Method for designing a modal equalizer for a low frequency sound reproduction
In a room with strong low-frequency modes the control of excessively long decays is problematic or impossible with conventional passive means. In this patent application a systematic methodology is presented for active modal equalization able to correct the modal decay behaviour of a loudspeaker-room system. Two methods of modal equalization are proposed. The first method modifies the primary sound such that modal decays are controlled. The second method uses separate primary and secondary radiators and controls modal decays with sound fed into at least one secondary radiator. Case studies of the first method of implementation are presented.
1. A method for designing a modal equalizer for low frequency sound reproduction in a predetermined space within a room and location therein, wherein the low frequency sound is within a range below 200 Hz, and wherein the room has a plurality of room modes, said method comprising:
determining the room modes, by determining corresponding rates of decay across the low frequency range;
selecting modes to be equalized based on the corresponding determined rates of decay;
determining center frequencies for each said selected modes; and
defining coefficients of an infinite impulse response (IIR) modal filter based upon the corresponding rates of decay for each of the selected room modes, characterized by
for each selected mode, designing a modal correction filter provided as a relation between an estimate of pole location and a desired pole location, where at least the estimated pole locations are determined from respective said rates of decay, and
forming the IIR modal filter as a cascade of the modal correction filters.
2. The method in accordance with claim 1 , further comprising: creating a discrete-time representation of the determined modes wherein the discreet-time description is a Z-transform.
3. The method in accordance with claim 2 , wherein said defining step includes shifting the estimated pole locations associated with the filter coefficients that include decay time constant information as a parameter.
4. The method in accordance with claim 1 or 2 or 3 , wherein the decay rates are defined by nonlinear fitting.
5. The method in accordance with claim 1 , wherein the determined modes are attenuated utilizing the defined filter coefficients by decreasing a Q value of each determined mode by affecting actively the sound field in the room.
6. The method in accordance with claim 1 , wherein the sound of at least one primary speaker is modified.
7. The method in accordance with claim 1 , wherein the sound of at least one secondary speaker is modified.
8. A method for controlling reverberation in a listening room, comprising:
generating a transfer function associated with a listening position within the room;
selecting at least one mode based upon the transfer function, from among those frequencies below 200 Hz that have magnitude levels that exceed the average level of mid-frequencies;
creating a discrete time representation based upon the at least one selected mode; and
generating infinite impulse response filter coefficients for each of said at least one selected mode using the discrete time representation, characterized by
for each selected mode, designing a modal correction filter provided as a relation between an estimate of pole location and a desired pole location, where at least the estimated pole locations are determined from the discrete time representation, and
forming the infinite impulse response filter as a cascade of the modal correction filters.
9. The method according to claim 8 , wherein the generating filter coefficients is based upon controlling reverberation by modifying sound produced by a primary radiator.
10. The method according to claim 8 , wherein the generating filter coefficients is based upon controlling reverberation by introducing additional sound produced by a secondary radiator.
11. A method for controlling reverberation in a listening room, comprising:
generating a transfer function associated with a listening position within the room;
selecting at least one mode for frequencies of interest based upon the transfer function;
creating a discrete time representation based upon the at least one selected mode; and
generating infinite impulse response filter coefficients for each said at least one selected mode using the discrete time representation,
wherein the selecting further comprises:
identifying potential modes for equalization based upon a target reverberation time;
calculating a decay rate corresponding to each of the potential modes;
comparing each decay rate with the target reverberation time to obtain the at least one selected mode; and
determining a center frequency associated with a spectral peak corresponding to each selected mode;
wherein the generating the infinite impulse response filter further comprises:
for each selected mode, designing a modal correction filter provided as a relation between an estimate of pole location and a desired pole location, where at least the estimated pole locations are determined from the discrete time representation, and
forming the infinite impulse response filter as a cascade of the modal correction filters.
12. The method according to claim 11 , further comprising: estimating the reverberation time based upon a volume of the room.
13. The method according to claim 11 , wherein the calculating the decay rate further comprises: fitting a model using non-linear least squares to measured time-series data.
14. The method according to claim 11 , wherein the determining the center frequency further comprises: fitting a second-order parabolic function to spectral transform values located around the spectral peak.
15. The method according to claim 11 , further comprising:
calculating a pole radius based upon the decay rate; and
calculating a pole angle based upon the center frequency.
16. The method according to claim 15 , wherein the creating the discreet time representation further comprises: modeling the room using a Z-transform representation based upon the pole radius and pole angle.
17. A system for controlling reverberation in a listening room having a plurality of resonant modes, each mode having a modal decay rate, comprising:
a radiator which produces sound in accordance with a signal; and
an equalizer, functionally coupled to the radiator, having modal poles determined based upon decay time of the respective resonant modes of the listening room, which modifies the signal to adjust each of the modal decay rates of the listening room, wherein the equalizer includes an infinite impulse response filter designed as a cascade of modal filters for each of the modal poles.
18. The system according to claim 17 , wherein the radiator is a primary radiator which produces sound in accordance with an input signal, and the equalizer modifies the input signal.
19. The system according to claim 17 , wherein the radiator is a secondary radiator which produces an additional sound in accordance with a corrective signal provided by the equalizer.