ADJUSTABLE BAND GAIN AND BREAK POINT SLOPES AND METHOD OF CONSTRUCTING SAME

Technical Field

jO001| The present in veniion generally relates to loudspeaker systems and more particularly to systems and method of equalizing the frequency response of loudspeaker systems.

Background Art

1000 1 Equalization is a wel l know and widely used process of adjusting the frequency response of a loudspeaker. To "equalize" loudspeaker system is to adjust the amplitude of the audio signal a different frequencies within the system's operating frequency range in order to correct for frequency dependent distortions and anomalies that appear in the f equency response of the system. Distortions in the frequency response can, for example, be introduced by components of the loudspeaker system itself or by the acoustic environment in which the system is used.

Equalization can also be used to adjust the frequency response to achieve a desired audio experience, for example, to create a particular sound for a particular performance at a particular venue.

[0 031 Equalizers are implemented using linear filters that alter the frequency response of the loudspeaker system within specific bands of frequencies. Different filtering techniques have been devised, each providing different capabilities. Standard first order shelving filters are often used for basic treble and bass controls in consumer products.

[000 1 For more sophisticated applications, control is increased by increasing the number of frequency bands that can be manipulated by the user. The more bands the more control. And the more controllable each band is the greater the capability is to fine tune the frequency response. With conventional equalization schemes the gain (cut or boost) within each frequency band gain can be readily controlled. However, this is not true with the shape of the bands at the bands break point frequencies. Each break point will be characterized by a slope, typically specified in terms of dB/ocfave, and the shape of the band can be adjusted by adjusting this slope. The slope will be relatively gradual where lower order filters are used and will become increasingly steep as the order of the filters increases. Control over the shape of the bands would give the operator increased flexibility to fine tune the system's frequency response to achieve desired sonic experiences. However, with conventional equalization schemes, user adjustments to the slope at the frequency break points cannot be made without simultaneously changing the band gain, an unworkable condition in practice. This limits the equalizer's capability to render fine adjustments in the response of an audio system.

Disclosure of Invention

{0005| The invention is directed to improvements in filters used for loudspeaker equalization and to a method of constructing such improved filters. The invention has particular application in multiband equalizers, but could be implemented to construct a single band filter of a single filtering section of a multiband filter. A filter implemented in accordance with the invention allows the user of an equalizer to independently adjust the band gain within a frequency hand and the break point slopes for the frequency band. Iniplemeiited as a multiband filter, the user can. independently adjust the band gain within each .frequency band and the break point slopes for each band of the multiband filter. The filter can be implemented digitally using cascaded digital biquad filters sections as hereinafter described.

{00061 A- fi er ⁿ accordance with the invention is comprised of at least one band filter section comprised an n-order high boost or cut shelving filter having a break point frequency, ω,ι, and an n-order low boost or cut shelving filter having a break point frequency, <¾, wherein ω$ m%. The order, n, of at least one, and preferably both of the shelving filters of the at least one band filter section can be selected for adjusting the slope of the shelving filter at one or both of its break point frequencies. The high and low shelving filters forming the at least one band filter section have substantially the same gain and produce a resultant hand gain for the band filter section. Gain correction means are provided for the selectable n-order high shelving filter and n- order low shelving fiber for correcting the resultant band gain to a base gain level . Such correction means provides a correction factor dependent on the order of the shelving filters selected.

{¾00?] User controlled shelving order selection means allow for setting the order, n, of one or both of the high and low shelving filters making up the at least one band filter section. By selecting the order of the shelving filters making up the band filters, die break point slope at the shelving filter's break point frequency can be adjusted. Additional user control means can be pro vided for adjusting the base gain of the gain corrected band of each band filter section. The gain adjustments and break point slope adjustments can be made independently without one affecting the other.

|OO08j Most suitably, the filter in accordance with the invention is a multiband filter comprised two or more band filter sections, each of which is comprised of at least one of the following; a n- order high boost and cut shelving filters having break point frequency, & and selectable n-order low boost and cut shelving filter having a. break -point frequency, OJ _¾ wherein to¾ < t¾. The order of at least one, and preferably all of the shel ving filters can be selected for adjusting the slope of the shelving filter at the break point frequency. The selectable high and/or low shelving filters forming an one band filter section have substantially the same gain and produce a resultant band gain for the band filter section. Gain correction means are provided for each selectable n- order high shelving filter and n-order low shelvmg filter for correcting the resultant band gain to a base gain level. Such correction means provides a correction factor dependent on the order of the shelving filters selected.

[0 09| User controlled shelving order selection means allow for setting the order, n, of one or both of the high and low shelving filters making up each band section. By selecting th order of the shelving filters making up an one of the band filters of the multiband filter, the break point slope at the shelving filter's break point frequency can be adjusted. Additional user control means can be provided for adjusting the base gain of the gain corrected band of each band filter section. The gain adjustments and break point slope adjustments can be made independently without one affecting the other.

|001(l| Break point slopes can be user adjusted by switching between available n-order boost and cut shelving filters making up each band filter section. For example, selectable n-order high and low shelving filters can be provided for n ^::: T (first order filter), n ^:::: 2 (second order filter), tv ^:: 3 (third order filter), etc. These selectabie n-order filters would provide for selectabie break point slopes of 6dB/octave, 12dB/ octave, 1 SdB/octave, etc. The band could be symmetric (the selected break point slopes are the same) or asymmetric (the selected break point slopes are different. Also, by setting the gains of adjacent bands to the same setting a breakpoint can be eliminated. In this case the adj cent equalization band would combine into a sin le wider band, whose breakpoint slopes could be adjusted. ((OOOO ^'' 11 11 || I inn a annootthheerr aassppeecctt ooff tthhee i innvveennttiioonn,, aa mmeetthhoodd o off c coonnssttrruuccttiinngg nn--oorrddeerr hhiigghh aanndd l looww sshheellvviinngg ffiilltteerrss ffoorr aa mmuullttiibbaanndd fifilltteerr hhaavviinngg ddeessiirreedd bbrreeaakk ppooiinntt ffrreeqquueenncciieess i iss pprroovviiddeedd ffoorr d diiffffeerreenntt v vaalluueess ooff n n.. T Thhee mmeetthhoodd iinnvvoollvveess cchhoooossiinngg aass aa b baassiicc b buuiillddiinngg bblloocckk aa fi firrsstt oorrddeerr ((nn~~ 11 )) f frreeqquueennccyy--nnoorrmmaalliizzeedd s shheellvviinngg f fiilltteerr f foorr p prroovviiddiinngg a a bbaassiicc s shheellvviinngg s shhaappee a anndd g gaaiinn l leevveell..

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(001 1 Fig. 1 is a block diagram of two cascaded high and Sow shelving filters for a multiband filter in accordance with the invention showing a gain correction factor (l gain) in line with the shelving filters.

[0015 j Fig, 2 A is a graph of a frequency response curve for a first order low boost gain shelving filter such as forms the basic building block of a multiband filter in accordance with the invention,

J0016J Fig. 2B is an s-plane representation of the poles and zeros therefor, with the frequency normalized ιο ω 1.

f00i 7| Fig. 3A is a s-plane .representation of the poles for a general second order Butterwoith low-pass filter.

[00181 Fig. 3B is another s-plane representation of the poles therefor with the zeros added to the s-plane outside of and in line the poles and the origi of the s-plane for produci ng a gain corrected second order low shelving filter.

[001 1 ig- 3C is graph of the -frequency response curve therefor.

[00201 Fig. 3D is an s-plane representation for the second order filter as shown in Fig. 3.B, showing the distance to the poles as compared to the distance to the zeros.

00211 tg. 4A is an s-plane representati n of the poles for a general third order Butierworth low-pass filter,

[00221 Fig. 4B is another s-plane representation thereof with the zeros added to the s-plane which are coincident with the three poles of the third order filter.

[0Q23J Fig. 4C is further s-plane representation thereof with the added zeros moved outside of the poles but kept in-line with the poles and the origin of the s-plane.

[00241 Fig. 5 A is an s-plane representation of the poies for a general forth order Butterworth low-pass filter.

[0025] Fig. SB is another s-plane representation of the poles therefor with the zeros added to the s-plane outside of and in-line with the poies and the origin of the s-plane for producing a gain corrected fourth order low shelving filter,

[00261 Fig. 6A is a frequency response curve for an n-order low shelving filter with a boost gain of 6 dB. (00271 Fig. 6B is a frequency response curve for an n-order high shelving filter with a boost gain of 6 dB.

(0028J Fig. 6C is the frequency response curve of a pass-hand filter comprised of cascaded reorder Sow and high shelving filters having the responses shown in Figs. 6A and όΒ„ which produce the desired frequency response, but before gain correction.

(00291 Fig- 6D is the frequency response curve thereof after gain correction,

J0030J Fig. 7 is the frequency response curve and phase response of a pass-band filter comprised of cascaded low and high shel ving filters of different orders for producing an asymmetric band filter.

{0031 | Fig. 8 is a graphical representation of a multiple gain bands and breakpoints with adjustable breakpoint slopes that can be produced with a roultiband filter nmltiband filter in accordance with the in ention.

(0032 _. 1 Fig. 9 is a block diagram of a biquad implementation of an exemplary multiband filter in accordance with the invention made up of two sections, each of which has an n-order high and low shelving filter, where the order of the shelving filter is selectable.

(00331 Fig. 1 OA- 1 OH provide tables of coefficients that can be used in the transfer functions for the biquads for different implementations of each shelving filter shown in the block diagram in Fig. 9.

(00341 Fig. 1 1 is an exemplary user interface for an operator of a processor having a nmltiband filter in accordance with the invention

^jl -Dg^ giiQO

(0035 _. 1 Filters in accordance with the invention will generally be employed in equalization systems for adjusting the frequency response of a loudspeaker system. The invention involves different combinations of standard first order shelving filters and non-standard higher order shelving filters. The architecture of the resulting filters can be used to transform the filter architecture of current audio control systems into digital biquad sections, resulting in expanded filtering capabilities, including the ability to shape frequency response at break point frequencies of a multiband system.

(00361 As used herein, band filter will be understood to include a band filter and a band filter, in the band filter described herein the amount of boost or cut for the band is adjustable. (00371 Fig. 1 illustrates in block diagram form the most basic implementation of a filter in accordance with the invention in a single band filter section 11 comprise of a hi h boost or cot shelving filter 13 having a break point frequency, and an low boost or cut shelving filter 15 having a break point frequency, where c i < «¾. As hereafter described, the order of the high and low shelving filters can be separately adjusted to adjust the slope of the filters at the shelving filters breakpoint frequencies a>j and <¾, Gain correction, denoted by block 17 is provided for adjusting the boost or cut gain of the band filter section independently of slope adjusiment at the breakpoints of the hi -pass and low shelving filters. With this basic implementation in mind the principles of the basic and higher order shelving filters used i the invention are now described. Basic Shelving ilter

(00381 First is noted the user requirements for a multiband equalization will require asymmetric band filters. Building such filters can be accomplished using different combinations of standard first order and non-standard high order shelving filters. Using such shelving filters as building blocks, filter architectures can be created which can be transformed into digital hiquad sections that are flexible and can be cascaded to provide adjustment controls contemplated, by the invention.

{0039J First, the basic building block of the filters of the invention needs to be defined. That is, the low boost shelving filter. From this basic building block all the derivations for low-pass and boost gain ftequency-normalized prototypes ( ω - 1 ) can be obtained. Later the low-pass to high-pass and boost to cut transforms from thi prototype will be derived.

|004(IJ A basic first order low boost-gain frequency-normalized shel ving filter is a well-known filter, and is given, in the analog domain, by;

Where Go is a gain parameter which determines the amplification at ώ ^:::: 0.

100411 By substituting ω for 6 in the above transfer function, it can be seen how the parameter Go, that is, the desired gain at DC, determines the position of the zero. When ω - 0 _S the transfer function becomes:

The frequency response for this shelving filter is shown in Fig. 2 A. The s-plane representation of the poles and zeros of the filter are shown in Fig. 2B, where the zero is seen to be on a straight line from the origin, namely, on the real axis.

Higher Order Shelving Filters

(0042J In order to construct higher order shel ving filters, one starts from a general Botterworth low-pass filter and then just add complex zeros to the complex poles in order to stop the monotomc attenuation at the desired points. For example, for a second order shelving filter, one starts with a Botterworth second ord

The■s-plane representation of the poles and zeros of this second order fi lter are shown in Fig. 3A, Adding zeros to above transfer function yields the following:

·. ·' ^■ .. < " . ■>

i> :.·. ^* " T . _; ; $ ^' -†" .·..

If as depicted in s-plane representation in. Fig. 3B, the zeroes are added on straight lines from the origin, the frequency response in Fig. 3C can be achieved.

|6043| But now there are complex poles and zeros whic need to be taken into account, and thus the relationshi between the position of the zeros and the desired gain need to be obtained. This relationship can be obtained with a useful trick; The magnitude of the s function for any given frequency ω can be obtained by just measuring the distance from poles and zeros to the ω points of the /cy axis. The magnitude of the

Where dpn is the distance from 'pole n ' to the o points at the &> axis and ckn is the distance from 'zero n' to the to points at the / ^' co axis, in the second order shelving filter example, the magnitude at r-=0 will be the product of the distances from all zeros to the point (0,0) divided by the product of the distance from all poles to the point. (0,0). This is illustrated in the s-plane representation for the second order filter shown in Fig. 3D. (00441 The above trick can be used to obtain the relation between the gain parameter Go and the position of the zeros. As illustrated in Fig. 3D, the poles all fall on a unit circle, so distance to ail of the poles are equal to one. At ω~0 ₅ one wants to obtain a desired gain. The gain parameter can be obtained from the following equation;

As the distance to the point (0,0) is the same for both zeros, one can get the position of the zeros related with the desired gain parameter:

S½ ^™ ½

{004SJ The relation of die zeros to the desired gain can now be substituted for the zeros of the second order equation. First the zeros can be put into rectangular form to make it easier to operate on them geometrically. One starts by putting the zeros at the same position than the poles:

The roots of th equation are

Then, to move the zeros in a straight line, one just needs to multiply their real and imaginary components by the obtained parameter, which is related with the desired amplification at ©-0:

By multiplying again the zeros, one gets the second order equation that he or she is looking for: The final second order shel ving equati

[9046J The same technique can now be used to obtain third and fourth order shelving filters. For third order .filter, the low pass Butterwoith prototype, split .in second order sections, is:

!. I

S 4· I 4- he three poles of this transfer function are

The s-plane representation of this poles is shown in Fig. 4A.

[0047J By using the same approach, zeros can be placed at the same position as the poles:

, _; > 4· I > · ^; 4 s 4 I

The resulting s-plane representatio is shown in Fig. 4B.

| 048| And now the desired gain can b related to the distance to all zeros by moving the zeros in a straight line from the origin (0,0) as illustrated in Fig. AC. By moving the zeros in this .fashion the shape of the shelving filter can by maintained. Again, all of the poles fall on a unit circle, but now there are three poles and three zeros. The relation for associating the distances to mm control will then be;

The distance to the point (0,0) is again the same for the three zeros, so the relation of the gain control parameter at DC in relation to the zero position, will be

[004 1 If that parameter is inc luded to control the zero's posi tion in the above third order equation, by using the sa geometric approach than w s done for the second order filter:

By getting again the s equations, on finally obtains:

... * ί ™ 4 ;¾ 4

[0050] Following the same steps to obtain the fourth, order filter, the low pass Butterworth prototype, split in sec

The s-p!ane representation of this ^' transfer itmction is shown m Fig. 5 A, which shows four poles. Adding four zeros and adhering to the requirement that, the zeros fail on a straight line passing through the origin results in an s-plane representation as shown in Fig. 5B.

j ^' OOSlj Therefore the relation of the position of the zeros with the DC amplification parameter will be given by:

Once again, The distance to the point (0,0) is again the same for the four zeros, so the relation of the gain control parameter at DC in relation to the zero position will be;

{00S2J The following transfer unction for the fourth order shelving filter prototype is finally obtained by putting the complex zeros in rectangular form, by introducing the obtained gain parameter and again by obtaining the second order functions in s domain as described above;

Any higher order filters can be obtained by following the same approach.

Boost to C ut Transform

| 053| All. the obtained filters have their cutoff normalized frequency at o c ^:::: 1. only in the case of boosting the gain at DC (GO >1), if cutting gain is desired with the above equations (i.e GO < I ) (o is moved to lower frequencies, in order to keep a symmetric frequency response for boost and cut, the transfer function needs to be inverted in the case of cut by swapping the poles and the zeros. Also, G _¾ needs to be replaced by I/Go by again using the distances to poles and zeros trick to get the magnitude response. When cut is desired. o is always less than 1.

Low to High Transform

[0054} All the filters obtained in the manner discussed above are low pass prototypes, in order to obtain the equivalent high pass filters, a low-pass to high-pass transformation must be done. The low-pass to high-pass transformation, is obtained by just substituting i/s for Λ\ For example, by making this substitution the -transfer function of a boost first order high-pass filter becomes:

The same transformation must be applied to all other equations for boost and cat. fi lters in order to obtain the high-pass filter prototypes.

Asymmetric Band Filters

100551 *n practical applications, asymmetric band filters are needed. Such asymmetric filters can be obtained from the above described building blocks.

{0056 Starting with the boost example, the band filter can be easily created by connecting in series a high and a Sow shelving filter with the sam boost gain. The frequency response of the low shelving filter is shown in Fig. 6A and frequency response of the high is shown in Fig. 6B. it is noted that the cutoff or break frequency for the low pass must be higher than the cutoff frequency for the high filter. The frequency response of the series (or cascaded) connected (or cascaded) is shown in Fig. 6C. in Fig. 6 A it is seen thai the cutoff frequenc to for the high shel ving filter is lOO ; in Fig. 68 it is seen that the cutoff frequency o¾ for the low shel ving filter is 8000Hz. These cutoff frequencies become the breakpoint frequencies of the pass-pass filter created by the two shelving filters as seen in Fig. 6C.

{0057) To achieve the desired gain form the band filter created in this manner will require gain adjustment. More specifically, the convolution of the series connected high and low shelving filters leads to a total gain in the band, and also out of the band. Generally, the desired gain will be the gain of the original high and low shelving filters. However, w ithout corrections the gain of the cascaded filters will be the square of the gain of the original filters as seen in Fig. 6C, where the original filters provide gain of 6db and the cascaded filters provide a gai of 12 db. (This occurs because the filters are cascaded and the gain of each shelving filter is mul tiplied in the frequency domain.) To obtain the desired gain, a gain correction factor, i/gain, can be added in series with the high and low filters. Providing such a. correction factor to the cascaded shelving filters having a frequency respond as shown in Fig. 6C will, result in. the frequency shown in Fig. 6D, the ban gain has been corrected back to 6db. The simple implementation of such gain corrected pass-band filter just described is shown in the earlier described block diagram in Fig, 1 . Using this simple structure, a band filter can he created with different higher order shelving filters to achieve different slopes at the two cutoff frequencies toi and c¾ of the composite band. And the slope at ωι can be different for the slope- at «¾ to create an asymmetric- band. An example of a frequency and phase response for an asymmetric pass-band filter is shown Fig. 7, wherein f 1 === 125 Hz, step! (slope) == 18 dB/Octive, £2 4000 Hz, step2 ^::::

6dB/Octive, and wherein the gain - 6,

|0058| The above-described building blocks for filters in accordance wit the invention can implemented using biquads. The biquad coefficients A to F are the analog second order section prototypes, and a complete bilinear transform is applied to each second order section in order to get the digital filter. Therefore, every pass-band region can be created with just 4 biquads, allowing independent step selections of 6 dB/octive to 24 dB/octive.

[0059] Fig. 8 graphically illustrates multiple gam bands and break points that can be produced by a rauitiband filter in accordance with the invention, and specifically shows five gain ands and fou frequency breakpoints. The slopes of each, of the breakpoints can. be independently adjusted by selecting the order of the shelving filter associated w ith the breakpoint. For example, selectable order of the shelving filter could be .1 ^sl order. 2 ^nd order ....up through an eighth order high and low shelving filters. The filters would be boost or cut filters as required. A gain band be bypassed by setting the gains on the left and right of the band to the same gain. |0O6(i | Fig. 9 illustrates a filter in accordance with the invention comprised of two sections. Each section is associated with a gain band and is comprised of a high shelving filter, a low shelving filter and gain correction for each of these shelving filter. Each shelving filter is associated with a break point frequency and is implemented by cascaded biquads characterized by transfer functions. The coefficients of transfer function for each hiquard can be altered to establish the desired property of the shelving filter, such as the order of the filter and whether it has a boost or cut gain charcteristic.

( 0611 More specifically, the illustrated filter, generally denoted by the numeral 101, has a first section 103 and second section 105. The first section has a high shelving filter portion 1.07 having a first break point frequency (break point 1} implemented by biquad blocks i 1. 1, 1 33, 1.15, .1 17, and a low shelving filter portion 109 connected, is series to the high shelving filter portion. The low shelving filter portion 109 has a second breakpoint frequency (break point 2) and is implemented by biquad blocks 1 19, 12 ! , 123, 125, The second section is connected in series to the first section and is comprised of a high shelving filter portion 127 having a third break point frequency (break point 3) implemented by fewer biquad blocks .131 , 133, and low shelving filter portion 129 connected is series to the high shelving filter portion 1 7. The low shelving filter portion 129 has a fourth breakpoint frequency (break point 4) and is implemented by the two biquad bloeks 135, 137,

(00621 Gain correction for each of the shelving filters is provided by the series connected gain correction block 139, 141 , 143, 145, associated , respectively, with shelving filters 107, 109, 127, and 129.

|0 63| Each of the biquads blocks for each of the shelving filters illustrated in Fig. 9 has a transfer function as indicated in each block. And the several transfer functions for the shelving filter have coefficients A, B, .. X in the case of filter section 1 , and coefficients A, B, ... X in the case of filter section 2. By manipulating these coefficients, the charac teristics of each filter section can be set and adjusted. In particular they can be set and adjusted so that the high and low shelving filters making up each filter section can be configured into selectable n-order boost or cut shelving filters, where n ranges f om 1. to 8.

{00641 Fi s 10A-10H provide in table form different combinations of coefficients for

establ ishing a range of different fil ter characteristics, including the slope in the f equency response at each of the breakpoint frequencies of the filter architecture shown in Fig, 9. Fig. I0A shows the coefficients needed for break point 1 (produced by a high shelving filter ) for the boost case for 8 different selectable slopes (slopes 1 -8), wherein slope I results from a first order high shelving filter, slope 2 results from a second order high shelving filter, etc, up to the eighth order shelving filter (slope 8). Fig. 0B shows the coefficients needed for breakpoint I for the cut case for 8 different selectable slopes (again slopes 1-8).

{0 651 Figs. 10C and 10D similarly show the coefficients for the boost and cut cases for break point 2 (produced by a low shelving filter) for 8 different selectable slopes.

(0066| Figs. 10E and 10F show the coefficients needed for break point 3 (produced by a high shelving filter) for the boost and cut cases for four different slopes. It is noted that the reduced number of a vailable slopes in this case is due to the reduced number of biquad sections used to implement the shelving filters in this second filter section. Figs. 10G and I OH show the coefficients needed for break point 4 (produced by a low shelving filter) for boost and cut cases, again for four different slopes. (00671 Seleciiott of the slopes for each break point of die filter gain bands along with gain adjustments within each gain band can be user adjusted through a programmed digital computer haviiMi a user interface such as shown in Fiou 1 1 ,

[0068] While an implementation of the invention has been described in considerable detail in the foregoing specification and accompanying drawings, it is not intended that the invention, be limited to such detail except as necessitated by the following claims.