed to the respective inverse filters.

The remaining channel, LFE, is mixed into each loudspeaker, assuming that the subwoofer is unavailable. It is note that the inverse filters used in the HIF1 method are the same with the upmixingHIF1 method.

3.4.3 HRTF-based Inverse Filtering for two listener (HIF2) method

The HIF2 method aims at the two listener mode with 5.1-channel inputs. The system formulations are shown in Eqs. (9) to (11). Since the inverse filters are two 2×2 matrices, the block diagram is the same as the HIF1 method, even though the design of the inverse filters is quite different from the HIF method.

3.4.4 HRTF-based Inverse Filtering for two listener by filter superposition (HIF2a) method

Like the function of the HIF2 method, the HIF2a method is developed to cope with two-listener mode with 5.1-channel input. Due to the linearity of acoustics, the design procedures of the HIF2a method can be separated into two steps. The first step is to design the inverse filters for each listener. Next step, by adding the calculated filter coefficients, two 2×2 inverse filter matrices can be obtained.

3.4.5 Point-receiver-based Inverse Filtering for single listener with upmixing (upmixingPIF1) method

The upmixingPIF1 method is a point-receiver-based inverse filtering method exploited for the scenario of single listener with two-channel inputs. This method is based on the concepts of the Pioneer’s^® MCACC [28] system but it is more accurate in frequency resolution since the FIR inverse filter is employed to compensate the acoustical plants instead of the simple equalization. The problem can be formulated as four SISO systems so that the four inverse filters can be obtained by Eq. (12).

The block diagram is shown in Fig. 11, in which the input signals are extended to four-channel and next fed to respective inverse filters.

3.4.6 Point-receiver-based Inverse Filtering for single listener (PIF1) method

Besides the upmixing processing, the scheme of the PIF1 method is the same as that of the upmixingPIF1 method since this approach is intended for the 5.1-channel input. As presented in Fig. 12, the center channel has to be weighted before mixing into the front-left and front-right channels. The front two channels and rear two channels are then fed to the respective inverse filters.

3.4.7 Point-receiver-based Inverse Filtering for two listener by filter superposition (PIF2a) method

The PIF2a method is a solution to the problem of the two listener mode with 5.1-channel input, also. Figure 12 shows the block diagram. Similar to the concept of the HIF2a method, the inverse filter is obtained by adding the filter coefficients designed for each control point. Thus, the structure of this method is in common with the PIF1 method.

3.4.8 Point-receiver-based Inverse Filtering for four listener (PIF4) method

Except the single and the two-listener modes, the PIF4 method is devised for four listener mode with 5.1-channel input. As mentioned in Eq. (13) and (14), the acoustical plant and matching model are both 4×4 matrices. Therefore, the 4×4 inverse filter matrix can be obtained by Eq. (3). Fig. 13 shows the block diagrams of the PIF4 method. The center channel is mixed into the front channels and next the front and rear-channel signals are filtered directly.