This specification describes a loudspeaker system in which two or more acoustic drivers share a common enclosure.
In one aspect, an apparatus includes an acoustic enclosure, a plurality of acoustic drivers mounted in the acoustic enclosure so that motion of each of the acoustic drivers causes motion in each of the other acoustic drivers, a canceller, to cancel the motion of each of the acoustic drivers caused by motion of each of the other acoustic drivers, and a cancellation adjuster, to cancel the motion of each of the acoustic drivers that may result from the operation of the canceller. The cancellation adjuster may adjust for undesirable phase and frequency response effects that result from the operation of the canceller. The
cancellation adjuster may apply the transfer function matrix
where each of the matrix elements Hxy represents a transfer function from an audio signal Vx applied to the input of acoustic driver x to motion represented by velocity Sy of acoustic driver y. The acoustic drivers may be a components of a directional array. The acoustic drivers may be components of a two-way speaker.
In another aspect, a method of operating a loudspeaker having at least two acoustic drivers in a common enclosure, includes determining the effect of the motion of a first acoustic driver on the motion of a second acoustic driver; developing a first correction audio signal to correct for the effect of the motion of the first acoustic driver on the motion of the second acoustic driver; determining the effect on the motion of the first acoustic driver of the transducing of the correction audio signal by the second acoustic driver; and developing a second correction audio signal to correct for the effect on the motion of the first acoustic driver of the transducing of the first correction audio signal by the second acoustic driver. The correction audio signal may correct the frequency response and the phase effects on the motion of the first acoustic driver of the transducing of the correction audio signal by the second acoustic driver. The second correction audio signal may be
where H is the transfer function matrix
where the matrix elements Hxy represent the transfer function from an audio signal Vx applied to the input of acoustic driver x to motion represented by velocity Sy of acoustic driver y. The method may further include determining matrix elements Hxy by causing acoustic driver y to transduce an audio signal, and measuring the effect on acoustic driver x of the transducing by acoustic driver y by a laser vibrometer. The method of claim 8, wherein the motion of acoustic driver is represented by a displacement.
Though the elements of several views of the drawing are shown and described as discrete elements in a block diagram and may be referred to as “circuitry”, unless otherwise indicated, the elements may be implemented as one of, or a combination of, analog circuitry, digital circuitry, or one or more microprocessors executing software instructions. The software instructions may include digital signal processing (DSP) instructions. Unless otherwise indicated, signal lines may be implemented as discrete analog or digital signal lines, as a single discrete digital signal line with appropriate signal processing to process separate streams of audio signals, or as elements of a wireless communication system. Unless otherwise indicated, audio signals may be encoded in either digital or analog form. For convenience, “radiating sound waves corresponding to channel x” will be expressed as “radiating channel x.”
Referring to
In the audio system of
The effect of cross-coupling can be seen in
Actual implementations of acoustic system of
Canceling transfer functions C11, C21, C22, and C12 can be derived as follows. The relationships of
H
11
·V
1
+H
12
·V
2
=S
1
H
21
·V
1
+H
22
·V
2
=S
2
The notation can be simplified by transforming this set of linear equations into matrix form. The transfer function matrix H contains all transmission paths in the system:
The input voltages are grouped into a vector v and the velocity or displacement into a vector S. In matrix notation, the system is described as
Or simply
H·{right arrow over (V)}={right arrow over (S)}
The relation between the input voltage and output voltage of the canceller is described by the linear equations:
C
11
·U
1
+C
12
·U
2
=V
1
C
21
·U
1
+C
22
·U
2
=V
2
Or in matrix notation
The velocities of the acoustic drivers can now be expressed as a function of the input voltages to the canceller.
The overall system transfer function is described by the product of H and C. We can simplify this equation by defining a matrix T, which describes the entire system transfer function.
H·C=T
With this, the equation of the input-output relationship of the system can be simplified to:
T also includes operations of conventional signal processor 17 and cancellation adjuster 15.
Assuming that the desired system transfer function T and the matrix H are known, the equation above can be solved for the canceller matrix C:
C=H
−1
·T
det H is the determinant of matrix H:
det H=H11·H22−H12·H21
Written out in matrix notation:
Thus, the coefficients of C are
The denominators in these fractions are the same.
The concept described above with canceller matrix and target function can be universally applied to enclosures with more than two acoustic drivers. For a system with n acoustic drivers the transfer function from the electrical inputs to the velocities of the cones would be described by an nxn matrix. The elements on the main diagonal describe the actively induced cone motion. All other elements describe the acoustic cross-coupling between all cones. The equalization matrix will also be an nxn matrix.
It should be noted that this method can be applied to systems with different acoustic drivers, for example a loudspeaker system with a mid-range acoustic driver and a bass acoustic driver sharing the same acoustic volume. This will result in an asymmetric transfer function matrix but can be solved using the same methods.
The elements in the target function matrix can describe arbitrary responses, such as general equalizer functions. This also allows to control the relative amplitude and phase of all transducers (e.g. for acoustic arrays).
C can be calculated in either frequency or time domain. When the coefficients of the target matrix have been determined and the voltage to velocity or displacement transfer functions Hxx have been measured, the coefficients of C are derived from those functions as described above.
Solving in the time domain always yields stable and causal filters. For this, the corresponding impulse responses for the matrix elements are determined. In this case, inverses of the impulse responses are determined by least-mean-squares (LMS) approximation. Information on LMS approximations can be found in Proakis and Manolakis, Digital Signal Processing: Principles, Algorithms and Applications Prentice Hall; 3rd edition (Oct. 5, 1995), ISBN-10: 0133737624, ISBN-13: 978-0133737622. The impulse responses can also be determined by other types of recursive filters.
The general solution for a 2×2 target matrix (a system with two acoustic drivers) is:
This is the same solution as described above.
Ideally, each acoustic driver's motion would be dependent on its corresponding input signal only. This would be represented as:
Only the diagonal elements of the target matrix are non-zero here.
The solution of this system is
Thus, the coefficients of C are
Which can be expressed as:
Common coefficients can be moved out of the canceller system, leaving coefficients that are different from unity only in the cross-paths. Referring to
If both acoustic drivers are driven by a single input (for example in a directional array), the elements of the second column in T are zero because the array is only driven by one input:
The solution is
The elements of C are
A special case of this operating mode is stopping the motion of the second cone, as described previously. In this case, T21 is also 0. The elements of C are
In this case, the term
is common to both elements and can be moved out in front of the system, leaving only H22 and −H21 as filter terms.
Again, the system can be described in matrix notation:
The solution is
det H=H11·H22·H33−H11·H23·H32−H21·H12·H33+H21·H13·H32−H31·H12·H23−H31·H13·H22
The final solutions for the elements of C are lengthy terms that are not shown here.
The derivation of cancellation transfer functions for implementations with three acoustic drivers sharing the same enclosure can be applied to implementations with more than three acoustic drivers.
The elements of H are determined using a cone displacement or velocity measurement. Laser vibrometers are particularly useful for this purpose because they require no physical contact with the cone's surface and do not affect its mobility. The laser vibrometer outputs a voltage that is proportional to the measured velocity or displacement.
For an enclosure with two acoustic drivers, transfer function H11 is measured by connecting two power amplifiers (not shown) to the two acoustic drivers and driving acoustic driver 12A with the measurement signal. Acoustic driver 12B is connected to its own amplifier that is powered up but which does not get an input signal. The laser vibrometer measures the cone motion of acoustic driver 12A. Transfer function h12 is measured by using the same setup and directing the laser at Driver 2.
The same technique can be used to measure transfer function Hxy in a system with y acoustic drivers by causing acoustic driver y to transduce an audio signal and measuring the effect on acoustic driver x using the laser vibrometer.
Transfer function H22 is measured like transfer function H11, only that now the amplifier of acoustic driver 12A has no input signal and acoustic driver 12B gets the measurement signal. Transfer function H21 is then determined by directing the laser vibrometer at acoustic driver 12A again while exciting acoustic driver 12B.
A simpler system for the compensation of cross-talk in an enclosure includes adding a phase inverted transfer function of voltage U1 to velocity S2 to the input voltage of Acoustic driver 12B. This solution is shown in
In the implementation of
S
1
=U
2
·H
12
+U
1
·H
11 (1)
S
2
=U
1
·H
21
+U
S
·H
22 (2)
now we can define functions based on the transfer functions H12 , H21, H11 and H22 as:
and apply G21 at filter 116A and G12 at filter 116B, resulting in modified movements S′1 and S′2 as:
S′
1
=S
1
−U
2
·G
12
·H
11
S′
2
=S
2
−U
1
·G
21
·H
22.
Substituting equations (1) and (2) for S1 and S2 respectively gives
The first and third terms cancel, resulting in
S′
1
=U
1
·H
11 and
S′
2
=U
2
·H
22,
Which means that the cross-coupling effects have been eliminated.
The system of
Numerous uses of and departures from the specific apparatus and techniques disclosed herein may be made without departing from the inventive concepts. Consequently, the invention is to be construed as embracing each and every novel feature and novel combination of features disclosed herein and limited only by the spirit and scope of the appended claims.
This application is a continuation-in-part of, and claims priority to, U.S. patent application Ser. No. 11/499,014 filed Aug. 4, 2006 and published Feb. 7, 2008 as published Pat. App. US-2008-0031472-A1 and also claims priority to U.S. Provisional Patent App. 61/174,726, filed May 1, 2009.
Number | Date | Country | |
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61174726 | May 2009 | US |
Number | Date | Country | |
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Parent | 11426512 | Jun 2006 | US |
Child | 12771541 | US | |
Parent | 11499014 | Aug 2006 | US |
Child | 11426512 | US |