BACKGROUND OF THE INVENTION 
     The present invention relates to electronic signal processing for loudspeakers and in particular to extending the low-frequency capability of loudspeakers. 
     Conventional electromagnetic loudspeaker drive units have two principal limits on their maximum acoustic output capability: excursion of the cone, and heat buildup. Excessive cone excursion adds distortion to the signal creating a desire to limit the cone excursion. Further, the drive unit temperature rises above tolerable limits if the electrical power-handling ability of the voice coil is exceeded and there is insufficient capacity for removing the resulting heat from the coil. Overly high temperatures ultimately result in a failure of the voice coil insulation, wire, and/or bonding of the voice coil to its former as the temperature of the internal parts becomes so great that electrical insulation and glue systems fail. 
     The maximum acoustic output limits may be changed if the loudspeaker drive unit is enclosed in a sealed or a vented box or a box equipped with a passive radiator in addition to the main driver. The maximum acoustic output limits may be further changed in more complex enclosures containing combinations of sealed sub-enclosures, vented sub-enclosures, or chambers equipped with passive radiators. 
     The limits on excursion of the loudspeaker drive unit at audio frequencies may also be changed by the presence of the enclosure because the acoustical load on the driver may be changed by the presence of the enclosure. The electrical power-handling ability may be changed by the presence of the enclosure because the enclosure typically adds to the thermal resistance of the system, and thus a given power input will produce a greater voice coil temperature rise for a driver enclosed in a box compared to a driver in free air. 
     Additionally, complete loudspeaker systems, as opposed to conventional drive units alone, have additional limits imposed on them due to upper limits on velocity of air in ports, or passive radiators undergoing excessive excursion. High velocity of air in the ports may cause extraneous noise, and passive radiator low frequency maximum excursion may be different from the maximum low frequency excursion of the principal drive units. 
     Good loudspeakers are designed for flat low-frequency response down to a practical lower limiting frequency, typically using methods explicated by Beranek and Locanthi in the 1950&#39;s. Beranek and Locanthi proposed electrical analogies for the electrical and mechanical systems of loudspeakers. These electrical analogies were brought to wide use as a practical system of measurements and application of those measurements by Thiele and Small in the 1960&#39;s and 70&#39;s. Complete low-frequency loudspeaker design work today is strongly influenced by the papers of Thiele and follow-on work by Small. Thiele produced a catalog of low-frequency responses, modeling loudspeakers as electrical high-pass filters. The models showed various alignments varying flatness of response, steepness of roll-off below the cutoff frequency, potential electrical equalization, group delay, excursion vs. frequency, and other factors. The Thiele-Small parameters have become the most prominent metric used nationally and internationally for the exchange of information about drivers, and have had enormous positive economic impact. 
     Low-frequency loudspeaker design today is typically an act of balancing a variety of specifications affecting bandwidth, frequency response over the bandwidth, maximum level capacity and its variation with frequency, various distortions, and cost. Among the target frequency response curves available for design from sources such as Thiele, some include separate electrical equalization before the power amplifier. Such equalization may be provided by an underdamped high-pass filter, with peaking of the high-pass filter response at the corner frequency of the high-pass filter made a part of the overall design. 
     An unaided (i.e., receiving an unfiltered input signal) loudspeaker mechanical and acoustical radiation system has a frequency response showing a particular low-frequency rolloff. Accurate sound production (i.e., a flat frequency response) may be extended to a frequency below the rolloff of the unaided loudspeaker mechanical and acoustical radiation system by providing electrical equalization in the form of an underdamped high-pass filter. Such electrical equalization increases the excursion of the associated loudspeaker driver at the peaking frequency of the high-pass filter and at frequencies around the peaking frequency. However, although such electrical equalization has the benefit of extending the system response below the rolloff frequency of the unaided loudspeaker mechanical and acoustical radiation system, because the electrical equalization increases the power below the rolloff frequency, the equalization raises both the electrical power dissipated as heat below the rolloff frequency and the excursion around and at the rolloff frequency, as shown in one example system and Thiele response alignment by Newman. These increases in heat and excursion may exceed a speaker&#39;s limits. 
     Once the utility of extending the bandwidth with a peaking high-pass filter became known, several inventors took the idea a step further to make the high-pass filter dynamic by various means, and with a varying fit to the excursion capability and power limits of the driver. Unfortunately, such attempts have failed to achieve the best possible fit of bandwidth extension while staying within the excursion and thermal limits of drivers. 
     Further, electrical equalization which includes a boost capability may be used to extend the frequency range downwards, but may also cause a reduction in the maximum sound pressure level capability vs. frequency typically by the same amount as the equalization vs. frequency response curve of the high-pass filter. Thus, a need remains for a system and method for extending low frequency performance of conventional loudspeaker driver-box systems, for example, open back, closed box, vented box, and their more complex variants composed of combinations of these types of parts, having limitation in their low-frequency response range and maximum sound pressure level capability vs. frequency. 
     The above described material and other related material is discussed in the following publications:
     Beranek, Leo L.,  Acoustics , McGraw-Hill, New York, 1954;   Burg, T. C., Gao, X., Dawson, D. M., “Robust control for the improvement of loudspeaker low-frequency response,” Southeastcon &#39;93 Proceedings, IEEE, 1993;   “Improving Loudspeaker Signal Handling Capability,” Application Note 104, That Corporation, Milford, Mass.;   Locanthi, B. N., “Application of Electric Circuit Analogies to Loudspeaker Design Problems,”  IRE Trans. Audio  PGA-4 (1952), reprinted  J. Audio Eng. Soc ., vol. 19, pps 775-785 (1971);   Newman, Raymond J. “Particular vented box loudspeaker system based on a sixth-order Butterworth response function,”  J. Acoust. Soc. Am., vol.  55, issue S1, April, 1974, pp. S29-30;   Small, Richard H., “Efficiency of Direct-Radiator Loudspeaker Systems,”  J. Audio Eng. Soc ., vol. 19, no. 10, 862-863, November 1971;   Small, Richard H., “Direct Radiator Loudspeaker System Analysis,”  J. Audio Eng. Soc ., vol. 20, no. 5, pp. 383-395;   Small, Richard H., “Vented-Box Loudspeaker Systems—Part 2: Large-Signal Analysis,”  J. Audio Eng. Soc ., vol. 21, no. 6, pp. 438-444, July/August 1973;   Thiele, A. N., “Loudspeakers in Vented Boxes: Parts I and II,”  J. Audio Eng. Soc ., vol. 19 no. 5 May, 1971, pp. 382-392 and no. 6 June, 1971, pp. 471-483; a reprint of  Proc. IRE  (Australia), vol. 22, p. 487-, 1961.   

     BRIEF SUMMARY OF THE INVENTION 
     The present invention addresses the above and other needs by providing electronic signal processing for loudspeakers. The signal processing addresses limitations of both drive unit(s) and their enclosure system. The enclosure systems may range from no enclosure through sealed boxes to vented or ported boxes, including bandpass design loudspeaker-box systems. The invention extends the unaided low-frequency limit of loudspeakers dynamically while staying within excursion limits of drive units and passive radiator(s), and within maximum velocity limits of the air in any port(s). 
     It is an object of the present invention to provide smooth and flat response to substantially lower frequencies than the unaided system for a given sound pressure level, while remaining within the excursion limits of the driver, excursion capability of any passive radiator, and velocity limit of any port. This objective is accomplished by processing a speaker input signal with a dynamic high-pass filter, where the filter varies from under to over-damped as a function of the speaker input signal to smoothly vary the center frequency and Q of the filter with the level magnitude spectrum of the input signal to provide a filtered speaker input signal matched to the capability of the driver. The amplitude response of the high-pass filter is smoothly adjusted by a controlling side chain, as a function of variations in input signal level. The controlling side chain adjusts the amplitude response from an underdamped and peaked response for low-signal levels to an overdamped rolled off response for higher levels. The response of the dynamic filter is utilized combined with the unfiltered response of the loudspeaker, the loudspeaker enclosure, and the effect of any ports or passive radiators, to produce a desired overall frequency response, varying with level. 
     One likely desired response is a flat frequency response, to the lowest frequency possible, for any given drive level over a range of levels, with a tolerance on response. The amplitude response of the dynamic high-pass filter is utilized to obtain the desired frequency response goal, consistent with staying within the capacity of excursion of drivers and possible passive radiators, and air velocity limits of any port. The principal dynamic high-pass filter may be any order above one, because order one (single pole) high-pass filters offer no potential for peaking and thus would not produce a benefit as foreseen by the invention. The frequency response of the high-pass filter is varied with input signal level to maintain flat response to a variable low-frequency limit. The frequency response is controlled to obtain an approximately equal excursion vs. level over a useful range of levels. 
     It is a further object of the present invention to limit the velocity of the air in any port to avoid the extraneous noise commonly called chuffing, and to limit the excursion of any passive radiator(s) to a maximum value consistent with the excursion capability of the radiator. 
     It is a further object of the present invention to equalize the speaker input signal to better match the output capacity of the driver-box vs. frequency. The equalization makes use of the observation that all box types, as well as no box at all, produce significantly more excursion of the driver below the nominal cutoff frequency of the loudspeaker system than above the cutoff frequency, as shown by Small. A separate frequency-band-limiting filter (e.g., low pass filter) is provided in a control side chain which controls the center frequency and Q of the dynamic high-pass filter. Controlling the center frequency and Q of the dynamic high-pass filter controls the level of the frequency content in program material below the nominal system low-frequency limit, which in turn limits the excursion of the loudspeaker drivers. The frequency-band-limiting filter includes a passband in the frequency range below the loudspeaker nominal operating range (i.e., the frequency range where the main driver experiences the most excursion), a transition band at approximately the lower corner frequency of the loudspeaker system, and a stopband at all higher frequencies. The imposition of such frequency-band-limiting filter permits matching the low-frequency bandwidth extension provided by the dynamic high-pass filter to the maximum permissible linear excursion of the driver. 
     For a relatively low-power system, the signal processing described above will extend the bandwidth of the system by boosting lower frequencies with an under-damped high-pass filter constrained to keep the system within excursion limits, and will protect the driver from over-excursion from signals that would normally be considered to be out of band. Higher-powered systems may include at least one additional limiting side chain generating a limiting signal applied after the dynamic high-pass filter in the signal path. The additional side chains provide limits based on the driver excursion, the velocity of air in ports or the excursion of any passive radiators, the onset of audible amplifier clipping, and/or the electrical power causing overheating of the driver. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
       The above and other aspects, features and advantages of the present invention will be more apparent from the following more particular description thereof, presented in conjunction with the following drawings wherein: 
         FIG. 1  is a first system according to the present invention for extending low frequency performance of a loudspeaker. 
         FIG. 2  shows a family of speaker excursion curves at various input signal levels demonstrating excursion limiting according to the present invention. 
         FIG. 3A  is a first portion of a second system according to the present invention for extending low frequency performance of a loudspeaker. 
         FIG. 3B  is a second portion of the second system for extending low frequency performance of a loudspeaker. 
         FIG. 4  is a graph of a limiting function as an excursion limit is approached. 
         FIG. 5  is a first method according to the present invention for extending the low frequency bandwidth of an audio system. 
         FIG. 6  is a second method according to the present invention for extending the low frequency bandwidth of an audio system. 
     
    
    
     Corresponding reference characters indicate corresponding components throughout the several views of the drawings. 
     DETAILED DESCRIPTION OF THE INVENTION 
     The following description is of the best mode presently contemplated for carrying out the invention. This description is not to be taken in a limiting sense, but is made merely for the purpose of describing one or more preferred embodiments of the invention. The scope of the invention should be determined with reference to the claims. 
     A first system  10   a  according to the present invention for extending low frequency performance of a loudspeaker is shown in  FIG. 1 . The system  10   a  includes a dynamic high-pass filter  14  having at least two poles and at least two zeros at the origin (which make it a high-pass filter). The dynamic high-pass filter  14  processes an unfiltered input signal  12  to generate a filtered signal  15  provided as an amplifier input signal to a power amplifier  16 , and power amplifier  16  amplifies the filtered signal  15  to provide a speaker signal  17  to a loudspeaker  18 . The loudspeaker  18  includes a speaker driver  18   a  residing in a speaker enclosure  38  and receiving the speaker signal  17 , and one or more optional passive radiators  21  (or vents) residing on a side of the speaker enclosure  38 . The system  10   a  is generally a relatively low-power system, for example, an approximately one watt to an approximately 20 watt system. 
     The dynamic high-pass filter  14  has a variable frequency and Q controlled by a first side chain  20 . The side chain  20  comprises a first low-pass filter  22 , a full wave rectifier  24 , and a first non-linear transfer function circuit  26 . The input signal  12  is provided to the low-pass filter  22  which processes the input signal  12  to generate a low-pass signal  23 , the full wave rectifier  24  processes the low-pass signal  23  to generate a rectified (or absolute value) signal  25 , and the non-linear transfer function circuit  26  processes the rectified signal  25  to generate a control signal  28  provided to a filter control port  14   a  on the high-pass filter  14 . 
     The low-pass filter  22  has a filter passband from DC up to approximately the lowest speaker resonant frequency of the speaker enclosure  38  and any vent or passive radiator  21 , a steep filter transition band rolling off the filter response around the speaker resonant frequency of the speaker enclosure  38  and any vent or passive radiator  21 , and a filter stopband above the speaker resonant frequency of the speaker enclosure  38  and any vent or passive radiator  21 . By placing the filter transition band of the low-pass filter  22  at approximately the lowest speaker resonant frequency of the speaker enclosure  38  and any vent or passive radiator  21 , any excursion which occurs below the speaker resonant frequency is controlled by the high-pass filter  14  based on the control signal  28  generated by the side chain  20 . 
     The output of the low-pass filter  22  is passed as low-pass signal  23  to the full wave rectifier  24  which computes the absolute value signal  25  of the signal  23  which accounts for both directions of excursion into and out of the speaker enclosure  38  by the loudspeaker driver  18   a . The absolute value signal  25  is passed to the first non-linear transfer function  26 . The transfer function  26  provides the control signal  28  to the dynamic high-pass filter  14  such that the filter  14  is extended to its maximum low-frequency and high Q limit at low levels of the signal  28 , and then above a threshold, to progressively and proportionally adjust the frequency and Q of the dynamic high-pass filter  14  such that approximately equal excursion is reached over a useful range of levels, the excursion set by the maximum limits of the loudspeaker  18 . 
     A family of transducer excursion curves a, b, c, d, and e for various levels of the input signal  12  applied to the system  1   a  (see  FIG. 1 ), are shown in  FIG. 2 . The curves a, b, c, d, and e demonstrate that when the level of the absolute value signal  25  is below a threshold set by the design of the first non-linear transfer function  26 , the maximum speaker excursion, below the principal low-frequency resonance, is kept to a limit and within a small variation over a useful range of levels of the input signal  12 . When the level of the absolute value signal  25  is above the threshold, an increasing control signal  28  is delivered to the control port  14   a  of the dynamic high-pass filter  14  and the filtered signal  15  provided to the loudspeaker  18  is kept to limits which do not cause over-excursion of the loudspeaker below resonance of the vent or passive radiator. 
     Both the frequency and Q of the high-pass filter  14  may be varied by the control signal  28  with the high-pass filter  14  ranging from an underdamped condition to an overdamped condition. The underdamped condition of the high-pass filter  14  is in response to low levels of the control signal  28  and results in a peaked frequency response with a frequency response peak at least somewhat below the primary resonance of loudspeaker driver  18   a , and speaker enclosure  38  with its associated vent or passive radiator. The primary resonance is the frequency of minimum cone motion and maximum vent output. The lower limiting frequency is usually considered to be the frequency at which the response is −10 dB below the in-band sensitivity of the system. 
     The overdamped condition of the high-pass filter  14  is in response to high levels of the control signal  28  and results in the dynamic high-pass filter  14  being overdamped and having a higher center frequency than at low levels of the control signal  28 . The overdamped response results in no peaking of the frequency response curve, and the driver excursion protection is maximized. In the underdamped condition of the high-pass filter  14 , the frequency response of the high-pass filter  14  may be used to extend the bandwidth of the total system typically by ⅓ to 1 octave in range, found as the frequency range extension accomplished by measuring the −3 dB overall system lower frequency limit. By careful control of the frequency and Q of the high-pass filter  14  versus level of the control signal  28 , a flat response within a given target tolerance on response, for example approximately ±1.0 dB, may be accomplished across a range of levels of the control signal  28 . As the level of the control signal  28  increases, the center frequency (which may not be the −3 dB frequency) of the high-pass filter  14  also increases, but is limited to maintain the excursion of the driver  18   a  to be kept within a specified excursion limit, such as x max , or x max +15%. The term x max  is a commonly used descriptor for loudspeaker limiting excursion; the units of x max  are linear dimensions such as millimeters. 
     The low-pass filter  22  produces a delay in the low-pass signal  23 . In order to overcome a resulting insertion delay (i.e., the time difference between the main and side chain paths) in the control signal  28 , and the variation with frequency (group delay) of the side chain low-pass filter  22 , an all-pass filter  13  (see  FIG. 1 ) may be inserted to process the input signal  12  provided to the high-pass filter  14 . The all-pass filter  13  preferably would have the same insertion delay as, and the average group delay of, the low-pass filter  22 . The all-pass filter  13  is preferably inserted in the main signal path between the input of the system  12  (after branching the signal  12  to the side chain  20 ) and before the dynamic high-pass filter  14 . A second all-pass filter (or filters) may also be placed in main channels of a subwoofer-satellite system to maintain equal time of arrival for sound emanating from subwoofer and satellite type systems. 
     A first portion of a second system  10   b  according to the present invention for extending low frequency performance of a loudspeaker is shown in  FIG. 3A  and a second portion of the second system  10   b  is shown in  FIG. 3B . The system  10   b  includes a bass manager  30 , the optional all-pass filter  13 , the dynamic high-pass filter  14 , a limiter  36  serially connected between the dynamic high-pass filter  14  and the power amplifier  16 , and the controlling side chain  20  of the system  10   a  (see  FIG. 1 ). The system  10   b  includes additional limiting side chain loops  60 ,  70 ,  80 , and  90  providing a limiting signal  50  to a limiter  36  located between the dynamic high-pass filter  34  and the power amplifier  16 . Other embodiments of the present invention include at least one of the side chains  60 ,  70 ,  80 , and  90 . 
     The bass manager  30  high-pass filters each of the main channels, for example, channels  12   a  and  12   b  for a two channel system, and outputs them to their respective signal chains. Additionally, the bass manager  30  sums the channels  12   a  and  12   b  and low-pass filters the sum to provide a combined low-passed (or bass) signal  31  to the all-pass filter  13  and to the first side chain  20 . In a conventional system, the combined low-passed signal  31  is sent on directly to a subwoofer amplifier and on to a subwoofer, or directly to a powered subwoofer. In the case of the present invention, the combined low-pass filtered signal  31  may be additionally processed as described herein using the present invention. The optional all-pass filter  13  processes the combined low-passed signal  31  to provide a delayed low-passed signal  33  to the dynamic high-pass filter  14 . The system  10   b  is typically a high-power system, for example, a greater than approximately 20 watt system. 
     In another embodiment, the second system  10   b  may receive a pre-filtered input signal  12  (see  FIG. 1 ) provided to the dynamic high pass filter  14  directly or through the all-pass filter  13 , and to the side chain  20 . In yet another embodiment not employ bass management, multiple implementations of the present invention may be used, channel by channel, in systems employing any number of channels. 
     The first limiting side chain loop  60  receives the filtered signal  15  generated by the dynamic high-pass filter  14 . The object of the first limiting side chain loop  60  is limiting the speaker excursion to prevent the driver  18   a  from degrading or failing due to excessive excursion, and to keep non-linear overload distortion to within reasonable limits. The first limiting side chain loop  60  comprises in-series, a driver(s) excursion predictor  62 , a second full wave rectifier  64 , and a second non-linear transfer function  66 . The excursion predictor circuit  62  is preferably a linear two-port network having a frequency response corresponding proportionally to driver excursion vs. frequency of the loudspeaker  18  comprising the loudspeaker driver  18   a , speaker enclosure  38  and any port(s) or passive radiators employed, such as shown as passive radiator  21 , and generates a predicted excursion signal  63  based on the filtered signal  15 . The rectifier  64  is preferably a peak-type to predict the peak excursion, with appropriate attack and release time constants, and processes the predicted excursion signal  63  to generate a rectified excursion signal  65 . The non-linear transfer function circuit  66  processes the rectified excursion signal  65  to generate a first limiting signal  67  comprising a zero or near zero output for low predicted excursions of the driver  18   a , and proportionally greater output as the predicted excursion limit of the driver  18   a  is approached, causing a limiting effect as graphed in  FIG. 4 . The non-linear transfer function  66  provides the first limiting signal  67  to the combining network  100 . 
     The second limiting side chain loop  70  receives the filtered signal  15  generated by the dynamic high-pass filter  14  and provides a second limiting signal  77  based on predictions of the velocity of air in any port, or of the excursion of a passive radiator  39 . The side chain loop  70  includes a port velocity or passive excursion predictor  72 , a third full wave rectifier  74 , and a third non-linear transfer function  76 . The side chain loop  70  generates a zero or near zero limiting signal  77  for low-level signals, and increases the limiting signal  77  as the port velocity predictions approach velocity limits or passive excursion predictions approach limits of the excursion of the passive radiator. 
     If the speaker enclosure  38  is a vented driver-box system, then the limiting side chain loop  70  comprises the following. The predictor  72  comprises a linear two-port system having one input port and one output port and having a frequency response corresponding proportionally to vent or port air velocity vs. frequency. The predictor  72  thus generates a prediction signal  73  of the vent or port velocity based on the filtered signal  15 . The rectifier  74  is preferably a peak-detecting rectifier having suitable attack and release time constants. The non-linear transfer function  76  produces zero or near zero third rectified signal  75  for a low value of the prediction signal  73 , and rapidly increasing the third rectified signal  75  for higher values of the prediction signal  73  (as a limit of non-turbulent air velocity is approached or exceeded), forming a limiting effect. An example of a maximum port velocity is approximately 35 m/s. The object of limiting the port velocity is to limit extraneous noise called “chuffing.” 
     If the driver-box system  38  includes a passive radiator  21  rather than a vent or port, then the limiting side chain loop  70  comprises the following. The predictor  72  is an excursion versus frequency predictor for the passive radiator, and is preferably a linear two-port having a frequency response corresponding proportionally to the passive radiator excursion vs. frequency. If the loudspeaker  18  employs a combination of one or more ports or passive radiators, then the predictor  72  is an excursion predictor for the worst case of any of the techniques in use versus frequency. The predictor  72  generates the prediction signal  73  based on the filtered signal  15  and provides the prediction signal  73  to the full wave rectifier  74 . The full wave rectifier  74  generates a third rectified signal  75  based on the prediction signal  73  and provides the rectified signal  75  to the non-linear transfer function  76 . 
     In either case, the third non-linear transfer function  76  processes the third rectified signal  75  to generate a second limiting signal  77  provided to the combining network  100 . 
     The side loop  80  limits or prevents audible clipping in the power amplifier  16  by processing the near instantaneous speaker signal  17  generated by the power amplifier  16  and comparing the output voltage of the instantaneous speaker signal  17  to the power supply rails +Vcc  40  and −Vcc  42 . As either voltage +Vcc or −Vcc is approached by the speaker signal  17 , an audible clipping detector  82  produces a detector output signal  83 . An audibility transfer function  84  processes the detector output signal  83  and generates a clipping signal  85  which predicts the occurrence of audible clipping distortion, in other words, the likelihood of the onset audible clipping or the likelihood that the clipping distortion will be audible, based on the detector output signal  83 . The audibility transfer function  84  may include a time constant corresponding to an estimate how long clipping must occur for it to become audible, the percentage of time in clipping, the spectral change resulting from clipping, or other transfer function providing a measure of clipping distortion. 
     The audibility transfer function  84  provides the clipping signal  85  to the fourth non-linear transfer function  86 . The fourth non-linear transfer function  86  follows an input/output curve such as shown in  FIG. 4 . The fourth non-linear transfer function  86  provides the limiting output signal  87  to the combining network  100 . At levels of the signal  85  where distortion remains below audibility, no effect on the control voltage  50  results. As the level where the signal  85  indicates that distortion is on the edge of becoming audible, the limiting output signal  87  of the non-linear transfer function  86  begins to rapidly increase, affecting the control voltage  50  and reducing or rendering audible distortion negligible. 
     The side loop  90  comprises a power limiting circuit including a multiplier  92 , a thermal time constant modeler  94 , and a fifth non-linear transfer function  96 . The electrical power applied to the speaker  18 , when evaluated with multiple concatenated time constants, is a reliable predictor of voice coil temperature. The voice coil temperature is in turn a reliable indicator of one principal kind of stress placed on loudspeaker  18 , namely thermal stress. The multiplier  92  receives the instantaneous speaker signal  17  from the output of the power amplifier  16  and a voltage  43  representing the current through the loudspeaker  18   a  from the top of a low value current-sensing resistor R 1  in series with a ground lead  44  of the loudspeaker  16 . The multiplier  92  generates a multiplied signal  93  proportional to the instantaneous power dissipated in the loudspeaker  16  and is of such a type wherein either polarity of voltage on either input  17  or  43  provides a positive going output. The signal  93  is provided to the thermal time constant modeler  94  which will normally have multiple time constants to mimic the voice coil  18   a  temperature in light of the thermal resistance between the voice coil  18   a  and ambient, the thermal resistance comprising the thermal resistance of the voice coil  18   a , and the transmission of heat to the surroundings of the voice coil  18   a . The thermal time constant modeler  94  generates an estimate of the power consumed by the voice coil  18   a  weighted by appropriate time constants to represent the temperature of the voice coil  18   a  and provides the power estimate  95  to the non-linear transfer function  96  which generates a fifth limiting signal  97  provided to combining network  100 . The non-linear transfer function  96  produces a zero limiting signal  97  for low levels of the power estimate  95 , and produces an increasing limiting signal  97  for power estimates  95  above a threshold, at a rate to limit power to in-turn limit voice coil  18   a  temperature to a maximum of voice coil temperature. The maximum voice coil temperature is selected to be consistent with the dissipation capability of the voice coil and temperature rise of copper or aluminum wire, its insulation, its glue systems, and the integrity of any former on which the voice coil is wound, the glue bond between the former and the cone, and any other involved structures. 
     The combining network  100  combines the outputs of any or all of the four limiting side chains  60 ,  70 ,  80 , and  90  to form a limiting signal  50  provided to the limiter  36  (see  FIG. 3A ). The signals  67 , 77 , 87 , and  97 , or any combination of them, are combined in the combining network  100 , the function of which is to select the highest of any of the signals  67 , 77 , 87 , and  97 , or a weighted combination of the signals  67 , 77 , 87 , and  97 , and supply the resultant limiting signal  50  to a limiter control port  36   a  the limiter  36  located in the signal path after the dynamic high-pass filter  14 . The limiter  36  limits the filtered signal  15  based on the limiting signal  50  to generate a limited amplifier input signal  35  provided to the amplifier  16 . The limiting may be a hard ceiling or may be an “over easy” type of limiting having no effect at low levels, then progressively more limiting effect, then hard limiting. 
     A first method according to the present invention is described in  FIG. 5 . An unfiltered input signal is provided to a dynamic high pass filter of an audio system at step  110 . The unfiltered input signal is also provided to a first side chain of the audio system at step  112 . The unfiltered input signal is provided to a low pass filter to generate a low pass signal at step  114 . A control signal is generated from the low pass signal at step  116 . The control signal is provided to a control port of the dynamic high pass filter at step  118 . The filter parameters of the high pass filter are adjusted based on the control signal at step  120 . The unfiltered input signal is filtered by the dynamic high pass filter to generate a filtered signal at step  122 . The filtered signal is provided to a power amplifier at step  124 . 
     A second method according to the present invention is described in  FIG. 6 . An unfiltered input signal is provided to a dynamic high pass filter of an audio system at step  130 . The unfiltered input signal is also provided to a first side chain of the audio system at step  132 . The unfiltered input signal is provided to a low pass filter in the first side chain to generate a low pass signal at step  134 . A control signal is generated from the low pass signal at step  136 . The control signal is provided to a control port of the dynamic high pass filter at step  138 . The filter parameters of the high pass filter are adjusted based on the control signal at step  140 . The unfiltered input signal is filtered by the dynamic high pass filter to generate a filtered signal at step  142 . Audio system measurements are provided to at least one of a group of side chains at step  144 . Outputs of at least one of the group of side chains are combined to generate a limiting signal at step  146 . The filtered signal is provided to an input of a limiter and the limiting signal is provided to a control port of the limiter at step  148 . The filtered signal is limited based on the limiting signal to generate a limited signal at step  150 . The limited signal is provided to a power amplifier at step  152 . 
     One skilled in the art will understand the foregoing as a description of feedforward control loops, used to predict excursion, power, etc., which are designed using control theory appropriate to such loops, such as scaling functions to make particular voltage or digital representation of voltage correspond proportionally to the effect being measured. Feedforward design may be preferred for its inherent stability, but feedback design through reorganization of the various blocks is clearly possible. 
     While the invention herein disclosed has been described by means of specific embodiments and applications thereof, numerous modifications and variations could be made thereto by those skilled in the art without departing from the scope of the invention set forth in the claims.
Low-frequency bandwidth extension in the form of dynamic electrical equalization may be applied to loudspeakers so long as the excursion capability of their drive units as well as velocity limits of any port(s) or excursion limits of any associated passive radiator(s), and the power limits of the drive units are not exceeded. The bandwidth extension maximizes low-frequency bandwidth dynamically such that excursion is fully utilized over a range of drive levels, without exceeding the excursion limit. Additional limiting control is available for port air velocity or passive radiator excursion, and loudspeaker drive unit electrical power. The system applies to open back, closed box, vented box, and more complex box constructions consisting of combinations of these elements for loudspeaker designs using design parameters appropriate to each system.