Phase equalization for multi-channel loudspeaker-room responses
A system and method for minimizing the complex phase interaction between non-coincident subwoofer and satellite speakers for improved magnitude response control in a cross-over region. An all-pass filter is cascaded with bass-management filters in at least one filter channel, and preferably all-pass filters are cascaded in each satellite speaker channel. Pole angles and magnitudes for the all-pass filters are recursively calculated to minimize phase incoherence. A step of selecting an optimal cross-over frequency may be performed in conjunction with the all-pass filtering, and is preferably used to select an optimal cross-over frequency prior to determining all-pass filter coefficients.
1. A method for minimizing the spectral deviations in the cross-over region of a combined bass-managed subwoofer-room and bass-managed satellite-room response, the method comprising:
defining at least one second order all-pass filter having all-pass filter coefficients selectable to reduce incoherent addition of acoustic signals produced by the subwoofer and the satellite speaker;
recursively computing the all-pass filter coefficients to minimize a phase response error, the phase response error being a function of phase responses of a subwoofer-room response, a satellite-room response, and the subwoofer and satellite bass-management filter responses; and
cascading the all-pass filter with at least one of the satellite speaker bass-management filter and subwoofer bass-management filter;
wherein computing the all-pass filter coefficients comprises:
selecting initial values for pole angles and magnitudes;
computing gradients ∇ ri and ∇ θi for pole angle and magnitude;
multiplying the angle and magnitude gradients ∇ ri and ∇ θi times an error function J(n) and times adaptation rate control parameters μ r and μ θ to obtain increments;
adding the increments to the pole angles and magnitudes to recursively compute new pole angles and magnitudes;
randomizing the pole magnitude if the pole magnitude is <1; and
testing to determine if the pole angle and magnitudes have converged, wherein if the if the pole angle and magnitudes have converged, the computing method is done, otherwise, the steps stating with computing gradients are repeated.
2. The method of claim 1 , wherein the gradients include frequency dependent weighting terms.
3. The method of claim 1 , wherein the error function J(n) is an average square error function of phase difference between the subwoofer phase, the satellite speaker phase, and the all-pass filter phase.
4. The method of claim 1 , wherein the average square error function includes a frequency dependent weighting.
5. The method of claim 1 , further including steps for optimizing the crossover frequency, comprising:
measuring a full-range subwoofer and satellite speaker response in at least one position in a room;
selecting a cross-over region;
selecting a set of candidate cross-over frequencies and corresponding bass-management filters for the subwoofer and the satellite speaker;
applying corresponding bass-management filters to the full-range subwoofer and satellite speaker response to obtain bass managed subwoofer and satellite speaker responses;
level matching the bass managed subwoofer and satellite speaker responses to obtain leveled subwoofer and satellite speaker responses;
summing the leveled subwoofer and satellite speaker responses to obtain a net bass-managed subwoofer and satellite speaker response;
computing an objective function using the net bass-managed subwoofer and satellite speaker response for each of the candidate cross-over frequencies; and
selecting the candidate cross-over frequency resulting in the lowest objective function.
6. A signal processor for minimizing the spectral deviations in the cross-over region of a combined bass-managed subwoofer-room and bass-managed satellite-room response comprising:
at least one second order all-pass filter, the at least one second order all-pass filter having all-pass filter coefficients selectable to reduce incoherent addition of acoustic signals produced by the subwoofer and the satellite speaker, the all-pass filter coefficients recursively computed to minimize a phase response error, the phase response error being a function of phase responses of a subwoofer-room response, a satellite-room response, and the subwoofer and satellite bass-management filter responses; and
at least one satellite speaker bass-management filter cascaded with the all-pass filter and a subwoofer bass-management filter;
wherein the all-pass filter coefficients are computed by
selecting initial values for pole angles and magnitudes;
computing gradients ∇ ri and ∇ θi for pole angle and magnitude;
multiplying the angle and magnitude gradients ∇ ri and ∇ θi times an error function J(n) and times adaptation rate control parameters μ r and μ θ to obtain increments;
adding the increments to the pole angles and magnitudes to recursively compute new pole angles and magnitudes;
randomizing the pole magnitude if the pole magnitude is <1; and
testing to determine if the pole angle and magnitudes have converged, wherein if the if the pole angle and magnitudes have converged, the computing method is done, otherwise, the steps stating with computing gradients are repeated.
7. The signal processor of claim 6 , wherein the gradients include frequency dependent weighting terms.
8. The signal processor of claim 6 , wherein the error function J(n) is an average square error function of phase difference between the subwoofer phase, the satellite speaker phase, and the all-pass filter phase.
9. The signal processor of claim 6 , wherein the average square error function includes a frequency dependent weighting.
10. The signal processor of claim 6 , wherein the crossover frequency is optimized by
measuring a full-range subwoofer and satellite speaker response in at least one position in a room;
selecting a cross-over region;
selecting a set of candidate cross-over frequencies and corresponding bass-management filters for the subwoofer and the satellite speaker;
applying corresponding bass-management filters to the full-range subwoofer and satellite speaker response to obtain bass managed subwoofer and satellite speaker responses;
level matching the bass managed subwoofer and satellite speaker responses to obtain leveled subwoofer and satellite speaker responses;
summing the leveled subwoofer and satellite speaker responses to obtain a net bass-managed subwoofer and satellite speaker response;
computing an objective function using the net bass-managed subwoofer and satellite speaker response for each of the candidate cross-over frequencies; and
selecting the candidate cross-over frequency resulting in the lowest objective function.