# jaakkopasanen/AutoEq

Automatic headphone equalization from frequency responses
Type Name Latest commit message Commit time
Failed to load latest commit information.
calibration Nov 18, 2018
compensation Dec 16, 2018
data Nov 28, 2018
img Feb 18, 2019
innerfidelity Mar 30, 2019
oratory1990 Mar 3, 2019
referenceaudioanalyzer Mar 30, 2019
results Mar 30, 2019
rtings Mar 30, 2019
.gitignore Feb 16, 2019
average.py Oct 14, 2018
calibration.py
check_min_phase.py
frequency_response.py Mar 30, 2019
image_graph_parser.py Nov 18, 2018
requirements.txt Jan 13, 2019
server.py
test_client.py Sep 2, 2018
test_ir.py Jan 26, 2019

# AutoEQ

AutoEQ is a project for equalizing headphone frequency responses automatically and it achieves this by parsing frequency response measurements and producing a equalization settings which correct the headphone to a neutral sound. This project currently has almost 2000 headphones covered in the results folder. See Usage for instructions how to use the results with different equalizer softwares and Results section for details about parameters and how the results were obtained.

AutoEQ is not just a collection of automatically produced headphone equalization settings but also a tool for equalizing headphones for yourself. frequency_response.py provides methods for reading data, equalizing it to a given target response and saving the results for usage with EqualizerAPO. It's possible to use different compensation (target) curves, apply tilt for making the headphones brighter/darker and adding a bass boost. It's even possible to make one headphone sound (roughly) like another headphone. For more info about equalizing see Equalizing

Third major contribution of this project is the measurement data and compensation curves all in a numerical format. Everything is stored as CSV files so they are easy to process with any programming language or even Microsoft Excel. See Data Processing for more technical description about how things were obtained and processed.

Sennheiser HD 650 equalization results plotted

## Usage

AutoEQ produces settings for EqualizerAPO GraphicEQ, parametric equalizers, convolution equalizer and fixed band eqs.

#### EqualizerAPO GraphicEQ

EqualizerAPO GraphicEQ settings look like this:

GraphicEQ: 20 0.0; 22 6.0; 23 6.0; 25 6.0; 26 5.9; 28 5.6; 30 5.3; 32 4.8; 35 4.3; 37 3.9; 40 3.5; 42 3.3; 45 3.0; 49 2.7; 52 2.6; 56 2.5; 59 2.1; 64 1.8; 68 1.9; 73 2.2; 78 1.7; 83 0.9; 89 0.3; 95 -0.2; 102 -0.7; 109 -1.1; 117 -1.5; 125 -1.9; 134 -2.2; 143 -2.5; 153 -2.6; 164 -2.5; 175 -2.5; 188 -2.6; 201 -2.7; 215 -2.5; 230 -2.4; 246 -2.3; 263 -2.2; 282 -2.0; 301 -1.9; 323 -1.8; 345 -1.5; 369 -1.5; 395 -1.4; 423 -1.2; 452 -1.0; 484 -1.0; 518 -1.0; 554 -0.8; 593 -0.5; 635 -0.4; 679 -0.5; 726 -0.3; 777 -0.2; 832 -0.4; 890 -0.6; 952 -0.4; 1019 -0.1; 1090 -0.5; 1167 -0.8; 1248 -1.0; 1336 -1.1; 1429 -1.3; 1529 -1.3; 1636 -1.6; 1751 -1.6; 1873 -1.4; 2004 -0.9; 2145 -0.7; 2295 -0.5; 2455 -0.2; 2627 0.1; 2811 -0.1; 3008 -0.6; 3219 -1.1; 3444 -1.0; 3685 -0.6; 3943 0.0; 4219 -0.0; 4514 -0.1; 4830 0.9; 5168 3.8; 5530 5.9; 5917 5.2; 6331 4.4; 6775 3.9; 7249 1.3; 7756 0.3; 8299 0.0; 8880 0.0; 9502 0.0; 10167 0.0; 10879 0.0; 11640 0.0; 12455 0.0; 13327 0.0; 14260 0.0; 15258 0.0; 16326 0.0; 17469 0.0; 18692 0.0; 20000 0.0

##### Parametric Equalizers

Parametric equalizers have filters with user adjustable gain, center frequency and quality Q. Keep in mind that parametric eq produced is not as accurate as graphic eq because there is limited number of filters. This might not have any significant difference in practice if there are enough filters available. Usually 10 filters produce very good results but as little as 5 can be good enough.

All parametric equalizer except Peace require you to configure the filter parameters manually with the software user interface. Some parametric equalizer use filter width (band width) instead of Q. Filter width can be calculated as: bw = Fc / Q where bw is the band width, Fc is center frequency and Q is quality.

Parametric eq settings can be used with Peace or any other parametric eq which has at least 5 bands available. Even fewer bands is possible but pre-computed results require to use minimum five first of the filters. Parametric equalizer filter parameters look like this:

Type Fc Q Gain
Peaking 28 Hz 0.46 6.3 dB
Peaking 162 Hz 0.91 -2.3 dB
Peaking 2237 Hz 1.94 -4.6 dB
Peaking 6093 Hz 2.26 -4.7 dB
Peaking 8251 Hz 3.71 -2.9 dB

#### Convolution Equalizers

Convolution equalizer settings are finite impulse responses (FIR filters) and are the most advanced kind of (LTI) filters. FIR filters make it possible to produce linear phase filters which some may prefer though generally minimum phase filters are recommended. Convolution equalizer settings are provided as WAV files. Pre-computed results include impulse responses with 44.1 kHz and 48 kHz but other sampling rates are supported as well. Import the WAV file with correct sampling frequency into the software to use convolution equalizer.

Minimum phase impulse response looks like this:

#### Fixed Band Equalizers

Fixed band eq is more commonly known as graphic equalizer but in order not to confuse with EqualizerAPO GraphicEQ it is called like that in this project. Fixed band equalizer is like parametric equalizer with several peaking filters but don't have adjustable frequency information, only gain. All other types are preferred over fixed band equalizers but on some devices these are the only available ones.

Fixed band equalizers have trouble compensating for narrow notches and peaks that fall between two bands. Good example is Sennheiser HD 800 with it's 6 kHz peak that is right in between 4 kHz and 8 kHz bands of standard 10-band equalizer. When using 10-band equalizer check if the fixed band equalization curve is very different than the desired equalization curve at some frequency and adjust the nearby filters by ear for best results.

Fixed band equalizer settings look like this:

Type Fc Q Gain
Peaking 31 Hz 1.41 6.1 dB
Peaking 62 Hz 1.41 3.0 dB
Peaking 125 Hz 1.41 -1.1 dB
Peaking 250 Hz 1.41 -2.2 dB
Peaking 500 Hz 1.41 -0.9 dB
Peaking 1000 Hz 1.41 0.1 dB
Peaking 2000 Hz 1.41 3.6 dB
Peaking 4000 Hz 1.41 -1.0 dB
Peaking 8000 Hz 1.41 -4.1 dB
Peaking 16000 Hz 1.41 -7.5 dB

#### Windows

has EqualizerAPO, HeSuVi, Peace and many media players with parametric equalizers such as Roon and Foobar2000.

#### Android

doesn't have any system-wide parametric equalizers but there are several options which all have different caveats.

Android has a native equalizer which can be controlled with Music Equalizer EQ app for system wide equalization without rooting. This is the best option for non-rooted users who use Spotify.

USB Audio Player PRO with Toneboosters plugin and Neutron Music Player are the most popular music players with parametric equalizers but are not free or provide system-wide equalization. USB Audio Player PRO might be the best option for non-rooted users who use Tidal.

Viper4Android is a system-wide convolution based equalizer (and much more) on Android but it requires rooting of the device. Viper4Android is supported with impulse response (WAV) files. For rooted users this is the best option.

#### Linux

has PulseEffects for PulseAudio which has parametric eq and convolution eq.

### HeSuVi

Easiest way is to install HeSuVi and select correct headphone model from the Equalizer tab. There is no need to download results from the results folder because HeSuVi ships with all of the recommended results. Please note that after installing HeSuVi will have surround virtualization on and if you don't want to use it you can select none.wav from the left side list on the Virtualization tab.

HeSuVi is GUI for EqualizerAPO which has almost all headphone surround virtualizations available. HeSuVi also provides a convenient graphical user interface for adjusting the equalizer, toggling eq on and off, adjusting preamp and saving and restoring multiple different configurations making it very easy to compare different eq settings.

If some reason HeSuVi doesn't include a headphone available in this project or if you wish to try out some other than the recommended result the file can be added manually. To add a preset into HeSuVi add the GraphicEq file into C:\Program Files\EqualizerAPO\config\HeSuVi\eq\custom. Then restart HeSuVi, select the new preset from the custom group in Equalizer tab and set volume attenuation for both channels to the highest positive gain value in preset.

HeSuVi GUI for EqualizerAPO

### Plain EqualizerAPO

It's possible to use plain EqualizerAPO and edit configuration file in C:\Program Files\EqualizerAPO\config\config.txt. Disable Include: example.txt, replace GraphicEQ: ... line with the one found in results and set Preamp: .... Using Sennheiser HD 650 would make config file look like this:

Preamp: -6 dB
# Include: example.txt
GraphicEQ: 20 0.0; 22 6.0; 23 6.0; 25 6.0; 26 5.9; 28 5.6; 30 5.3; 32 4.8; 35 4.3; 37 3.9; 40 3.5; 42 3.3; 45 3.0; 49 2.7; 52 2.6; 56 2.5; 59 2.1; 64 1.8; 68 1.9; 73 2.2; 78 1.7; 83 0.9; 89 0.3; 95 -0.2; 102 -0.7; 109 -1.1; 117 -1.5; 125 -1.9; 134 -2.2; 143 -2.5; 153 -2.6; 164 -2.5; 175 -2.5; 188 -2.6; 201 -2.7; 215 -2.5; 230 -2.4; 246 -2.3; 263 -2.2; 282 -2.0; 301 -1.9; 323 -1.8; 345 -1.5; 369 -1.5; 395 -1.4; 423 -1.2; 452 -1.0; 484 -1.0; 518 -1.0; 554 -0.8; 593 -0.5; 635 -0.4; 679 -0.5; 726 -0.3; 777 -0.2; 832 -0.4; 890 -0.6; 952 -0.4; 1019 -0.1; 1090 -0.5; 1167 -0.8; 1248 -1.0; 1336 -1.1; 1429 -1.3; 1529 -1.3; 1636 -1.6; 1751 -1.6; 1873 -1.4; 2004 -0.9; 2145 -0.7; 2295 -0.5; 2455 -0.2; 2627 0.1; 2811 -0.1; 3008 -0.6; 3219 -1.1; 3444 -1.0; 3685 -0.6; 3943 0.0; 4219 -0.0; 4514 -0.1; 4830 0.9; 5168 3.8; 5530 5.9; 5917 5.2; 6331 4.4; 6775 3.9; 7249 1.3; 7756 0.3; 8299 0.0; 8880 0.0; 9502 0.0; 10167 0.0; 10879 0.0; 11640 0.0; 12455 0.0; 13327 0.0; 14260 0.0; 15258 0.0; 16326 0.0; 17469 0.0; 18692 0.0; 20000 0.0


EqualizerAPO has a graphical user interface for adjusting configurations. Launch the editor from C:\Program Files\EqualizerAPO\Editor.exe.

EqualizerAPO Editor GUI

### Peace

Peace is a GUI for manipulating parametric eq filters with EqualizerAPO. Peace also has visualization for the end result equalization frequency response, profile manager for multiple different eq settings and a switch for disabling everything among other features. Load eq settings into Peace by clicking Import button and select the ParametricEQ.txt file.

Peace with full GUI for EqualizerAPO

### PulseEffects

PulseEffects is a PulseAudio (Linux) module with wide variety of signal processing tools including parametric equalizer. Adjust filter parameters by clicking the cog button on each filter andset type to "Peak", frequency to given center frequency to Fc and width to Fc / Q. Adjust gain with the slider.

### USB Audio Player PRO

USB Audio Player PRO is and Android app with improved USB audio drivers for usage with USB DACs. USB Audio Player PRO is not system-wide but works with local files and many streaming services though not with Spotify. USB Audio Player has Toneboosters Morphit plugin which has parametric equalizer. This app and the plugin are not free.

### Music EQ Equalizer

The best app for system wide equalization on Android (without rooting) is Music Equalizer EQ which is a 10-band standard equalizer. Gains for each band can be adjusted with only 1 dB resolution but this isn't a problem because the average error is then only 0.25 dB, hardly noticeable. Bigger problem is the potential narrow peaks and notches between the bands' center frequencies since there isn't really anything that can be done for those. See notes about fixed band equalizers.

App starts in presets view so you need to click the left arrow in the top left corner to get to manual view. Here you can adjust the bands. Set each band level to closest value to what the equalization settings ask. Pre-computed results only support standard 10-band equalizers which have band center frequencies at 31, 63, 125, 250, 500, 1000, 2000, 4000, 8000 and 16000 Hz. Q values are not adjustable so you don't have to worry about those even though they are given in the result settings.

## Results

The main principle used by AutoEQ for producing the equalization function is to invert error curve. Error is the difference between raw microphone data and the compensation (target) curve. If headphone's frequency response is 4 dB below the target at 20 Hz equalization function will have +4 dB boost at 20 Hz. In reality simply inverting the error is not sufficient since measurements and equalization have several problems that need to be addressed, see Technical Challenges for more details.

Results provided in this project currently have all the headphone measurements from Innerfidelity, Headphone.com, oratory1990, Rtings and Reference Audio Analyzer. Results are organized by source/target/headphone so a Sennheiser HD 650 measured by Innerfidelity and tuned to a target by SBAF-Serious would be found in innerfidelity/sbaf-serious/Sennheiser HD 650. Multiple measurements of a same headphone by a same measurement entity are averaged. All different measurements for averaging have been renamed with snXXX (serial number) or sample X in the end of the name to distinguish from the averaged data which has no suffixes in the name.

oratory1990 measurements have been done on Gras 43AG and 43AC couplers, the same which were used to develop Harman target responses by Olive et al. and therefore use Harman target responses for the equalization targets. These results are recommended over all other measurements because of this reason. Harman target data is in the compensation folder.

Innerfidelity and Headphone.com measured headphones have SBAF-Serious target only. This is a modified version of Innerfidelity target curve produced by Serious user on Super Best Audio Friends forum. This curve doesn't have any glaring problems and is quite well balanced overall. Curve was turned into a compensation for raw microphone data and tilted 0.2 dB / octave brighter. Innerfidelity measurements are recommended over Headphone.com measurements because SBAF-Serious target was developed for Innerfidelity. SBAF-Serious curve was modified to be suitable for Headphone.com measurements by calibrating it. CSV data files for Innerfidelity and Headphone.com are at innerfidelity/resources/innerfidelity_compensation_sbaf-serious.csv and headphonecom/resources/headphonecom_compensation_sbaf-serious.csv, respectively.

Rtings measured headphones have frequency response made for this project. This treble average target is using an average of frequency responses of all Rtings measured headphones in the treble range with small manual reduction of the 9kHz peak and the Rtings native response below 2500 Hz without bass boost. Three different targets were compared in listening tests and the treble average target was found to sound the best. Other two were the Rtings native target curve and calibrated and uncalibrated versions of SBAF Serious target curve. Rtings uses the same measurement system as Innerfidelity uses so in theory the uncalibrated SBAF Serious target should work similarly with Rtings but listening tests found the treble average target to be slightly better. Rtings have a very informative video about how they are doing the measurements and how did they came up with the target they use.

Reference Audio Analyzer measurements are done one multiple different measurement systems and the compensation curve used in the images is not known. Results in this project take the Reference Audio Analyzer measurements as is and no compensation curve has been developed. There also is no bass boost applied to Reference Audio Analyzer measurements since they look to be lacking bass in many cases compared to other measurements leading to natural bass boost when using zero vector as the compensation curve.

Innerfidelity 2017 compensation curve is the result of Tyll Hertsens calibrating his measurement head on the Harman reference listening room and is a significant improvement over the old compensation curve used in PDFs. However 2017 curve seems to underestimate 2 to 5 kHZ region by several dB leading the equalization to boost those frequencies too much. See the original post and the sequel on Innerfidelity for more details. Data can be found in innerfidelity/resources/innerfidelity_compensation_2017.csv

Headphone.com compensation curve is used by Headphone.com with their Frequency Response graphs but this seems to underestimate treble even more than the 2017 Innerfidelity curve leading to even brighter equalization. Data location: headphonecom/resources/headphonecom_compensation.csv

None of these targets have bass boost seen in Harman target responses and therefore a +4dB boost was applied for all on-ear headphones, +6dB for in-ear headphones and no boost for earbuds. Harman targets actually ask for about +6dB for on-ears and +10dB for in-ears but since most headphones cannot achieve this with positive gain limited to +6dB a smaller boost was selected. Above 6 to 8kHz data is filtered more heavily to avoid measurement artifacts and no positive gain (boost) is applied. In the upper treble measurements are less reliable and boosting them too much will cause serious problems while having some narrow dips is not a problem at all.

## Equalizing

frequency_response.py is the tool used to produce the equalization results from measurement data. There is no fancy graphical user interface but instead it is used from command line.

### Installing

• Download AutoEQ zip and exctract to a convenient location. Or just git clone if you know what that means.
• Download and install Python3.6. Python 3.7 is not supported yet. Make sure to check Install Python3 to PATH
• Install virtualenv. Run this on command prompt. Search cmd in Windows start menu.
pip install virtualenv

• Go to AutoEQ location
cd C:\path\to\AutoEq-master

• Create virtual environment
virtualenv venv

• Activate virtualenv
venv\Scripts\activate

• Install required packages
pip install -r requirements.txt

• Verify installation
python frequency_response.py -H


When coming back at a later time you'll only need to activate virtual environment again

cd C:\path\to\AutoEq-master
venv\Scripts\activate


### Command Line Arguments

usage: frequency_response.py [-h] --input_dir INPUT_DIR
[--output_dir OUTPUT_DIR] [--standardize_input]
[--new_only] [--calibration CALIBRATION]
[--compensation COMPENSATION] [--equalize]
[--parametric_eq] [--fixed_band_eq] [--fc FC]
[--q Q] [--ten_band_eq]
[--max_filters MAX_FILTERS] [--fs FS]
[--bit_depth BIT_DEPTH] [--phase PHASE]
[--f_res F_RES] [--bass_boost BASS_BOOST]
[--iem_bass_boost IEM_BASS_BOOST] [--tilt TILT]
[--max_gain MAX_GAIN]
[--treble_f_lower TREBLE_F_LOWER]
[--treble_f_upper TREBLE_F_UPPER]
[--treble_max_gain TREBLE_MAX_GAIN]
[--treble_gain_k TREBLE_GAIN_K] [--show_plot]

optional arguments:
-h, --help            show this help message and exit
--input_dir INPUT_DIR
Path to input data directory. Will look for CSV files
in the data directory and recursively in sub-
directories.
--output_dir OUTPUT_DIR
Path to results directory. Will keep the same relative
paths for files found in input_dir.
--standardize_input   Overwrite input data in standardized sampling and
bias?
--new_only            Only process input files which don't have results in
output directory.
--calibration CALIBRATION
File path to CSV containing calibration data. Needed
when using target responses not developed for the
source measurement system. See calibration
directory.
--compensation COMPENSATION
File path to CSV containing compensation (target)
curve. Compensation is necessary when equalizing
because all input data is raw microphone data. See
"compensation", "innerfidelity/resources" and
--equalize            Will run equalization if this parameter exists, no
value needed.
--parametric_eq       Will produce parametric eq settings if this parameter
exists, no value needed.
--fixed_band_eq       Will produce fixed band eq settings if this parameter
exists, no value needed.
--fc FC               Comma separated list of center frequencies for fixed
band eq.
--q Q                 Comma separated list of Q values for fixed band eq.
--ten_band_eq         Shortcut parameter for activating standard ten band eq
optimization.
--max_filters MAX_FILTERS
Maximum number of filters for parametric EQ. Multiple
cumulative optimization runs can be done by giving
multiple filter counts separated by "+". "5+5" would
create 10 filters where the first 5 are usable
independently from the rest 5 and the last 5 can only
be used with the first 5. This allows to have muliple
configurations for equalizers with different number of
bands available. Not limited by default.
--fs FS               Sampling frequency for impulse response and parametric
eq filters. Defaults to 44100.
--bit_depth BIT_DEPTH
Number of bits for every sample in impulse response.
Defaults to 16.
--phase PHASE         Impulse response phase characteristic. "minimum",
"linear" or "both". Defaults to "minimum"
--f_res F_RES         Frequency resolution for impulse responses. If this is
20 then impulse response frequency domain will be
sampled every 20 Hz. Filter length for impulse
responses will be fs/f_res. Defaults to 10.
--bass_boost BASS_BOOST
Target gain for sub-bass in dB. Has sigmoid slope down
from 35 Hz to 280 Hz. "--bass_boost" is mutually
exclusive with "--iem_bass_boost".
--iem_bass_boost IEM_BASS_BOOST
Target gain for sub-bass in dB. Has sigmoid slope down
from 25 Hz to 350 Hz. "--iem_bass_boost" is mutually
exclusive with "--bass_boost".
--tilt TILT           Target tilt in dB/octave. Positive value (upwards
slope) will result in brighter frequency response and
negative value (downwards slope) will result in darker
frequency response. 1 dB/octave will produce nearly 10
dB difference in desired value between 20 Hz and 20
kHz. Tilt is applied with bass boost and both will
affect the bass gain.
--max_gain MAX_GAIN   Maximum positive gain in equalization. Higher max gain
allows to equalize deeper dips in frequency response
but will limit output volume if no analog gain is
available because positive gain requires negative
digital preamp equal to maximum positive gain.
Defaults to 6.0.
--treble_f_lower TREBLE_F_LOWER
Lower bound for transition region between normal and
treble frequencies. Treble frequencies can have
different smoothing, max gain and gain K. Defaults to
6000.0.
--treble_f_upper TREBLE_F_UPPER
Upper bound for transition region between normal and
treble frequencies. Treble frequencies can have
different smoothing, max gain and gain K. Defaults to
8000.0.
--treble_max_gain TREBLE_MAX_GAIN
Maximum positive gain for equalization in treble
region. Defaults to 0.0.
--treble_gain_k TREBLE_GAIN_K
Coefficient for treble gain, affects both positive and
negative gain. Useful for disabling or reducing
equalization power in treble region. Defaults to 1.0.
--show_plot           Plot will be shown if this parameter exists, no value
needed.


### Examples

Equalizing Sennheiser HD 650 and saving results to my_results/HD650:

python frequency_response.py --input_dir="innerfidelity\data\onear\Sennheiser HD 650" --output_dir="my_results\HD650" --compensation="innerfidelity\resources\innerfidelity_compensation_sbaf-serious.csv" --equalize --bass_boost=4 --show_plot


Equalizing Beyerdynamic DT990 without saving results

python frequency_response.py --input_dir="headphonecom\data\onear\Beyerdynamic DT990" --compensation="headphonecom\resources\headphonecom_compensation.csv" --equalize --bass_boost=4 --show_plot


Equalizing Beyerdynamic DT990 to SBAF-Serious target

python frequency_response.py --input_dir="headphonecom\data\onear\Beyerdynamic DT990" --compensation="headphonecom\resources\headphonecom_compensation_sbaf-serious-brighter.csv" --equalize --bass_boost=4 --show_plot


Equalizing all Headphone.com on-ear headphones and saving results to results\onear\sbaf-serious\headphonecom. There is a lot of headphones and we don't want to inspect all visually so we'll omit --show_plot

python frequency_response.py --input_dir="headphonecom\data\onear" --output_dir="results\headphonecom\sbaf-serious" --compensation="innerfidelity\resources\innerfidelity_compensation_sbaf-serious.csv" --equalize --bass_boost=4


Equalizing Beyerdynamic DT 770 to sound like HiFiMAN HE400S. 80ohm version of DT 770 is only available in Headphone.com measurements and HE400S only in Innerfidelity measurements so we'll use calibration. To make the bass sound the same we'll omit bass boost.

python frequency_response.py --input_dir="headphonecom\data\onear\Beyerdynamic DT770" --output_dir="my_results\Beyerdynamic DT770" --compensation="innerfidelity\data\onear\HiFiMAN HE400S\HiFiMAN HE400S.csv" --calibration="calibration\headphonecom_raw_to_innerfidelity_raw.csv" --equalize --show_plot


Viewing HiFiMAN HE400S raw microphone data

python frequency_response.py --input_dir="innerfidelity\data\onear\HiFiMAN HE400S" --show_plot


Feel free to experiment more.

### Server

AutoEQ has a HTTP server for clients such as graphical user interfaces or web apps. This is the API documentation. Currently only one route /process exists.

#### POST /process

Request
JSON request with MIME-type of application/json and data:

• calibration [float]|str Calibration data. Either name of the calibration curve as string (see below for supported curve names) or list of floats matching frequency data.
• compensation [float]|str Compensation data. Either name of the compensation curve as string (see below for supported curve names) or list of floats matching frequency data.
• equalize bool Run equalization?
• parametric_eq bool Optimize peaking filters for parametric eq?
• max_filters int|[int] Maximum number of peaking filters for filter optimization run. Can be omitted for automatic selection. Can also be a list in which case there will be multiple runs, each building on top of the previous filters.
• bass_boost float Bass boost amount in dB for over-ear headphones. Mutually exclusive with iem_bass_boost.
• iem_bass_boost float Bass boost amount in dB for in-ear headphones. Mutually exclusive with bass_boost.
• tilt float Target frequency response tilt in db / octave.
• max_gain float Maximum positive gain in dB. Higher equalization values will be clipped.
• treble_f_lower float Lower bound for treble transition region.
• treble_f_upper float Upper boud for treble transition region.
• treble_max_gain float Maximum gain in treble region.
• treble_gain_k float Gain coefficient in treble region.

Response
JSON response with data:

• equalization [float] Equalization curve.
• equalized_raw [float] Raw frequency response after equalization.
• equalized_smoothed [float] Smoothed frequency response after equalization.
• error [float] Error curve.
• error_smoothed [float] Smoothed error curve.
• filters [[float]] List of parametric eq peaking filters. Each item contains center frequency (Fc), quality (Q) and gain.
• frequency [float] Frequency data.
• max_gains [float] List of maximum gains for each parametric eq filter group frequency response.
• n_filters [float] List of number of filters in each parametric eq filter group
• raw [float] Raw frequency response.
• smoothed [float] Smoothed frequency response.
• target [float] Target frequency response.

## Calibration

Innerfidelity and Headphone.com have different kind of measurement systems and since there is no any kind of standard calibration for headphone frequency response measurements the data produced by these systems are not directly compatible with each other. Same individual headphone will measure differently in the two systems. This actually applies for all of the existing measurement systems.

To have comparable equalization results and to be able to use all compensation curves for both measurements a calibration was done. Calibration made is not as reliable as a real calibration where a set of reference headphones are measured on both systems and outputs compared but instead a same headphone models but different individual units were used. All headphones with same name were selected from Headphone.com measurement database and Innerfidelity measurement database and results were compared model-wise. Final calibration curve was produced by averaging all the measurement pairs and smoothing the averaged curve. This method is problematic because there are large differences between individual headphones due to manufacturing and placement on the measurement head. Standard deviation is quite high about 5dB at 20Hz but still it's probably closer to truth than not using any calibration at all.

Pictured data is for calibrating Headphone.com measurement to Innerfidelity measurement or in other words estimating how an individual headphone measured by Headphone.com would look like if it was measured by Innerfidelity.

Calibration data is not used as is in the results but instead Innerfidelity SBAF-Serious compensation curve was calibrated to be suitable for Headphone.com measurements. Calibration can be used between Innerfidelity and Headphone.com mainly to make headphones sound like other headphones when both models are from different sources.

Same calibration procedure was done for Innerfidelity and Rtings measurements.

## Technical Challenges

Simply inverting headphone frequency response deviation from target response does not usually produce sufficient results. Some problems are caused by imperfections in measurements, some are reliability issues and some are practical end-user problems. Rtings has a good video on Youtube about measurement system challenges and solutions which is definitely worth checking out. Innerfidelity also has a very educational video on Youtube about measurments and what constitutes as a neutral sound. Main takeoffs are that bass and treble measurements are very inconsistent, neutral sound is not very well defined yet and on-ear headphones have big reliability problems in 8 to 9kHz range due to resonances which move when headphone placement is changed. Harman international has done some solid research into preferred headphone frequency response but since that research was done on a different measurement system the target does not apply directly to Innerfidelity (Summer 2018) and Headphone.com measurements.

There is very little that can be done for fighting bass inconsistencies because the same problems will be there whether equalization is used or not. Headphones simply have different bass responses on different listeners (heads). Therefore bass is taken as is in AutoEQ and equalized as if there was nothing wrong with it. You're mileage may wary. Luckily bass has smaller impact on music and having too much bass (especially sub-bass) doesn't create problems of the same magnitude as having too much treble.

Moving resonances around 8 to 9kHz may cause big problems if not taken into account. Spikes and dips in this range are of great amplitude and very narrow. If one equalizes these spikes and dips according to frequency response measurement in worst case scenario a spike will move in a place of dip when headphone is moved and therefore the spike is amplified significantly leading to very sharp and piercing sound signature. To counter these problems by default AutoEQ uses heavy smoothing and limited positive gain above 6 to 8kHz. This way the equalization will follow a broader trend of the region and will not care so much about narrow spikes and dips. Also positive gain is limited to 0dB as an extra safety measure against amplifying moved spike. Suppressing a narrow dip even further is not an optimal thing to do but in practice has little negative effect on the sound. Both of these measures will also alleviate upper treble measurement inconsistencies above 11 to 12 kHz.

A practical end-user problem is if too high positive gain is allowed which asks for equal amount of negative digital pre-amp to prevent clipping. This negative preamp will limit maximum volume produced by the system if there is no analog gain available. If a dedicated headphone amplifier is available or if the motherboard/soundcard can drive the headphones loud enough even when using high negative preamp larger --max_gain values can be uses. By default --max_gain is set to +6dB to not to cripple user's volume too much. Max gain will clip the equalization curve which produces sharp kinks in it. Sharp changes in equalization may produce unwanted equalization artifacts. To counter this AutoEQ rounds the corners whenever max gain clips the curve.

## Parametric Equalizer

AutoEQ has an optimizer to fit several peaking filters to the desired equalization curve. Optimization is part heuristic initialization and part mathematical optimization.

In the initialization phase peaks are detected from the target curve and a peaking filter is created to match the peak's height (gain) and location (frequency). This way the optimizer finds suitable number of filters to optimize. If bass region has no peaks and therefore is missing filters entirely, maximum of two filters will be added at 20 Hz and 60 Hz.

A way to limit the number of filters used is provided with max_filters parameter. If there are too many filters after initialization, some filters are removed. First filters with small gain (< 0.2 dB and < 0.33 dB) are removed. If there are too many filters after reduction of small gain filters, nearby filters are attempted to merge. Merged filter will be in the mid point of the merged filters. If merging filters did not reduce the count enough, smallest filters are removed until count matches maximum allowed number of filters. Image below shows initialization for 1More MK801 headphone. Red dots are the peaks of filters before reduction and green dots are the peaks after reduction.

Equalization target and initial peak filters for optimization before and after filter number limitation

After suitable number of filters have been achieved and filter center frequencies and gains have been set to appropriate values a mathematical optimization is performed to fit sum frequency response of all filters to match as close as possible the desired curve. Optimization is based on gradient descent and will attempt to minimize mean squared error between the sum frequency response of the filters and the target. When improvements in the error are getting too small to make a practical difference the optimization is stopped. Animation below shows progress from the initialization to a close finished curve.

Optimization of parametric eq filters (click to play)

Below is the end result of optimizing only 5 peaking filters to equalization curve of 1More MK801 headphone. Parametric eq curve deviates from the fine equalization curve in some points but all in all follows the target surprisingly well. The two equalization curves have hardly audible difference. Some headphones are not as easy to equalize properly with limited number of bands because highly erratic curves are impossible to be estimated with only a few peaking filters.

1More MK801 with parametric equalization

## Data Processing

Measurement data for this project was obtained by crawling Innerfidelity, Headphone.com, oratory1990 and Rtings databases. For Innerfidelity that means downloading all PDFs, turning them into images with Ghostscript, parsing images with Python PIL package and saving the numerical data. Numerical data obtained this way is an average of the blue and red curves in the frequency response. These curves have been compensated with the old compensation curve which does not match human perception at all. The old compensation curve was then applied in inverse to turn the compensated data into raw microphone data. This raw microphone data is stored in innerfidelity/data. On-ear, in-ear and ear-bud data is separated because they ask for different AutoEQ parameters.

Headphone.com measurements were downloaded as images, both raw and compensated data. Images were parsed into numerical format and raw data saved to headphonecom/data. Both datas were used to obtain Headphone.com compensation curve by calculating differences between raw and compensated data.

oratory1990 data processing is similar to Innerfidelity because oratory1990 measurements are distributed as PDFs. Compensation curves used for oratory1990 measurements are the Harman target curves.

Rtings measurements were obtained in a similar fashion as the Headphone.com measurements were. Two new compensation curves were developed in addition to the native curve used by Rtings in their measurement reports.

Reference Audio Analyzer measurements were gotten the same way. Images downloaded and a image parser was developed to read the numerical data. Reference Audio Analyzer doesn't have compensation curve by AutoEQ project but instead simply trusts the compensated data provided by Reference Audio Analyzer.

Data processing tools are not meant as a user friendly and robust software but instead to be able to be ran once to obtain the raw data.

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