Abstract:
A set of filters is configured to distribute input signals representing a single perceptual axis to first and second physically separate arrays of loudspeakers comprising at least first and second transducers, such that the arrays of loudspeakers will create an array pattern corresponding to the input signals when the input signals are between a first frequency and a second frequency.

Description:
BACKGROUND 
     This description relates to acoustic transducer array signal processing. 
     Acoustic transducers (sometimes called drivers) of loudspeaker systems may be grouped in arrays (for example, acoustic dipoles or pairs of acoustic monopoles) to increase the power of, or to directionally control the magnitude and phase of, the radiation from the transducers. Arrays may take the form of acoustic dipoles or pairs of acoustic monopoles, for example. 
     As shown in  FIG. 7 , an acoustic dipole  702  (for example, an open-backed speaker that radiates sound equally from the front and rear faces of its diaphragm) effectively radiates energy in two lobes  704   a  and  706   a  centered along an axis  707  at θ=±90 on graph  700 , with the waves from the front and back canceling out along the mid-plane  708  of the dipole  702  at θ=0. The region of cancellation, referred to as a null, can be used to create psychoacoustic effects, such as altering the direction from which a sound is perceived to originate. As shown in  FIGS. 7B and 7C , the lobes may be asymmetric ( 704   b ,  706   b  in  FIG. 7B ;  704   c ,  706   c  in  FIG. 7C ), and there may be nulls on only one plane (e.g., along null axis  710  in  FIG. 7B ) or on more than one plane (e.g., along null axes  712 ,  714  in  FIG. 7C ).  FIG. 7B  also illustrates that there may be variation between an ideal radiation pattern  716  and an actual radiation pattern  718  generated by real transducers (not shown). 
     SUMMARY 
     In general, in one aspect, filters operate on an input signal to provide output signals and cross-feed signals to transducers of first and second arrays so that a plurality of transducers of the first array produce destructive interference in a first frequency range; the transducers of the first array do not produce destructive interference in a second frequency range; and a first transducer of the first array and a first transducer of the second array produce destructive interference in the second frequency range. 
     Implementations may include one or more of the following features. 
     The first frequency range includes a range of frequencies for which the corresponding wavelengths are greater than twice a spacing between the transducers in the first array. The range of frequencies is also one for which the corresponding wavelengths are less than twice a spacing between the first and second array. The second frequency range includes a range of frequencies for which the corresponding wavelengths are greater than twice a spacing between the first and second array. The first frequency range includes frequencies between about 1 kHz and about 3 kHz. The second frequency range includes frequencies below about 1 kHz. 
     The first frequency range includes frequencies between an upper frequency and a lower frequency and the filters includes; in series, an inverting low-pass filter having a corner frequency at the upper frequency and a high-pass filter having a corner frequency at the lower frequency, providing output signals to the first transducer of the first array; and an all-pass filter phase-matched to the high-pass filter and providing output signals to the second transducer of the first array. The filters are configured to delay the output signal to the first transducer of the first array relative to the output signal to the second transducer of the first array. The filters attenuate the cross-feed signals to the transducers of the second array when the input signal is in the first frequency range. The first frequency range includes frequencies between an upper frequency and a lower frequency and the filters include; a low-pass filter having a corner frequency at the lower frequency and providing cross-feed signals to the second array; and an all-pass filter phase-matched to the low-pass filter and providing output signals to the first array. 
     The second frequency range includes frequencies below a first upper frequency and the filter include: an inverting low-pass filter having a corner frequency at the upper frequency and providing cross-feed signals to the second array; and an all-pass filter phase-matched to the inverting low-pass filter and providing output signals to the first array. The filters attenuate the output signals to a second transducer of the first array when the input signal is in the second frequency range. The second frequency range includes frequencies below a first upper frequency and the filters include: a first high-pass filter having a corner frequency at the first upper frequency and providing output signals to the second transducer of the fist array; a first all-pass filter phase-matched to the high-pass filter and providing output signals to the first transducer of the first array; and a second all-pass filter phase-matched to the first all-pass filter and providing cross-feed signals to the first transducer of the second array. The filters also include: a second high-pass filter having a corner frequency at the first upper frequency, providing cross-feed signals to a second transducer of the second array, and phase matched to the second all-pass filter. The filters provide output signals and cross-feed signals to the second transducer of the first and second array in a third frequency range including frequencies below a second upper frequency that is lower than the first upper frequency. The filters include: first and second low-pass filters having corner frequencies at the second upper frequency and providing output signals and cross-feed signals to the second transducer of each of the first and second arrays, respectively; and first and second all-pass filters phase matched to the first and second low-pass filters, respectively, and to each other, and providing output signals and cross-feed signals to the first transducer of each of the first and second arrays, respectively. 
     The filters also provide the output signals and cross-feed signals to the transducers of the first and second arrays so that no destructive interference is produced in a third frequency range. The third frequency range includes a range of frequencies for which the corresponding wavelengths are less than twice a spacing between the transducers in the first array. The third frequency range includes frequencies above about 3 kHz. The third frequency range includes frequencies above a lower frequency, and the filters are configured to cause the first transducer of the first array to be to be active, and to attenuate the output signals to the second transducer of the first array when an input signal is above the lower frequency. The filters include a low-pass filter having a corner frequency at the lower frequency and providing output signals to the second transducer of the first array. The filters are also configured to attenuate the cross-feed signals to the transducers of the second array when the input signal is in the third frequency range. The filters include: a first low-pass filter having a corner frequency at the lower frequency and providing output signals to the second transducer of the first array; a second low-pass filter having a corner frequency at or lower than the lower frequency and providing cross-feed signals to the second array; and an all-pass filter phase-matched to the second low-pass filter and providing output signals to the first array. 
     The filters include a first all-pass filter providing output signals to a first summing input of the first array, a second all-pass filter providing output signals to an input to the first transducer of the first array, a first low-pass filter and a first high-pass filter in series and providing output signals to a first summing input to the second transducer of the first array, a second low-pass filter providing output signals to a second summing input to the second transducer of the first array, a third low-pass filter providing cross-feed signals to a first summing input of the second array, a third all-pass filter providing cross-feed signals to an input to the first transducer of the second array, a fourth low-pass filter and a second high-pass filter in series and providing cross-feed signals to a first summing input to the second transducer of the second array, and a fifth low-pass filter providing cross-feed signals to a second summing input to the second transducer of the second array. The second and fifth low-pass filter have corner frequencies at a lower frequency; the third low-pass filter and the first and second high-pass filters have corner frequencies at an intermediate frequency; and the first and fourth low-pass filters have corner frequencies at an upper frequency. The filters also include a sixth low-pass filter providing a cross-feed signal to a second summing input of the first array; a fourth all-pass filter providing an output signal to a second summing input of the second array; and in which a first signal input is coupled to the first all-pass filter and the third low-pass filter, and a second signal input is coupled to the fourth all-pass filter and the sixth low-pass filter. 
     The filters also provide the output signals and cross-feed signals to the transducers of the first and second arrays so that the transducers of the first array do not produce destructive interference in a an additional frequency range; and a plurality of transducers of the first array and a plurality of transducers of the second array produce destructive interference in the additional frequency range. The additional frequency range includes frequencies below about 550 Hz. 
     The filters also operate on a second input to provide output signals and cross-feed signals to the transducers of the second and first arrays so that a plurality of transducers of the second array produce destructive interference in the first frequency range; the transducers of the second array do not produce destructive interference in the second frequency range; and the first transducer of the first array and the first transducer of the second array produce destructive interference based on both the first input signal and the second input signal in the second frequency range. The first input signal is a left-side signal and the second input signal is a right-side signal. 
     In general, in one aspect, filters operate on an input signal to provide output signals and cross-feed signals to drive transducers of first and second arrays so that transducers of the first array produce substantially different degrees of destructive interference in respectively first and second frequency ranges; and a transducer of the first array and a transducer of the second array produce destructive interference in the second frequency range; in which first signals driving the first array and second signals driving the second array are not identical. 
     Advantages include enhancing low-frequency output efficiency of a loudspeaker system that includes speaker arrays, where each array works independently to create nulls in acoustic radiation at high frequencies, and the arrays work together to create nulls at lower frequencies. The combination of closely-spaced transducers within each array and greater spacing between the arrays allows efficient radiation of power for both high frequency and low frequency signals. The perceptual axis can be positioned beyond the physical range of the arrays. 
     Other features and advantages will be apparent from the description and the claims. 
    
    
     
       DESCRIPTION 
         FIG. 1  is a schematic view of an audio system. 
         FIGS. 2-5  and  6 B- 6 E are block diagrams of an audio system. 
         FIG. 6A  is a table. 
         FIG. 7A-7C  are graphs. 
     
    
    
     By combining acoustic sources to form arrays and processing acoustic signals that are delivered to the sources and to the arrays, the radiation patterns of a loudspeaker system that includes the arrays can be controlled to achieve a variety of goals for the acoustic energy that is radiated by the loudspeaker system to a listener, including generating various types of radiation patterns which can be more complex than the radiation patterns of the individual sources. The acoustic signal processing can include delaying, inverting, filtering, phase-shifting, or level-shifting the signals applied to each transducer relative to the signals applied to other transducers. At given points in space in the vicinity of the system, the acoustic output from the transducers may, for example, interfere constructively (increasing sound pressure) or destructively (decreasing sound pressure). Nulls can be created to take desired shapes and steered to a desired angles. For simplicity of understanding, we will view directivity in a descriptively useful plane, such as a horizontal plane. In the horizontal plane, we may discuss steering a “null axis” to a desired angle. However it should be understood that in three-dimensional space the null may have a three dimensional shape, such as a conical shell, where the angle of the shell walls are varied. For the case of a dipole-type source, the cone angle is 180 degrees, and the shape of the null deteriorates to a simple plane. For a cardioid shape, the cone angle is zero degrees, and the null shape deteriorates to a simple line. 
     Some aspects of driving acoustic transducers are discussed in co-pending application titled “Reducing Resonant Motion in Undriven Loudspeaker Drivers,” filed Aug. 4, 2006, and incorporated here by reference. 
     Because the effects of the signal processing on the radiated acoustic energy are dependent on the frequencies of the signals (and therefore of the acoustic waves) and on the relative positions of the transducers, various combinations of signal processing and groupings of transducers may be used to create desired acoustic effects in various ranges of frequencies. 
     The signal processing may be performed using either analog or digital signal processing techniques. Analog signal processing systems typically use analog filters formed using op amps and various passive components arranged to accomplish desired filtering functions. Digital signal processing can be accomplished in various types of digital systems, such as a general-purpose computer, controlled by software of firmware, or a dedicated device such as a digital signal processing (DSP) processor. Discrete components and analog and digital systems may be used in combination. These signal processing components and systems may be centrally located or distributed (or a combination of the two) among the speaker arrays, individual transducers, or other system components, such as receivers, amplifiers, and equalizers. 
     Trade-offs among efficiency, frequency range, and control of directivity are required when using a destructive interference. In some examples, a predetermined radiation pattern with a null along a null axis oriented at a desired angle can be achieved up to a frequency for which the spacing between two transducers is one-half the wavelength of the acoustic output. Above such a frequency, multiple lobes and nulls begin to appear, which may conflict with an intended effect. The efficiency of a system (the amount of acoustic energy, or power, that can be delivered to the listening environment, for a fixed amount of power input) directly depends on the spacing between the speakers. Larger spacing gives higher efficiency but (as explained) reduces the maximum frequency at which directivity can be controlled. In some examples, an array may have small spacing between its own transducers to maintain control at high frequencies, and large spacing between transducers from different arrays, to provide sufficient output power at low frequencies. 
     In some examples, as shown in  FIG. 1 , an audio system includes two speaker arrays, a left array  100 L and a right array  100 R, meant to be located on corresponding sides of a listening environment  103  and to reproduce corresponding left and right signals of, for example, a stereo source. Signals intended for one side or the other can be manipulated and cross-fed to the opposite side in order to achieve a radiation pattern that can, for example, direct a null toward the listener (or in another desired direction) while enhancing the system&#39;s efficiency. 
     Each array  100 L,  100 R includes two transducers, which we refer to as left outer transducer  104 , left inner transducer  106 , right inner transducer  108 , and right outer transducer  110 . The transducers may or may not be identical. In one frequency range, for example, a higher frequency range (frequencies with a wavelength less than twice the separation between individual transducers within each array), each array works independently and only one transducer is used in each array, so no nulls are produced. At moderate frequencies (for example, frequencies with a wavelength less than twice the separation between the separate arrays), each array again works independently to reproduce its corresponding left and right signals and to steer those signals using the combination of that array&#39;s transducers to produce nulls. At lower frequencies, the arrays work together using one or both transducers in each. 
     For a left channel signal, the left array  100 L steers a null in a desired direction, shown by null axis  112 , by using its two transducers  104 ,  106  with appropriate signal processing to achieve a predetermined radiation pattern. An example of appropriate signal processing feeds a left channel signal to the outside transducer  104  and an identical but out-of-phase left channel signal to the inside transducer  106 . (This assumes the two transducers  104  and  106  are identical. If they are not, the two signals may not be identical.) The desired null axis direction can be controlled by introducing delay between the two identical but out-of-phase left channel signals, or by filtering the signal fed to one transducer differently than the signal fed to the other transducer. If desired, the efficiency of array  100 L can be increased by attenuating the signal applied to the transducer  106  relative to that applied to the transducer  104  (or attenuating the signal applied to transducer  104  relative to that applied to transducer  106 ). Similar behavior occurs for a right channel signal, with a null along the null axis  116  arising from the right array  100 R. 
     The two transducers of each of the two arrays have a relatively small spacing  107 ,  109 , for example, in the range of 5 cm to 7 cm on center, while the spacing  111  between the two arrays is wider, for example, in the range of 50 cm to 70 cm. This allows the arrays to be conveniently placed on either side of a typical computer or television monitor. In some examples, the transducers within each array are 6.5 cm apart on center. 
     At lower frequencies, the two more widely spaced arrays can be used together as if they were a single speaker array. In one lower frequency range, e.g., 550 Hz-1 kHz, one transducer from each array, e.g., outer transducers  104  and  110 , are used together as two elements of an array driven so that their acoustic outputs interfere destructively to create a desired radiation pattern, characterized by a null along the null axis  114  between them. The wider element spacing in this frequency range results in increased efficiency of sound radiation by the combined arrays. In another low frequency range, e.g., below 550 Hz, the transducers  104  and  106  from the left array  100 L are fed identical signals and are used to form a first acoustic source; the transducers  108  and  110  from the right array  100 R are also fed identical signals and are used to form a second source, where the two sources combine to form a single array. The signals sent to the opposite side from which they were intended (i.e., left-side signals fed to the right array  100 R) are sometimes referred to in this description as cross-feed signals. The signals sent to the first source and second source are processed as described earlier to create a null along the same null axis  114  described above for higher frequencies. That is, the signal fed to the transducers  104  and  106 , in this low frequency range, is identical but of opposite polarity relative to the signal fed to the transducers  108  and  110 . One signal may also be delayed with respect to the other, may be filtered with respect to the other, and/or may be attenuated with respect to the other. For example, the signal fed to the transducers  108  and  110  may be delayed relative to the signal fed to the transducers  104  and  106 , it may be attenuated by some amount (e.g. 2 dB), and/or it may be filtered (for example, with a low pass filter). A benefit of this arrangement is that the system has more radiating area in this frequency range, (i.e., from all four transducers) which increases the system&#39;s maximum output capability. This serves to both achieve the desired radiation pattern and increase the overall output power capability of the system. In general, for arrays with multiple transducers, selectively altering the numbers of transducers that are operating in various frequency ranges can be used to improve system efficiency and maximum output capability, while achieving a desired radiation pattern over a wider range of frequencies. 
     Another effect of the arrays is that sound images can be placed well to the left of the left array or well to the right of the right array. This can be accomplished by orienting the null axis in a desired direction. The locations of these sound images (the location from which a listener interprets sound as originating) are referred to as the left and right perceptual axes  118  and  120 . The orientation of perceptual axes can be controlled by controlling the orientation of null axes. An example of the signal processing used to crate nulls along the null axes is described below, in increasing detail starting from the most basic array building block and adding each functional feature of the signal processing in turn. For the sake of simplicity, this description focuses on the left input signal. As will be seen, the same processing is applied to deliver the right input signal to the appropriate transducers. 
     The null along the left null axis  112  is created by splitting the left input signal  204  into two paths and applying a low-pass filter  202  to the signal sent to the left inner transducer  106 , as shown in  FIG. 2 . The full spectrum signal is sent to the left outer transducer  104 , which acts as the primary transducer for this signal  204 . The low-pass filter  202  prevents signals having frequencies above 3 kHz from reaching the inner transducer  106 . The outer transducer  104  can also be angled outward (see  FIG. 1 ) to reduce left-channel high-frequency content from reaching the listener  102  ( FIG. 1 ). The filter  202  also inverts the phase of the signal to create the acoustic null along the null axis  112 , with the inner transducer  106  acting as the canceling transducer for this signal  204 . In some examples, a 21 μs delay is introduced by the filter  202  to steer the null axis  112  toward the listener  102 . Attenuating the filter  202  by 2 dB increases the overall system efficiency without significantly degrading the psychoacoustic effects. 
     This signal filter  202  used in conjunction with the signal splitting and transducer geometry shown in  FIGS. 1 and 2  can render a convincing left perceptual axis which can be displaced from the physical location of the transducers, but, due to the close proximity of the primary and canceling transducers, there are low frequency output limitations. Moving the transducers  104  and  106  farther apart could address this but would require a larger array enclosure and would limit the upper frequency for which the system could control the direction of the null axis  112 . 
     To improve the low frequency efficiency of the array, the right outer transducer can be used as the canceling transducer for low frequencies. In effect, the right array  100 R is used as if it were a part of the left array  100 L, rather than as a separate loudspeaker intended for right-channel signals. In the example of  FIG. 3 , this concept is implemented for frequencies below 1 kHz by filtering and inverting the left input  204  with a low-pass filter  306  and applying this signal (i.e., cross-feeding it) to the right array  100 R. In some examples, the choice of cross-feed frequency (in this example, 1 kHz) will depend on the capability of the transducers and their spacing as well as subjective decisions about the placement of the perceptual axis. If the null along the null axis  114  is desired to be directly between the speaker arrays, no delay is required in the filter  306 . In some examples, the low-frequency null was found to tolerate 3 dB of attenuation on the canceling transducers without perceptual degradation. 
     With the canceling signal below 1 kHz now cross-fed to array  100 R, it is useful to eliminate output from transducers  106  and  108  over this frequency range in a way that does not disrupt the phase relationship already established between the left inner and outer transducers. This can be achieved, for example, by using a pair of high-pass filters  310  and  312  and matching all-pass filters  302  and  314  (dashed arrows  322  and  324  indicate phase matching). The all-pass filters  302  and  314  also phase-matched to each other, as shown by the dashed arrow  325 . 
     Applying the 1 kHz high pass filter  310  to the left inner transducer  106  without the matching all-pass filter would introduce a new phase shift that would disrupt the established null along the null axis  112 . To avoid disturbing the null along the null axis  112 , the phase of the all-pass filter should match that of the highpass filter over the band of interest (&lt;1 kHz, in this example) within a tolerance of approximately +/−30 degrees. Performance can be improved if the phase match occurs over a larger frequency range, and phase is matched to a tighter degree, such as to approx. +/−15 degrees. Another all-pass filter  304  is applied to the left array input and phase-matched (again within +/−30 degrees) to the right low-pass filter  306  to keep the cross-feed signal in phase with the primary signal. The null formed by the combined outputs of the left transducers  104  and  106  is restricted to the frequency range of 1 kHz to 3 kHz due to the operation of the filters  202  and  310 . In other words, for a left input signal  204  within the frequency range of 1 kHz˜3 kHz, the left array  100 L independently achieves a null along the null axis  112 . For a left input signal  204  in the frequency range below 1 kHz, the left outer transducer  104  and the right outer transducer  110  together combine to form a null along the null axis  114 . A right signal can be processed in a similar fashion. 
     The low frequency performance of this system can be enhanced by using the inner transducers in combination with their corresponding outer transducers in a selected frequency range, for example, a frequency range lower than the frequency range described earlier where only the outer transducers were operating (for example, below 550 Hz). As shown in  FIG. 4 , a pair of low-pass filters  402  and  404  are added in parallel with the existing filters  310  and  312  to filter the signal input to the left and right inner array transducers  106  and  108 , and provide it, mixed with the parallel higher-frequency signals by mixers  410  and  412 , to those transducers. Below 550 Hz, filters  402  and  404  are matched in phase (within +/−30 degrees) to filters  302  and  314 , shown by dashed arrows  406  and  408 . The dashed arrow  325  showing phase-matching between the all-pass filters  302  and  314  is removed for clarity in  FIG. 4  and later figures. 
     As shown in  FIG. 5 , most of the filters described so far are the same on the left and right sides, assuming that the left and right arrays are identical, so very little must be added to produce the same effects for the right input  502 . If the left and right arrays are not identical, the filter parameters for the left and right signal paths may need to be adjusted to take into consideration the array discrepancies. A low-pass filter  514  (which matches the filter  202 ) provides an inverted signal to the right inner transducer  108 , so that the combined output from the transducers  108  and  110  will produce a null along null axis  116  ( FIG. 1 ) for a moderate frequency range (1 kHz˜3 kHz in this example). A low-pass inverting filter  506 , which matches the characteristics of the low-pass filter  306 , receives the right signal input  502  and provides a right cross-feed signal to the left array  100 L so that right-channel low-frequency signals radiated by elements from each array will produce a null along a null axis similar to that achieved for the left channel, in some examples along the same null axis  114  as the left-channel signals. As on the left, an all-pass filter  504  is added to the right input and phase-matched to the right cross-over filter  506 , as shown by dashed arrow  512  (the other dashed phase-matching arrows are removed for clarity). Mixers  510  and  508  combine the primary signals with the cross feed signals for both arrays. Each of the filters occurring after the first stage (i.e., after one of filters  304 ,  306 ,  504 , or  506 ) produces a signal that is treated as both an output signal based on the input signal for its own side and a cross-feed signal based on the input signal for the opposite side. For example, the signal output from low-pass filter  404  is referred to as both an output signal based on the left input signal  204  and a cross-feed signal based on the right input signal  502 , as already filtered by the low-pass cross-feed filter  506 . Both signals are fed to the left inner transducer  106 . 
     In  FIG. 6A , table  600  summarizes the frequency ranges over which each transducer is active in  FIG. 4 , including attenuation, delay, and phase shift on each transducer.  FIGS. 6B-6E  shown the active filters and signal paths for each range. Phase relationships are shown relative to the primary transducer(s), where “+” indicates a primary transducer for each range, and “−” indicates a canceling transducer. Transducer symbols with white backs indicate that the transducer is inactive in that frequency range (that is, signals in that range have been substantially attenuated out of the input for that transducer). Table  600  and  FIGS. 6B-6E  indicate filtering of the left input  204  only. A symmetric table, not shown, would describe the filtering of the right input  502 . 
     For left channel signal below 550 Hz, as shown by row  602  and  FIG. 6B , both left transducers (outer transducer  104  and inner transducer  106 ) in left array  100 L are active and in-phase (symbols  604 ,  606  in table  100 ) relative to each other due to the filters  302  for the left outside transducer  104  and  402  for the left inside transducer  106 . The two right transducers (outer  110  and inner  108 ) in right array  100 R are active and in phase relative to each other, but, as a whole, they are out of phase with the left transducers, as a whole, as shown by symbols  608 ,  610 . There is also a 3 dB attenuation from the cross-feed low-pass filter  306 . The low-pass filter  404  provides the low-frequency signal (already inverted by the filter  306 ) to the right inner transducer. This combination of outputs of transducers from two arrays provides a desired radiation pattern and is responsible for the null along the null axis  114 . The two transducers of each array behave as a single acoustic source, and the source spacing is the spacing between the arrays (as opposed to the spacing between individual array elements) which increases radiation efficiency in this frequency range and also increases the maximum output capability of the system. With this configuration, two arrays behave as a single large array. 
     In the range of 550 Hz to 1 kHz of the left channel signal, shown by row  612  and  FIG. 6C , the outer transducers  104 ,  110  are the same as in the lower range ( 614 ,  620 ), while the inner transducers  106 ,  108  are off ( 616 ,  618 ) due to the combination of the low-pass filters  402  and  404  and the high-pass filters  310  and  312 . The outputs from the outer transducers  104  and  110  form a null along a null axis, which may be the null axis  114 . In this range, the two arrays  100 L,  100 R are also behaving as a single large array, increasing low frequency output efficiency. However, only one transducer from each array is operating to avoid interfering with the inverted signals from the high-pass filters  310  and  312  (around 1 kHz in the example). The acoustic null along the null axis  114  could be steered by introducing a delay between the signal applied to the various transducers, if desired. 
     The null along the null axis  112  in the range of 1 to 3 kHz for the left channel signal is produced from the left transducers only, as shown in row  622  and  FIG. 6D . The left outer transducer  104  is on as usual ( 624 ), while the left inner transducer  106  is attenuated (to increase system maximum output power), phase-reversed (to create the null) ( 626 ), and delayed (to steer the null axis  112 ) by the low-pass filter  202 . In this frequency range, both of the right transducers  108 ,  110  are off ( 628 ,  630 ) due to low-pass filter  306 . There is no cross-feed in this frequency range. 
     Above 3 kHz, as shown in row  632  and  FIG. 6E , the right transducers  108 ,  110  remain off ( 638 ,  640 ), and the left inner transducer  106  is also turned off ( 636 ) by filter  202 . Only the left outer transducer  104  remains on ( 634 ). 
     In general, by using the respective elements of each individual array to independently control that array&#39;s radiation pattern at higher frequencies, and using both arrays jointly in some manner to control the radiation pattern of the combined array output at lower frequencies, efficiency can be maintained or improved at low frequencies and directivity controlled over a wider frequency range. Since the widely-spaced arrays improve total system efficiency, the system can deliver more power at low frequencies, compared to a system that only used each array to control its own side&#39;s signal. 
     As noted above, similar techniques can be used to deploy arrays having any number of transducers. The details of frequencies to filter, which signal to invert, shift, or delay, and where to position the transducers will depend on such factors as the number of transducers, characteristics of the transducers, the output desired, the environment where the arrays are to be used, and the power output capability of each transducer. 
     Other embodiments are within the scope of the following claims.