Acoustic Transducer Array Signal 'Processing BACKGROUND This description relates to acoustic transducer array signal processing. Acoustic transducers (sometimes called drivers) of loudspeaker systems may he grouped in arrays (for example, acoustic dipoles or pairs of acoustic monopoles) to increase the power of, or to directionally control the magnitude mid 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 figure 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 iobes 704a and 706a centered along an axis 707 at ()=±90 on graph 700, with the waves from the front and back canceling out along the mid-plane 708 of the dipole 702 at 0:= 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 figures 7B and 7C, the lobes may be asymmetric (704b, 706b in figure 7B; 704c,.706c in figure 7C), and there may be nulls on only one plane (e.g., along null axis 710 in figure 7B) or on. more than one plane (e.g., along null axes 712,714 in figure 7C). Figure 7B also illustrates that there may be variation between an ideal radiation pattern 716 and an actual radiation pattern 7.18 generated by real transducers (not'shown). SUMMARY In general, in one aspect, filters operate on an input signal to provide output signals arid 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 die second array produce destructive interference in the second frequency range. Implementations may include one or more of tiie 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 include: in series, an'.inverting low-pass fitter 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 lo.vyer 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 tillers include: an inverting low-pass tiller 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 haying a comer 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, '['he .filters also include: a aec.ond 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 kHZThe third frequency range includes-frequencies above a lower frequency., and the filters are configured to cause the first transducer of the first array to he 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 ami 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 iow-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 comer 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 comer 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 ouiput signal, to a second summing input of the second array; and in which a. first signal input is coupied 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 arid 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 m the additional frequency range. The additional .frequency range includes frequencies below about 550 Ife. The filters also operate on a second input signal 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 leftside 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 mid 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.radiatioti.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 Figure I is a schematic view of an audio system, Figures .2-5arid 6B-6E are block diagrams of an audio system. Figure 6 A is a table. Figure 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 outputfrom 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 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 August 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 aid 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, or 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-oils among efficiency, frequency range, and control of directivity are required when using 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 (he 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 he controlled. In some examples, ah 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. figure 1, an audio system includes two speaker arrays, a let! array TOOL and a right array IGOR, meant to be located on corresponding sides of a Listening environment 103 and to reproduce corresponding ieft 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's efficiency. Bach array100L, 100R includes two transducers, which we refer to as left outer transducer 104, left inner transducer 106, right inner transducer 10B, 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'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 100L 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 betxveen the two identical but out-of-phase left channel signals, or by filtering the signal fed to one transducer difrerentlv than the signal led to the other transducer, if desired, the efficiency of array 100L eau.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 100R. 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 em 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 k.Ez, 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 lo\v frequency range, e.g., below 550 Hz, the transducers 104. and 106 from the left array 100L are fed identical signals and are used to form a first acoustic source; the transducers 108 and .110 from the right array 100R 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 die right array 100R) 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 signa! 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 he 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'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 widv 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 fay 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 create 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 inpxrt signal As vviil 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 patlis and. applying a low-pass •filter 202 to the signal sent to the left inner transducer 106, as shown in figure 2, The full spectrum signal is sent to the left outer transducer 1.04, which acts as the primary transducer for this signal 204, The low-pass filter 202 prevents signals having frequencies above 3KHz from reaching the inner transducer 106. The outer transducer 104 can also be-angled outward {.see figure 1) to reduce left-channel high-frequency content from reaching .the'listener 102(figure 1). The filter 202 also inverts the phase of the signal to create the acoustic null along the nulJ axis 112, with the inner transducer 106 acting as the canceling transducer for this signal 204. In some examples, a 21 us delay is introduced by the .filter 202 to steer the null axis 112 toward the listener 'i'02. Attenuating the filter 202 by 2 dB increases the overall system efficiency without significantly degrading the psychoacoustic effects. This single filter 202 used in conjunction with the signal splitting and transducer geometry shown in..figures 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 i 12. To improve tlie low frequency efficiency of the array, the right outer transducer can be used as the canceling transducer for low frequencies. En effect,.the right array 1OOR is used as if it were a part of the left array 1QOL, rather than as a separate loudspeaker intended'for right-channel signals, in the example of figure 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 100R. In some examples, the choice of cross-feed frequency (in this example, 1 kJ-Ix) 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 1.00R, it: is usefisl 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 ali-pass filters 302 and 314 are also .phase-matched to each other, as shown by the dashed arrow 325. Applying the I 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 (