Cross-over frequency selection and optimization of response around cross-over
A system and method provide at least a single stage optimization process which maximizes the flatness of the net subwoofer and satellite speaker response in and around a cross-over region. A first stage determines an optimal cross-over frequency by minimizing an objective function in a region around the cross-over frequency. Such objective function measures the variation of the magnitude response in the cross-over region. An optional second stage applies all-pass filtering to reduce incoherent addition of signals from different speakers in the cross-over region. The all-pass filters are preferably included in signal processing for the satellite speakers, and provide a frequency dependent phase adjustment to reduce incoherency between the center and left and right speakers and the subwoofer. The all-pass filters are derived using a recursive adaptive algorithm.
1. A signal processor configured to select a cross-over frequency to attenuate a spectral notch in a cross-over region, the signal processor comprising a configuration to:
measure a full-range subwoofer and satellite speaker response in at least one position in a room, the full range subwoofer and satellite speaker response characterized by;
select a cross-over region from the full range subwoofer and satellite speaker response;
select a set of candidate cross-over frequencies and corresponding bass-management filters for the subwoofer and the satellite speaker;
apply corresponding bass-management filters to the full-range subwoofer and satellite speaker response to obtain bass managed subwoofer and satellite speaker responses;
level match the bass managed subwoofer and satellite speaker responses to obtain leveled subwoofer and satellite speaker responses;
sum the leveled subwoofer and satellite speaker responses to obtain a net bass-managed subwoofer and satellite speaker response;
compute an objective function measure using the net bass-managed subwoofer and satellite speaker response for each of the candidate cross-over frequencies; and
select the candidate cross-over frequency resulting in the lowest objective function measure.
2. The signal processor of claim 1 , wherein the configuration to compute an objective function measure comprises a configuration to compute a spectral deviation measure.
3. The signal processor of claim 2 , wherein the configuration to compute an objective function measure comprises a configuration to compute a measure of the variation of the spectral response at discrete frequencies in the cross-over region, from an average spectral response taken over the entire cross-over region.
4. The signal processor of claim 1 , wherein the configuration to compute an objective function measure comprises a configuration to compute a standard deviation based measure.
5. The signal processor of claim 4 , wherein the configuration to compute an objective function measure comprises a configuration to compute a frequency weighted standard deviation based measure.
6. The signal processor of claim 1 , wherein the configuration to measure a full-range subwoofer and satellite speaker response comprises a configuration to measure a Room Transfer Function (RTF).
7. The signal processor of claim 6 , wherein the configuration to measure the RTF comprises a configuration to transmit a logarithmic chirp signal to a speaker, and deconvolve a response at a listener position, wherein the Fourier transform of the response yields the RTF.
8. The signal processor of claim 6 , wherein the configuration to measure the RTF comprises a configuration to transmit a pseudo-random sequence a speaker, and deconvolve the response at a listener position.
9. The signal processor of claim 1 , wherein the configuration of the signal processor further comprises a configuration to perform all-pass filtering following high pass filtering to reduce incoherent addition of acoustic signals from at least one satellite speaker and a subwoofer.
10. The signal processor of claim 9 , wherein the configuration to perform all-pass filtering comprises a configuration to apply all-pass filtering derived by adaptively minimizing a phase term.
11. The signal processor of claim 1 , wherein the configuration of the signal processor further comprises a configuration to perform 1/N octave smoothing of the net bass-managed response.
12. The signal processor of claim 11 , wherein the configuration to perform 1/N octave smoothing of the net bass-managed response comprises a configuration to perform ⅓ octave smoothing of the net bass-managed response.
13. The signal processor of claim 1 , wherein the configuration to compute the objective function measure comprises a configuration to compute a multiplicity of objective function measures for a multiplicity of candidate cross-over frequencies at the multiplicity of different listen locations, and further comprises a configuration to average the multiplicity of objective function measures over the multiplicity of different listen locations to obtain an average objective function measure for each of the multiplicity of candidate cross-over frequencies, and
wherein selecting the candidate cross-over frequency resulting in the lowest objective function measure comprises selecting the candidate cross-over frequencies which provides the lowest average objective function measure.
14. The signal processor of claim 13 , wherein the configuration to compute a multiplicity of objective function measures comprises a configuration to compute a multiplicity of spectral deviation measures.
15. A signal processor for attenuating an incoherent addition of satellite speaker and subwoofer acoustic signals, the signal processor comprising a configuration to:
measure the full-range subwoofer and satellite speaker response in at least one position in a room, the full range subwoofer and satellite speaker response characterized by;
select a cross-over region from the full range subwoofer and satellite speaker response;
select a set of candidate cross-over frequencies and corresponding bass-management filters for the subwoofer and the satellite speakers;
apply the corresponding bass-management filters to the subwoofer and satellite speaker full-range response;
level match the bass managed subwoofer and satellite speaker response;
sum the subwoofer and satellite speaker response to obtain a net bass-managed subwoofer and satellite speaker response;
compute an objective function measure using the net bass-managed subwoofer and satellite speaker response for each of the candidate cross-over frequencies;
select the candidate cross-over frequency resulting in the lowest objective function measure;
filter speaker signals using the selected cross-over frequency and corresponding bass-management filters; and
perform all-pass filtering on the filtered speaker signals to further attenuate spectral notches.
16. The signal processor of claim 15 , wherein the configuration to perform all-pass filtering on the filtered speaker signals to further attenuate spectral notches comprises a configuration to perform all-pass filtering on the filtered speaker signals provided to the satellite speakers.
17. A signal processor for selecting a cross-over frequency to attenuate a spectral notch in a cross-over region, the signal processor comprising a configuration to:
measure a full-range subwoofer and satellite speaker response in at least one position in a room the full range subwoofer and satellite speaker response characterized by;
select a cross-over region from the full range subwoofer and satellite speaker response;
select a set of candidate cross-over frequencies and corresponding bass-management filters for the subwoofer and the satellite speaker;
apply corresponding bass-management filters to the full-range subwoofer and satellite speaker response to obtain bass managed subwoofer and satellite speaker responses;
level match the bass managed subwoofer and satellite speaker responses to obtain leveled subwoofer and satellite speaker responses;
sum the leveled subwoofer and satellite speaker responses to obtain a net bass-managed subwoofer and satellite speaker response;
compute an objective function measure using the net bass-managed subwoofer and satellite speaker response for each of the candidate cross-over frequencies;
select the candidate cross-over frequency resulting in the lowest objective function;
attenuate variations in the cross-over region by:
define 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 compute 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.
18. The signal processor of claim 17 , wherein the configuration to process a speaker channel with the all-pass filter comprises applying at the least one second order all-pass filter in a satellite channel level matching.
19. The signal processor of claim 17 , wherein the configuration to cascade the all-pass filter comprises cascading the all-pass filter with the satellite speaker bass-management filter.
20. The signal processor of claim 18 , wherein the configuration to cascade the all-pass filter comprises a configuration to cascade a plurality of all-pass filters with a plurality of satellite speaker bass-management filter.