Coates Dallas) ABSTRACT automatic loudspeaker equalization (ALE)

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STARTER GUIDE
Coates Dallas) ABSTRACT
automatic loudspeaker equalization (ALE) program supports following Texas Instruments digital audio processors TAS3001 TAS3002 TAS3004 TAS3103
Digital Audio Solutions
This application note addresses developing application-specific coefficients TAS3103 digital audio processor. TAS3103 digital audio processor three-channel audio processor. Many audio processing features provided TAS3103, including sixteen biquad filters channel speaker equalization Loudness compensation unique each channel Dynamic range compression expansion
automatic loudspeaker equalization (ALE) program provides user-friendly environment which fully capability TAS3103 given application. Specifically, provides ability Develop equalization filters Specifying filter type(s) parameters Specifying desired speaker response given measured speaker response Tailor loudness compensation achieve specified audio presentation dynamic range parameters
This application note consists three major sections, with each section addressing three previously listed capabilities.
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Contents
Initial Setup Steps Filter Coefficient Generation Manual Filter Generation.5 Graphic Filter Generation Equalization Filter Generation Dynamic Range Compressor (DRC) Coefficient Generation Overview.17 Parameter Specification Computation.18 Threshold Settings Compression Expansion Settings.19 Offset Settings Transfer Function Plot Transfer Function File.20 Loudness Compensation Filter Design Loudness Compensation Transfer Function Loudness Biquad Filter Transfer Function.23 Using Specify Design Loudness Compensation Transfer Function.25 Specifying H(z) Using Predetermined Biquad Coefficients Specifying H(z) Using (Bell-Shaped) Filters.29 Specifying H(z) Using Bass Shelf Filters Specifying H(z) Using Treble Shelf Filters.31 Specifying H'(z) (The Loudness Biquad Filter) Using Predetermined Biquad Coefficients Loudness Compensation Volume Command
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Figures
Figure Automatic Loudspeaker Equalizer Figure Edit Filters Panel Figure Graphically-Created Desired Response Curve Figure Create Response Curve Panel Figure Edit Master Points Panel. Figure Resultant Response Graphic Filter Design Example Figure Edit TAS3xxx Data Panel Figure Filter File: Starter_Example_01.EQ310X. Figure Speaker Response Example Curve6.raw Figure Speaker Response Curve6.raw After Smoothing Figure Desired Response Overlaid Onto Smoothed Speaker Response Figure Desired Response Curve After Manual Alteration Tolerance Bands Figure Filter Design Settings Panel Figure Computed Filter Response Figure Filters Comprising Computed Filter Response Figure Filter File: Starter_Example_02.EQ310X Figure Dynamic Range Compression Figure Example Dependence Input Signal Level Channel Gain Figure File: Starter_Example_02.DR310X Figure Device Configuration Tool (DCT) Panel Figure TAS3103 Loudness Processing Block Figure Biquad Filter Transfer Function Derivation Figure Create Loudness Filter Panel Figure Base Type Coefficients Loudness Panel Figure Loudness Compensation Transfer Function H(z) Coefficients Entered Directly Figure Loudness Compensation File Predetermined H(z) Coefficients Figure Base Type Loudness Panel Figure Bass Base Type Loudness Panel Figure Loudness Compensation Transfer Function H(z) Created Using Bass Filter Figure Treble Base Type Loudness Panel Figure Loudness Compensation Transfer Function H(z) Created Using Treble Filter Figure Loudness Coefficients Loudness Panel Figure Loudness Compensation Transfer Function H(z) Created Using Loudness Coefficients Figure Programming Parameters f(volume_setting) Figure Loudness Compensation Plots Commanded Volume Output
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Initial Setup Steps
software package provided with every TAS3103EVM, also available users wish purchase TAS3103EVM. Requests package alone also sent digitalaudio@ti.com, along with descriptions intended use. first step using software package unzip install Upon opening installed package, shown Figure appears. This only applies when using create equalization (EQ) filter coefficients default GUI. other GUIs accessed generating dynamic range compression coefficients generating loudness compensation filter coefficients.
Create Desired Response Curve
Replace Section Curve Graphically
Copy Master Points from Curves Edit Grid
Generate Curves from Master Points Edit Grid
Sample Curve
Smooth Curve
Draw Filters
Stop Calculation
Figure Automatic Loudspeaker Equalizer
first step that needs taken using click Device button select TAS3100. Next, sample rate application being address needs set. This done clicking View button selecting Settings. Frequency Limits should come does not, select Frequency Limits panel that comes default setting Sampling Frequency seen 44100 (44.1 KHz). this correct, enter correct value click button. sample rate properly set.
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Filter Coefficient Generation
Manual Filter Generation
generate filter, click Edit button select Edit Filter Parameters. panel shown Figure results.
Figure Edit Filter Parameters Panel
Butterworth-1HP Butterworth-1LP single-pole Butterworth high-pass low-pass filters. Butterworth-2HP Butterworth-2LP two-pole order) Butterworth high-pass low-pass filters. High Pass-LR Pass-LR Linkwitz-Riley high-pass low-pass filters commonly used building audio cross-over filters. programmed frequency these filters frequency rather than standard frequency. plateau filter gain frequencies above upper band edge, peaks selected gain between upper lower band edges, exhibits single-pole roll below lower band edge. high plateau filter gain frequencies below lower band edge, peaks selected gain between upper lower band edges, exhibits single-pole roll above upper band edge. VARi high Vari filters order low-pass highpass filters with selectable peaking selected 3-dB frequency. allpass filter second-order unity-gain filter with monotonically decreasing phase over frequency band specified. filter bell-shaped filter with gain outside programmed bandwidth, peak gain specified within specified bandwidth. notch filter order notch filter. treble shelf bass shelf standard order shelf filters. frequency treble shelf filters frequency with respect response frequencies above frequency. frequency bass shelf filters frequency with respect response frequencies below frequency. Chebyshev-1HP Chebyshev-1LP filters order Type-I Chebyshev high-pass low-pass filters (the this case references type Chebyshev filter rather than order filter). Once filter type selected specified clicking appropriate entering required parameters), clicking Draw Filters button generates filter's response. response meets requirements, Edit button select Generate TAS3xxx Data generate biquad coefficients required implement specified response. Going Edit button selecting
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Edit TAS3xxx Data displays values generated biquad coefficients, provides means manually editing coefficient file needed. Additional filters specified cascaded with filters previously selected specified returning Edit Filters panel, selecting another filter type, entering parameters. Clicking Draw Filters button places specified filter cascade with filters defining response currently displayed, generate composite response. save composite response, Edit button select Generate TAS3xxx Data. more filters, repeat Edit Filters Draw Filters sequence until response required obtained. given filter addition does produce response desired, eliminated going Edit Filters panel, highlighting filter eliminated, clicking right button mouse, clicking Confirm Filter Deletion panel that appears. results, having eliminated filter, click again Draw Filters button. displayed response response desired, TAS3103 coefficients implementing this response need generated then saved. Clicking Edit button selecting Generate TAS3xxx Data generates coefficients. generated data then saved file clicking File button selecting Save TAS3xxx Program Data. file name directory selected, file extension must remain EQ310X. Retaining this extension makes file compatible with TAS3103 DAS-DCT GUI, from this GUI, filter downloaded into TAS3103 chip. There confusion over differences roles Save TAS3xxx Program Data"and Generate TAS3xxx Data. When first opened filter suite created, clicking Save TAS3xxx Program Data both generates saves filter coefficient set. Ever after, however, Generate TAS3xxx Data must selected before Save TAS3xxx Program Data selected order save latest changes previously generated filter suite save newly generated filter set.
Graphic Filter Generation
also provides ability draw required response, then derive filter coefficients required attain drawn response. bell-shaped filters used exclusively when deriving filters implement drawn responses). this feature, first necessary File button select Open Response File. Files with both .txt extensions .raw extensions used specify response, long they have structure shown below. Data column magnitude response frequency specified. 12.20703, 24.41406, 36.62109, 48.82813, 61.03516, Data -39.43244 -39.74691 -40.19416 -40.70994 -41.2616
these files input speaker response curves. previously recorded speaker response input into using Open Response File selecting desired response. user then draws desired speaker. Having drawn desired speaker response, then commanded generate filter that implements drawn filter response with respect response reference. (The desired response also input file. This option discussed next section). begin construction graphically-specified filter response, response must first input. When filters created implement specified drawn response, they created provide specified response given selected response starting point. illustrate this process, example presented. start, File button, select Open Response File, then select zerodb.txt. This selection results reference response (shown straight blue line). Next necessary draw filter response desired. draw filter response, click Create Desired Response Curve button. Place mouse desired start point draw straight-line segments create filter response desired. When done, click Create Desired Response Curve button
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again. This causes magenta boundary lines drawn. These lines define excursions allowable generating filter response from desired response drawn. example response graphically created shown Figure includes blue response curve.
Figure Graphically-Created Desired Response Curve
mistake made drawing desired response, clicking Create Desired Response Curve button third time will bring window shown Figure Selecting deletes drawn desired response curve.
Figure Create Response Curve Panel
graphically created response also saved desired response file clicking File button selecting Save Desired Response. file name directory which store file specified, important maintain extension .crv. .crv files illustrated next section. Once drawn, transferring points describing desired response into computation grid enables manual refinements made drawn desired response. This transfer accomplished clicking Copy Master Points From Curves Edit Grid button. panel shown Figure comes
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Figure Edit Master Points Panel
This panel shows frequency amplitude Master inflection points drawn response curve. These Master points edited manually. example, amplitude point changed from 4.928685 9.0. Master points also deleted added. delete Master point, simply right-mouse click Master point deleted then click button Confirm Master Point Deletion panel. Master points added going empty Edit Master Points panel (the with Point column) typing frequency amplitude point added. time change manually made Master points, Offset Upper button Offset Lower button must clicked apply upper lower tolerances revised Master points. Edit Master Points panel also used manually change upper lower range tolerance curves. Changing tolerance range values manually accomplished entering revised tolerance range value clicking appropriate Upper Tolerance Lower Tolerance buttons. Upper Tolerance Lower Tolerance tabs Edit Master Points panel, other hand, used when desired change tolerance level setting given individual Master point. observe effect manual adjustments drawn response, Generate Curves from Master Points Edit Grid button must activated. save adjustments made drawn response, click File button select Save Desired Response. drawn desired response curve tolerance curves also graphically edited. graphically edit drawn response curve tolerance curve, click Replace Section Curve Graphically button. Then place cursor section curve modified drag mouse draw modified shape. Note that this time shape drawn follows path mouse, restricted straight-line segments. Terminate curve modification releasing mouse point response tolerance curve. start stop points graphic modification must always original curve. Once response curve tolerance curves required, clicking Calculate button selecting Modified Response generates filters. (Several filters required attain desired response. Modified Response Pause selection stops process after each filter added, requiring user click button Continue Calculation panel that comes between filter calculations, continue process). While filters being derived, Stop Calculation button third button from right becomes red. This important feature computation process
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require minutes complete, light only indication that program computationally active. filters being calculated current modified response curve appears prior modified response curve appears yellow. Clicking Stop Calculation stops calculation retains those filters completed point program stopped. resultant graphic filter design drawn filter response example depicted previously shown Figure
Figure Resultant Response Graphic Filter Design Example
Once filter calculated, derive biquad coefficients resultant response necessary first click Edit button select Copy Generated Filters Edit Grid. This results automatically generated filters appearing Edit Filters panel, shown Figure biquad coefficients these filters cannot generated until filters reside Edit Filters panel. Once Edit Filters panel, manual modifications made, clicking Edit button selecting Generate TAS3xxx Data generates biquad coefficients. Edit TAS3xxx Data panel shown Figure appears. Application specific data, such Speaker Model Speaker Serial etc. entered this panel, biquad coefficients generated manually modified typing changes.
Figure Edit TAS3xxx Data Panel
Clicking File button selecting Save TAS3xxx Program Data creates file containing filter coefficients, along with application specific data. directory store file
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file name selected, file extension must remain .EQ310X. content .EQ301X file example illustrated presented Figure seen, this example results generation three biquad filters, each filter labeled heading (Q1, Q3). When TAS3103 retrieves this file discards information, replaces number sub-address (x##), downloads coefficients into specified TAS3103 filter bank.
NAME: A:\Starter_Example_01.EQ310X Date 12/27/02 Speaker Model Starter_Guide_Speaker Speaker Serial Starter_Guide_Serial Speaker Manufacturer: Starter_Guide_Manufacturer Sample Rate Description Starter_Guide_EQr Filter Parameters EQ-1, 5.149749, 2006.389480, 309.887964, Yes, EQ-2, -5.204320, 14088.737454, 13022.071425, Yes, EQ-3, -4.825576, 1575.456844, 22050.000000, Yes, Channel Number
Figure Filter File: Starter_Example_01.EQ310X
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Equalization Filter Generation
This section addresses using create equalization filters. doing many other features will described including logarithmic sampling, sample smoothing, frequency boundary manipulation, tolerance boundary manipulation, previous example, Response file zerodb.txt reference response shown straight blue line. This choice allowed drawn response response filter generated. Another Response file provide means generating equalization filters directly from response curves speakers. this, Response file response curves speakers, drawn response desired speaker response. this case, creates suite filters transform speaker response from raw, unprocessed response drawn, desired, response. And, addition being able specify desired speaker response drawing desired response, desired speaker response also specified inputting Desired Response file .crv file. illustrate process, speaker response curve6.raw imported into going File button, selecting Open Response File, clicking curve6.raw. This curve represents response speaker equalized, shown Figure
Figure Speaker Response Example Curve6.raw
points that comprise curve6.raw linearly placed frequency. first task convert point placement logarithmic grid improve efficiency computation process. many applications improvement processing time significant, attained with compromise quality equalization process). convert response curve logarithmic grid, click Sample Curve button, enter desired number logarithmically sampled points (300 typically used), then click contend with sharp discontinuities Response curve while generating filter suite required deliver desired response, excessive computation time excessive number generated filters results. combat this problem, smoothing function provided smooth shape response curve prior initiating computation process. Eliminating sharp discontinuities response curve notably improves calculation time filter count, little effect overall effectiveness resulting suite equalization filters. smoothing process applied simply clicking Smooth Curve button. Figure shows response curve that results after
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clicking Smooth Curve button four times. Note that sharp discontinuities have been eliminated.
Figure Speaker Response Curve6.raw After Smoothing
Next desired filter response imported going File button, selecting Open Desired Response File, and, this example, selecting desired_app_note.crv. [.crv files must generated within program drawing editing required) desired response, then saving desired response going File button selecting Save Desired Response, being sure maintain .crv extension.] resulting graphic shown Figure blue graph response, black graph desired response, magenta graphs tolerance bounds about desired response.
Figure Desired Response Overlaid Onto Smoothed Speaker Response
seen, this example tolerance bound computational stress points calculating filters bring response desired response within tolerance specified tolerance band occur steep slopes desired response curve. tolerance bands relieved these sections desired response, both calculation time generated filter count reduced. modify tolerance bands manually, first click Replace Section Curve Graphically button. Then click ends section upper lower tolerance band manually modified, drag mouse shape curve desired, being sure complete dragging mouse tolerance band other section being modified. Figure shows results
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manually modifying tolerance bands bounding steep slopes desired response curve which frequency sections KHz.
Figure Desired Response Curve After Manual Alteration Tolerance Bands
more modification made before generating equalization filters. equalization process need extend down default lower frequency bound upper frequency bound (Nyquist frequency). Adjusting frequency bounds more reasonable settings further reduces computation time filter count. adjust frequency bounds, click View button select Settings. This brings panel shown Figure seen, lower frequency bound been upper bound been KHz. (Also note that sampling frequency been 44.1 KHz.). When desired frequency bounds have been set, Apply button must clicked.
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Figure Filter Design Settings Panel
filters ready calculated. Click Calculate button select Modified Response. computed filter response that results shown plot Figure (The yellow plot modified response prior calculation final filter).
Figure Computed Filter Response
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This particular example required bell-shaped equalization filters, these filters shown Figure
Figure Filters Comprising Computed Filter Response
file containing these sets filter coefficients created Clicking Edit button selecting Copy Generated Filters Edit Grid transfer generated filters Edit Grid domain. Clicking Edit button selecting Generate TAS3xxx Data generates biquad coefficients Clicking File button selecting Save TAS3xxx Program Data creates .EQ310X file containing filter coefficients, along with added application specific data.
content file shown Figure
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NAME: C:\Program Files\Texas Instruments Inc\DAP Config Tool 2.0\Starter_Example_02.EQ310X Date 2/21/03 Speaker Model Speaker Serial Speaker Manufacturer: Sample Rate Description Filter Parameters EQ-1, 9.997519, 5265.459281, 13930.606494, Yes, EQ-2, 11.797349, 344.547785, 2194.327307, Yes, EQ-3, -6.285571, 745.270301, 1432.655445, Yes, EQ-4, 11.882147, 13.814435, 97.755808, Yes, EQ-5, 6.096446, 124.661630, 307.354841, Yes, EQ-6, -7.208300, 608.987920, 5701.820308, Yes, EQ-7, 5.372781, 380.760577, 2985.929232, Yes, EQ-8, -4.855725, 568.281489, 4456.470584, Yes, EQ-9, 5.259423, 79.508570, 818.863435, Yes, EQ-10, 3.996107, 13.110451, 165.030929, Yes, EQ-11, -3.798699, 36.377875, 217.753747, Yes, Channel Number
Figure Filter File Starter_Example_02.EQ310X
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Dynamic Range Compressor (DRC) Coefficient Generation
filter design default appearing when package opened. dynamic range compressor (DRC) GUI, first click Device button select TAS3100. Then click Design button select Dynamic Range Compression TAS3100. shown Figure appears.
Figure Dynamic Range Compression
black curve transfer curve represents input level into DRC. blue line actual transfer curve DRC.
Overview
TAS3103 provides three regions operation, defined threshold variables green lines vertical projections these threshold points. three regions defined referenced Region Region Region Regions left region, applies input levels equal below Region central middle region, applies input levels equal below above Region right region applies input levels above
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Within each region, compression (output increases every increase input) expansion (output increases every increase input) specified, ratio programmable. addition, offset curve from input curve specified threshold points offset curve from input curve threshold referred Offset2, offset curve from input curve threshold referred Offset1.
Parameter Specification Computation
There seven variables that define operation DRC: Thresholds Compression Expansion Gains Region Region Region Offsets Offset1 Offset2
thresholds define three regions operation. Within each region, compression expansion selected, degree compression expansion within each region inputting appropriate compression expansion ratio. Offset1 Offset2 boost transfer function threshold points serve place anchor gain transfer function shape compression expansion ratios.
Threshold Settings
threshold settings either using slider associated with each threshold point, entering values into windows under sliders. However, threshold points cannot independent processing gains programmed into TAS3103. thresholds referenced signal level into TAS3103, rather signal level into DRC. threshold point input relative signal levels into TAS3103, necessary take processing gain loss) between TAS3103 input port DRC. Assume, example, processing gain structure shown Figure When audio signal input into TAS3103, 8-bit headroom established above incoming audio data. addition, bits processing resolution added below bits reserved data input word sizes bits. result 48-bit word, this word size used digital audio processor within TAS3103. when audio data routed DRC, only upper bits this 48-bit word used. This results attenuation signal level into bits dB). Channel processing gain dedicated mixer into change this apparent attenuation signal level into DRC. example, figure following page, mixer gain into DRC, coupled with channel gain changes attenuation signal level into attenuation summary, threshold points audio signal levels into DRC. Signal levels into TAS3103, channel gain with TAS3103, dedicated mixer that routes channel output audio must comprehended selecting these threshold settings.
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Gain Channel Processing 48-Bit Word
48-Bit Word Headroom
Headroom
Input Port
Resolution
Resolution
Channel Processing Gain
Figure Example Dependence Input Signal Level Channel Gain
Compression Expansion Settings
Selecting, each region, either Compression button Expansion button Dynamic Range Compression panel, makes choice compression expansion each three regions DRC. value ratio must equal greater than 1.0, with value giving transfer function slope equal slope input curve. compression, ratio means that output level changes every change input. expansion, ratio means that output level changes every input changes.
Offset Settings
Entering value desired Offset window provided Dynamic Range Compression panel sets Offset2. Offset1 entered same way, using Offset window, commanding tool automatically compute Offset1. Selecting Derive Offset button Specify Offset button Dynamic Range Compression panel makes this choice. Threshold serves fulcrum pivot point transfer function. There discontinuity transfer function This means that compression and/or expansion plots regions must join threshold point intersection must offset from input curve value Offset2. Offset2 positive, cut, point intersection below input curve value Offset2. Offset2 negative, boost, point intersection above input curve value Offset2. input level compression and/or expansion plots regions required intersect. There discontinuity transfer function threshold transfer curve region which starts with value Offset2 relative input curve, offset from input curve value Offset1 when plot intersects vertical green line projection avoid such discontinuity Offset1 must computed knowing values Offset2, compression expansion coefficient relieve users from having perform this computation, provides option specifying Offset1 having program automatically compute Offset1 value such that there
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discontinuity threshold This option selected clicking Derive Offset1 button Dynamic Range Compression panel. Once parameters have been entered, clicking Apply button enters data, resultant transfer curve plotted.
Transfer Function Plot
transfer function parameter settings selected viewed clicking Apply button once parameters have been set. window example previously shown, settings follows: Thresholds -150.8 Compression Expansion Gains Region Compression Region 1.7:1 Expansion Region Compression Offsets Offset1 Offset2 Automatically Computed
Unlike 48-bit word size used rest digital audio processor, only uses 32-bit precision. then -192 bits -192 dB). This means that levels below sees constant input level thus computed gain coefficient remains fixed value computed when input -192 This effect seen example plot.
Transfer Function File
Once desired transfer function obtained, result saved file clicking File button selecting Save DRC2 File. directory store file, file name selected, file extension must remain .DR310X. content .DR301X file example illustrated shown Figure threshold values offset values 48-bit numbers (25.23 format Section 3.1.2 TAS3103 data manual). compression expansion ratios 28-bit numbers (5.23 format Section 3.1.1 TAS3103 data manual).
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{T1} {T2} {O1} {O2} {k0} {k1} {k2}
Figure File Starter_Example_02.DR310X
.DR310X extension enables TAS3103 Device Configuration Tool (DCT) identify file file. panel shown Figure
Figure Device Configuration Tool (DCT) Panel
seen, file created tool selected tool downloaded specified TAS3103 channel.
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addition transfer function, complete specification also requires specifying time constants energy estimator attack decay filters. energy estimator derives estimate value audio data stream into DRC. programmable parameters, ae), effective time window over which estimate made accordance with equation
window
Alpha
equation only uses Alpha_e) requires that both Alpha_e Alpaha_e) entered. output gain coefficient that used adjust level audio stream. Attack Decay parameters control transition time changes computed gain coefficient. Four parameters define operation Attack Decay element. Parameters Alpha_d Alpha_d) decay release time constant, used when coefficient change boosting volume level. Parameters Alpha_a Alpha_a) attack time constant, used when coefficient change cutting volume level. time constants determined equations below, where attack time constant decay time constant.
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Loudness Compensation Filter Design
listener's perception loudness given tone relative other tones different frequencies constant over range volume settings. Lower frequency tones perceived dropping faster volume level relative higher frequency tones volume decreased. This same phenomenon also occurs, lesser degree, higher frequency tones relative mid-range tones. Typically, loudness compensation involves boosting bass content, sometimes treble content, audio volume decreased. TAS3103 provides both biquad loudness filter define portion frequency spectrum (bass treble) adjusted loudness, four variables that implement function f(volume) that controls volume adjustment. TAS3100 loudness filter design provides graphic facility which define parameters loudness filter four variables that define f(volume). excellent paper loudness compensation Loudness Compensation: Abuse Tomlinson Holman Frank Kampmann. This article appeared Journal Audio Engineering Society, July August 1978, Volume Number
Loudness Compensation Transfer Function Loudness Biquad Filter Transfer Function
block diagram TAS3100 loudness compensation process shown Figure noted that because parallel paths that make loudness compensation block, frequency response loudness biquad filter overall frequency response loudness compensation block. Typically, user wants specify frequency response loudness compensation block itself, worry about topology loudness compensation block. provides this capability. also provides option programming loudness biquad filter directly. Figure composite loudness compensation transfer function seen
Loudness Compensation Composite Transfer Function
H(z)
Plot Volume
H'(z)
Plot Gain
where H'(z) transfer function biquad loudness filter defining portion spectrum adjusted volume,
Plot Volume
commanded volume setting,
Plot Gain
Plot Gain
loudness adjustment coefficient defined f(volume).
Plot Volume
same
Plot Volume
(2)LO
FUNCTION f(Volume)
Plot Gain
Magnitude Truncation
TAS3103 LOUDNESS COMPENSATION
H'(z) LOUDNESS COMPENSATION FILTER
Audio Stream
Output Plot
Volume Loudness Compensation Processed Audio Stream
Figure TAS3103 Loudness Processing Block
transfer function biquad filter derived shown Figure
BiQuad Filter
Vin(z) Vout(z) Vin(z) b1z-1 b2z-2] Vout(z) [a1z-1 a2z-2]
Vout(z)[1 a1z-1 a2z-2] Vin(z) b1z-1 b2z-2] b1z-1 b2z-2] a1z-1 a2z-2]
Vout(z)
H'(z)
Vin(z)
Figure Biquad Filter Transfer Function Derivation
transfer function H'(z) biquad filter derived from biquad equivalent transfer function H(z) follows, assuming Plot Volume
Plot Gain
obtain biquad coefficients H'(z), denominator coefficients overall loudness biquad transfer function H(z) subtracted from numerator coefficients overall loudness biquad transfer function H(z) form numerator coefficients loudness biquad transfer function H'(z). denominator coefficients same both transfer functions.
Using Specify Design Loudness Compensation Transfer Function
filter design default appearing when package opened. TAS3100 loudness compensation filter design GUI, first click Device button select TAS3100. Then click Design button select Design Loudness Filters TAS3100. (Note that Dynamic Range Compressor present, Design Filters must first selected then Design Loudness Filters TAS3100 selected). Loudness Compensation that comes includes Create Loudness Filter panel shown Figure Four options provided specifying Loudness Compensation Transfer Function H(z).
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Enter user-specific biquad coefficients that directly implement H(z) Create H(z) using (bell-shaped) transfer characteristic Create H(z) using bass shelf transfer characteristic Create H(z) using treble shelf transfer characteristic (used compensation addresses treble)
fifth option entering biquad coefficients Loudness Biquad filter H'(z) Loudness Compensation Block also provided.
Specifying H(z) Using Predetermined Biquad Coefficients
Base Type Coefficients Create Loudness Filter panel used when equivalent biquad coefficients composite loudness transfer function H(z) have been determined independent means. illustrate Base Type Coefficients tab, click Base Type Coefficients bring panel shown Figure this example, equivalent biquad coefficients composite loudness compensation transfer function H(z) assumed have been independently calculated, assuming 44.1-kHz sampling frequency, 1.985723853 -0.9858528375 1.0029180049 -1.985723853 0.9829348325
These coefficients have been entered, decimal, coefficient windows provided panel. Figure indicates which window references which coefficient. Note that requirement that negative values coefficients entered. Caution: panel Figure also implies that coefficients entered hexadecimal numbers. This option functional, work must remain decimal domain. However, correctly outputs final coefficient values hexadecimal format when creating output file xx.LD310X. When coefficients have been entered, clicking button Create Loudness Filter panel results plot overall loudness compensation transfer function. This plot shown Figure seen, nothing more than bell-shaped filter with following parameters: Gain Bandwidth Center Frequency Should full lower frequency range appear plot Figure necessary back Design Filters clicking Design selecting Design Filters. Then click File, select Open Response File open zerodb.txt. This step activates Automatic Loudspeaker Equalizer GUI. Then click View, select Settings, click Frequency Limits tab, enter lower frequency limit desired Lower Frequency Limits window. Then clicking Design selecting Loudness Filters TAS3100l brings back Loudness filter Design GUI, with plot extended down lower frequency limit selected. Also, while still Automatic Loudspeaker Equalizer GUI, sampling rate also changed clicking View, selecting Settings, clicking Frequency Limits tab, entering desired sampling frequency Sampling Frequency window.
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Treble Shelf Filter Define H(z) Transfer Function
Create H(z) Directly Entering Equivalent BiQuad Filter Coefficients
Create H(z) Indirectly Entering BiQuad Coefficients Loudness BiQuad Filter H'(z)
(Bell-Shaped) Filter Define H(z) Transfer Function
Bass Shelf Filter Define H(z) Transfer Function
Figure Create Loudness Filter Panel
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Figure Base Type Coefficients Loudness Panel
Figure Loudness Compensation Transfer Function H(z) Coefficients Entered Directly
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desired edit coefficients H(z), click Edit select Select Filters Edit Graphically. Then click generated curve transfer function. Create Loudness Filter panel reappears. Then click Base Type Coefficients tab. entered coefficients reappear altered required. Clicking button results second curve being generated. this second curve desired response, clicking Edit, selecting Delete Filters Graphically, then clicking first curve generated eliminates first curve, leaving only desired response graphed. When response desired been successfully plotted, TAS3103 biquad filter coefficients must next generated. Clicking Edit, selecting Select Filter TAS3XXX Data File Graphically, clicking desired response curve accomplishes this. filter coefficients generated. Clicking File selecting Save LD31 Data brings Save panel. file name folder selected, extension LD310X must retained. This extension allows TAS3103 recognize file loudness compensation file. content file generated shown Figure with coefficient identifiers side added clarity.
1.985723733 -0.9858527183 0.0029178857 -0.0029178857
Figure Loudness Compensation File Predetermined H(z) Coefficients
noted that coefficients Figure same biquad coefficients that were entered H(z). fact, coefficients biquad coefficients H'(z); automatically computes these biquad coefficients that they directly downloaded into TAS3103 without requiring further mapping coefficients.
Specifying H(z) Using (Bell-Shaped) Filters
H(z) also specified selecting type filter desired composite loudness compensation function. Using bell-shaped filters options. filters specify H(z), select Base Type Create Loudness Filter panel shown Figure panel shown Figure appears. illustrate panel, enter filter parameters implemented H(z) biquad coefficients used previous example, which are: Gain Bandwidth Center Frequency These parameters entered using appropriate windows panel associated with Base Type selection. Having entered parameters, clicking plots H(z) transfer function resulting from these gain, bandwidth, center frequency selections. plot obtained using previous parameters identical plot shown Figure response desired response plotted, TAS3103 biquad filter coefficients generated clicking Edit, selecting Select Filter TAS3XXX Data File Graphically, clicking desired response curve. Clicking File selecting Save LD31 Data saves data, once file name directory entered.
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Figure Base Type Loudness Panel
Specifying H(z) Using Bass Shelf Filters
Bass Shelf filters specify H(z), select Bass Base Type Create Loudness Filter panel shown Figure panel shown Figure appears.
Figure Bass Base Type Loudness Panel
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response parameters entered Figure Bass Gain Bass Boost this example) Frequency shown Figure
Figure Loudness Compensation Transfer Function H(z) Created Using Bass Filter
Clicking Edit, selecting Select Filter TAS3XXX Data File Graphically, clicking desired response curve generates TAS3103 biquad filter coefficients Bass Filter response. Clicking File selecting Save LD31 Data saves data, once file name directory entered.
Specifying H(z) Using Treble Shelf Filters
Treble Shelf filters specify H(z), select Treble Base Type Create Loudness Filter panel shown Figure panel shown Figure appears. response parameters entered Figure Treble Gain Bass Frequency 2000 shown Figure Clicking Edit, selecting Select Filter TAS3XXX Data File Graphically, clicking desired response curve generates TAS3103 biquad filter coefficients Treble Filter response. Clicking File selecting Save LD31 Data saves data, once file name directory entered.
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Figure Treble Base Type Loudness Panel
Figure Loudness Compensation Transfer Function H(z) Created Using Treble Filter
SLEA014 2003 Application Report
Specifying H'(z) (The Loudness Biquad Filter) Using Predetermined Biquad Coefficients
There cases when desired specify composite loudness compensation transfer function using predetermined coefficients loudness biquad filter. Selecting Loudness Coefficients Create Loudness Filter panel shown Figure provides this capability. Upon selecting this tab, panel shown Figure appears.
Figure Loudness Coefficients Loudness Panel
Figure lists loudness biquad coefficients obtained entering predetermined coefficients composite loudness compensation transfer function H(z). Figure shows these same coefficients entered Loudness Coefficients panel. Figure shows resultant response entering these coefficients. curve overall loudness compensation response H(z) resulting from entering coefficients shown Figure listed Figure expected bell-shaped response. green curve response H'(z), loudness biquad filter itself, shown emphasize that H(z) H'(z) same.
Application Report
SLEA014 2003t
Green plot H'(z) plot H(z)
Figure Loudness Compensation Transfer Function H(z) Created Using Loudness Coefficients
Loudness Compensation Volume Command
addition specifying composite loudness transfer function H(z), programmable loudness function block f(volume_setting) must also specified complete loudness compensation design. files generated include parameters that govern f(volume_setting), does provide ability specify these parameters display purposes. With this ability, family curves filter design chosen plotted function volume setting, allowing user directly visualize loudness compensation achieved given loudness filter design. output function block f(volume_setting) expressed terms four programmable loudness compensation coefficients
(volume setting (volume setting
where: logarithmic gain logarithmic offset gain offset
0.5, 0.0, 1.0, 0.0, example, f(volume setting) becomes
(volume setting volume setting
SLEA014 2003 Application Report
noted Figure output f(volume_setting), labeled Figure feeds gain-control mixer. output loudness biquad filter H'(z) also feeds same gain-control mixer. output this gain-control mixer then summed with volume-adjusted audio data stream. result loudness-adjusted audio. Loudness compensation then allows given spectral segment audio data stream determined loudness biquad filter H'(z)) given delta adjustment volume determined programmable function f(volume_setting). output soft volume loudness compensation block previous example 0.5, 0.0, 1.0, AudioOut
Plot Gain
AudioIn [volume_setting H'(z)
volume setting
Figure shows windows entering given Create Loudness Filter panel.
f(volume_setting)
volume setting
Figure Programming Parameters f(volume_setting)
Plot Volume window used enter commanded volume setting. Plot Gain window output function f(volume_setting). Performance plots created entering commanded volume setting Plot Volume window clicking Apply button. computed value f(volume_setting) seen Plot Gain window clicking Calculate Plot Gain window. Some loudness compensation schemes apply fixed loudness adjustment coefficient range volume settings. this application, when volume setting crosses volume range boundary, controller issues fixed loudness adjustment coefficient. TAS3103 both support this implementation loudness compensation. TAS3103, computation f(volume_setting) turned entering value loudness adjustment coefficient, this case, implemented writing value coefficient C-parameter (refer Figure 21). ALE, computation f(volume_setting) turned very same entering value Then entering desired fixed loudness adjustment coefficient desired volume command Plot Volume, clicking Calculate Plot Gain button, then clicking Apply button yields resultant plot volume command loudness adjustment coefficient entered.
Application Report
SLEA014 2003t
Figure shows suite plots volume_setting versus f(volume_setting) function
volume setting
0.5, 0.0, 1.0, 0.0. noted that commanded
volume setting decreases value, amount bass boost relative rest audio spectrum increases. This phenomenon purpose loudness compensation.
Volume Setting 0.25
Plot Color Green Blue Orange Yellow
Volume Setting 0.125 0.0625 0.03125 0.015625 0.0078125
Plot Color Neon Pink Dark Green Light Blue Blue Green Violet
Figure Loudness Compensation Plots Commanded Volume Output
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Coates Dallas) ABSTRACT automatic loudspeaker equalization (ALE)

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