In one embodiment, the remote computing environment 110 includes computing resources, such as one or more servers 120 and one or more storage units 130. One or more applications 140 that provide higher-level services may execute/operate on the remote computing environment 110 utilizing the computing resources of the remote computing environment 110.

In one embodiment, the remote computing environment 110 provides an online platform for hosting one or more online services (e.g., an audio streaming service, a video streaming service, etc.) and/or distributing one or more applications. For example, an application 260 may be loaded onto or downloaded to the electronic device 110 from the remote computing environment 110 that maintains and distributes updates for the application 260. As another example, a remote computing environment 110 may comprise a cloud computing environment providing shared pools of configurable computing system resources and higher-level services.

FIG. 2 illustrates an example of a portion of a hearable device 300 inserted within an ear canal 410 of an individual ear 400, in one or more embodiments. In one embodiment, the hearable device 300 comprises a pair of in-ear earbuds 300, wherein one earbud 300 of the pair is partially inserted within the ear canal 410. The ear canal 410 extends from an eardrum 420 within the ear canal 410 to an opening through which a portion of the earbud 300 is inserted.

As shown in FIG. 2, the portion of the earbud 300 inserted plugs up the ear canal 410, creating a closed cavity. At low frequencies, sound pressure response is the same at any point inside the ear canal 410 (i.e., inside the closed cavity). At higher frequencies, however, wavelength is in the order of the length of the ear canal 410, such that sound pressure response varies at any point inside the ear canal 410. Specifically, the geometry (e.g., length, width, curvature, etc.) of the ear canal 410 determines how sound pressure response varies inside the ear canal 410, at the eardrum 420, and also near a speaker driver of the earbud 300.

A transfer function described how an input id transferred to sound pressure as a function of frequency. Let T* generally denote a pre-defined/given target sound pressure in dB (decibel)-SPL (sound pressure level). Let SPL_drumgenerally denote a sound pressure response in dB-SPL at an eardrum 420, and let SPL_NFmicgenerally denote a sound pressure response in dB-SPL at a microphone 330 of an earbud 300. Let C generally denote a transfer function which is decomposable into transfer functions H and G, where H is a transfer function from a speaker terminal voltage of an earbud 300 to a sound pressure response SPL_NFmicat a microphone 330 of the earbud 300, and G is a transfer function from the sound pressure response SPL_NFmicat the microphone 330 to a sound pressure response SPL_drumat an eardrum 420 (i.e., G=SPL_drum−SPL_NFmicin dB).

Due to geometric and physiological differences of individual ears 400, individual (i.e., personalized) transfer functions H_Iand G_Ivary for each individual ear 400. An individual transfer function H_Ifor the individual ear 400 can be measured directly using the microphone 330 of the earbud 300. An individual transfer function G_Ifor the individual ear 400, however, cannot be measured directly and must be estimated instead.

Conventional equalization algorithms use a generic transfer function G (i.e., fixed and not personalized) derived from a test setup that uses a test fixture (e.g., a mannequin, etc.).

One or more embodiments provide PEQ of an earbud using an individual transfer function G_I. Sound at an eardrum within an ear canal of an individual ear (that the earbud is within proximity of, e.g., partially inserted within the ear canal if the earbud is an in-ear earbud) is controlled based on the individual transfer function G_I.

In one embodiment, a parametric base transfer function G₀is utilized which can be individualized by changing its parameters. An individual transfer function G_Ican be estimated based on the base transfer function G₀, where the base transfer function G₀can be individualized via parameter modification.

In one embodiment, an improved estimate of an individual transfer function G_Ican be inferred from one or more measurements of an individual transfer function H_I.

FIG. 3A illustrates an example graph plot 500 comparing various transfer functions G, in one or more embodiments. A horizontal axis of the graph plot 500 represents frequency expressed in Hertz (Hz). A vertical axis of the graph plot 500 represents sound pressure amplitude expressed in dB. As shown in FIG. 3A, the graph plot 500 includes: (1) a first curve 510 representing a measured transfer function G_measuredobtained using an industry standard test fixture, such as a head and torso simulator, (2) a second curve 520 representing a simulated transfer function G_simulatedobtained using the same industry standard test fixture, and (3) a set 530 of curves representing a plurality of individual transfer functions G_Iobtained using finite element simulations of a plurality of different ears (e.g., 20 different ears) and a plurality of different earbud positions (e.g., 5 different earbud positions) in each ear.

Based on the graph plot 500, the PEQ system 310 takes into account the following observations regarding an individual transfer function G_I: (1) an individual transfer function G_Ivaries with different ear geometries and insert positions, but generally follows the shape/trend of the measured/simulated transfer function G_measured/G_simulated, (2) at low frequencies, there is no variance among individual transfer functions G_I, (3) around 800 Hz to 4000 Hz, variance among individual transfer functions G_Istarts to increase, but the shape/trend of the individual transfer functions G_Iis well defined with broad peaks and dips, (4) above 4000 Hz, variance among individual transfer functions G_Ibecomes very large and intractable, (5) between 1200 Hz and 2400 Hz, peaks of individual transfer functions G_Iappear to line up along a line, and (6) at 1800 Hz, variance among individual transfer functions G_Ireach 3 dB (95% confidence interval).

FIG. 3B illustrates an example graph plot 540 comparing different individual transfer functions H_Iand G_I, in one or more embodiments. A horizontal axis of the graph plot 540 represents frequency expressed in Hz. A vertical axis of the graph plot 540 represents sound pressure expressed in dB-SPL. As shown in FIG. 3B, the graph plot 540 includes: (1) a first set 550 of curves representing a plurality of individual transfer functions H_Iobtained using finite element simulations of a plurality of different ears (e.g., 20 different ears) and a plurality of different earbud positions (e.g., 5 different earbud positions) in each ear, and (2) a second set 560 of curves representing a plurality of individual transfer functions G_Iobtained using the same finite element simulations. For visualization purposes, the first set 550 of curves are offset by 20 dB.

Based on the graph plot 540, the PEQ system 310 takes into account the following observation regarding an individual transfer function G_Ifor a particular ear: below 4000 Hz, an individual transfer function G_Ifor a particular ear can be inferred from an individual transfer function H_Ifor the same particular ear. For example, as shown in FIG. 3B, the frequencies at which peaks (e.g., P₁, P₂, P₃, etc.) of the individual transfer functions G_Ioccur are at the same frequencies at which the individual transfer functions H_Iexhibit dips (e.g., D₁, D₂, D₃, etc.). Therefore, a peak gain G_peakin dB of an individual transfer function G_Iappears to grow linearly with frequency f.

FIG. 3C illustrates an example graph plot 565 of a linear function 566 describing a direct relationship between a frequency f(G_max) of a maximum gain G_maxof an individual transfer function G_Iand a frequency f(H_min) of a minimum gain H_minof an individual transfer function H_I, in one or more embodiments. A horizontal axis of the graph plot 565 represents frequency f(H_min) expressed in Hz of dips of the individual transfer functions H_Iin FIG. 3B. A vertical axis of the graph plot 565 represents frequency f(G_max) expressed in Hz of peaks of the individual transfer functions G_Iin FIG. 3B. As shown in FIG. 3C, the frequency f(G_max) appears to grow linearly with the frequency f(H_min).

FIG. 3D illustrates an example graph plot 570 of a linear function 580 describing a direct relationship between a peak gain G_peakof an individual transfer function G_Iand a center frequency f_cof a local minima in the gain of the pressure at a microphone of a hearable device partially inserted within an ear canal of an individual ear, in one or more embodiments. A horizontal axis of the graph plot 570 represents center frequency f_cexpressed in Hz of dips of the individual transfer functions H_Iin FIG. 3B. A vertical axis of the graph plot 570 represents peak gain G_peakexpressed in dB of the individual transfer functions G_Iin FIG. 3B. As shown in FIG. 3D, the peak gain G_peakappears to grow linearly with the center frequency f_c.

In one embodiment, the linear function 580 may be represented in accordance with equation (1) provided below:

G
peak

=

-

2
.
3

+

0
.
0

⁢
4
⁢
2
*

f
.

(
1
)

One or more embodiments provide an improvement over using a generic transfer function G derived from a test setup that uses a test fixture.

FIG. 4 illustrates an example PEQ system 600, in one or more embodiments. In one embodiment, the PEQ system 310 in FIGS. 1-2 is implemented as the PEQ system 600. In one embodiment the PEQ system 600 comprises a test unit 610, a measurement unit 620, an inference unit 630, and a calculation unit 640.

In one embodiment, the test unit 610 is configured to: (1) detect an insertion of an earbud 300 (that the system 600 is integrated in) into an ear canal 410 of an individual ear 400, and (2) in response to the insertion, deliver an audio test signal to a transducer 320 of the earbud 300 for playback inside the individual ear 400, wherein the audio test signal represents a test tone or a sample of music. In one embodiment, the audio test signal is pre-programmed into a memory of the earbud 300. In another embodiment, the audio test signal is obtained from an electronic device 200. In yet another embodiment, the audio test signal is content chosen by a listener/user (e.g., music, speech, etc.) for audio playback.

In one embodiment, the measurement unit 620 is configured to trigger a microphone 330 of the earbud 300 to directly obtain one or more measurements of an individual transfer function H_Ifor an individual ear 400, wherein the one or more measurements capture one or more sound pressure responses SPL_NFmicat the microphone 330 during playback of an audio test signal inside the individual ear 400. In one embodiment, the one or more measurements are iteratively obtained.

In one embodiment, the inference unit 630 is configured to: (1) receive one or more measurements of an individual transfer function H for an individual ear 400 (e.g., from the measurement unit 620), and (2) based on the one or more measurements, estimate (i.e., derive/infer) an individual transfer function G_Ifor the individual ear 400. In one embodiment, an individual transfer function G_Iis estimated using machine learning or general regression techniques. In one embodiment, an individual transfer function G_Iis iteratively estimated.

In one embodiment, the inference unit 630 individualizes/personalizes a transfer function G for an individual ear 400 (i.e., estimates an individual transfer function G_I) using a parametric base transfer function G₀with one or more parameters adjusted/individualized (“individualized parameters”) for the individual ear 400. For example, in one embodiment, the base transfer function G₀is constructed from a combination of four biquads (i.e., second-order filters), wherein each biquad k is defined by a center frequency

f
c
k

,

a gain, and Q, and k∈[1,4].

The inference unit 630 estimates (i.e., derives/infers) one or more individualized parameters for an individual ear 400 (i.e., parameter modification) based on one or more measurements of an individual transfer function H_Ifor the individual ear 400. Specifically, in one embodiment, a transfer function G for the individual ear 400 is individualized/personalized by adjusting both a center frequency

f
c
k

and a gain of a biquad k. For example, a center frequency

f
c
2

of the second biquad is adjusted/set to the frequency at which the measured individual transfer function H_Ihas a minimum, and a gain of the second biquad is adjusted/set to the gain value at the center frequency

f
c
2

,

resulting in an individual transfer function G_Ifor the individual ear 400 that is equal to a peak gain G_peakat the center frequency

f
c
2

.

In another embodiment, a transfer function G for the individual ear 400 is individualized/personalized by adjusting only a center frequency

f
c
k

of a biquad k (e.g., adjusting only a center frequency

f
c
2

of the second biquad).

In another embodiment, a transfer function G for the individual ear 400 is individualized/personalized by adjusting only G_peak.

In one embodiment, the calculation unit 640 is configured to: (1) obtain a pre-defined/given target sound pressure response T* (e.g., pre-programmed into a memory of the earbud 300 or obtained from an electronic device 200), (2) receive one or more measurements of an individual transfer function H_Ifor an individual ear 400 (e.g., from the measurement unit 620 or the inference unit 630), (3) receive an estimated individual transfer function G_Ifor the individual ear 400 (e.g., from the inference unit 630), and (4) calculate a PEQ value PEQ for the individual ear 400 based on the target sound pressure response T*, the one or more measurements of the individual transfer function H_I, and the estimated individual transfer function G_I. In one embodiment, the calculation unit 640 calculates the PEQ value PEQ using units of dB, in accordance with equation (2) provided below:

PEQ
=

T
*

-

H
I

-

G
I

.

(
2
)

In one embodiment, the calculation unit 640 is further configured to: (1) receive an audio playback signal for playback inside the individual ear 400 (e.g., from an electronic device 200), (2) apply the PEQ value PEQ within the audio full range (low, mid and high frequencies) to the audio playback signal, and (3) deliver the resulting equalized audio playback signal to the transducer 320 for playback inside the individual ear 400.

FIG. 5A illustrates an example graph plot 700 of various transfer functions G, in one or more embodiments. A horizontal axis of the graph plot 700 represents frequency expressed in Hz. A vertical axis of the graph plot 700 represents sound pressure expressed in dB. As shown in FIG. 5A, the graph plot 700 includes: (1) a first curve 710 representing an individual transfer function G_Iestimated via the inference unit 630 using a parametric base transfer function G₀and one or more individualized parameters, (2) a second curve 720 representing the base transfer function G₀, (3) a third curve 730 representing a first biquad of the base transfer function G₀, (4) a fourth curve 740 representing a second biquad of the base transfer function G₀, (5) a fifth curve 750 representing a third biquad of the base transfer function G₀, and (6) a sixth curve 760 representing a fourth biquad of the base transfer function G₀.

FIG. 5B illustrates another example graph plot 800 of various transfer functions G and errors between some of the transfer functions G, in one or more embodiments. A horizontal axis of the graph plot 800 represents frequency expressed in Hz. A vertical axis of the graph plot 800 represents sound pressure expressed in dB. As shown in FIG. 5B, the graph plot 800 includes: (1) a first curve 810 representing a ground truth transfer function G_GTobtained using finite element simulations, (2) a second curve 820 representing an individual transfer function G_Iestimated via the inference unit 630 using a parametric base transfer function G₀and one or more individualized parameters, (3) a third curve 830 representing the base transfer function G₀, (3) a fourth curve 840 representing an error between the ground truth transfer function G_GTand the base transfer function G₀, and (5) a fifth curve 850 representing an error between the ground truth transfer function G_GTand the individual transfer function G_I.

FIG. 5C illustrates an example graph plot 900 of an error between a ground truth transfer function G_GTand a parametric base transfer function G₀, in one or more embodiments. A horizontal axis of the graph plot 900 represents frequency expressed in Hz. A vertical axis of the graph plot 900 represents sound pressure expressed in dB. As shown in FIG. 5C, the graph plot 900 includes: (1) a first curve 910 representing a mean error between the ground truth transfer function G_GTand the base transfer function G₀, and (2) a 95% confidence interval 915 delineated by upper and lower bounds.

FIG. 5D illustrates an example graph plot 920 of an error between a ground truth transfer function G_GTand a first individual transfer function G_I, in one or more embodiments. A horizontal axis of the graph plot 920 represents frequency expressed in Hz. A vertical axis of the graph plot 920 represents sound pressure expressed in dB. The first individual transfer function G_Iis estimated via the inference unit 630 which adjusts both

f
c
2

and G_peak. As shown in FIG. 5D, the graph plot 920 includes: (1) a first curve 930 representing a mean error between the ground truth transfer function G_GTand the first individual transfer function G_I, and (2) a 95% confidence interval 935 delineated by upper and lower bounds.

As shown in the graph plots 900 and 920, at frequencies below 4000 Hz, adjusting both

f
c
2

and G_peakgreatly reduces the variance of error compared to just using the base transfer function G₀, and also reduces mean error between 1.5 kHz and 4 kHz frequencies.

FIG. 5E illustrates another example graph plot 940 of an error between a ground truth transfer function G_GTand a second individual transfer function G_I, in one or more embodiments. A horizontal axis of the graph plot 940 represents frequency expressed in Hz. A vertical axis of the graph plot 940 represents sound pressure expressed in dB. The second individual transfer function G_Iis estimated via the inference unit 630 which adjusts only

f
c
2

.

As shown in FIG. 5E, the graph plot 940 includes: (1) a first curve 950 representing a mean error between the ground truth transfer function G_GTand the second individual transfer function G_I, and (2) a 95% confidence interval 955 delineated by upper and lower bounds.

As shown in the graph plots 900 and 940, at frequencies below 4000 Hz, adjusting only

f
c
2

greatly reduces the variance of error compared to just using the base transfer function G₀, however the mean error appears to remain unchanged.

FIG. 5F illustrates another example graph plot 960 of an error between a ground truth transfer function G_GTand a third individual transfer function G_I, in one or more embodiments. A horizontal axis of the graph plot 960 represents frequency expressed in Hz. A vertical axis of the graph plot 960 represents sound pressure expressed in dB. The third individual transfer function G_Iis estimated via the inference unit 630 which adjusts only G_peak. As shown in FIG. 5F, the graph plot 960 includes: (1) a first curve 970 representing a mean error between the ground truth transfer function G_GTand the third individual transfer function G_I, and (2) a 95% confidence interval 975 delineated by upper and lower bounds.

As shown in the graph plots 900 and 960, at frequencies below 4000 Hz, adjusting only G_peakreduces the mean error compared to just using the base transfer function G₀, however the variance of error is not significantly reduced.

Let NFM generally denote a NF microphone 330 of an earbud 300, let ERP generally denote an ear reference point of a head and torso simulator, and let DRP generally denote a drum reference point of the head and torso simulator. Let H_NFMgenerally denote a transfer function H for the NFM, and let H_DRPgenerally denote a transfer function H for the DRP. Let G_HATSgenerally denote an average frequency response of 14 inserts (H_DRP−H_NFM) of an earbud 300 measured using the head and torso simulator (HATS).

G_HATSis used in PEQ to estimate sound pressure at an eardrum 420 within an ear canal 410. At low frequencies, G_HATStends to zero assuming the wavelengths at these frequencies are very long, so that the ear canal 410 acts as a pressure chamber, resulting in sound pressure at the NFM and sound pressure at the DRP having the same frequency response.

FIG. 6A illustrates an example graph plot 1000 of ERP-DRP in PEQ, in one or more embodiments. A horizontal axis of the graph plot 1000 represents frequency expressed in Hz. A vertical axis of the graph plot 1000 represents sound pressure difference expressed in dB. The graph plot 1000 includes a first curve representing ERP-DRP, i.e., difference between sound pressure at the ERP and sound pressure at the DRP.

FIG. 6B illustrates an example graph plot 1010 of measurements for 14 inserts of an earbud 300 that are measured using a head and torso simulator, in one or more embodiments. A horizontal axis of the graph plot 1010 represents frequency expressed in Hz. A vertical axis of the graph plot 1010 represents sound pressure expressed in dB. The graph plot 1010 includes: (1) a first set of curves (“NFM”) representing sound pressure at the NFM for the 14 inserts, and (2) a second set of curves (“DRP”) representing sound pressure at the DRP for the 14 inserts.

Air pressure leakage (or air leakage) may occur when there is insufficient coupling between an earbud 300 and an ear canal 410/a head and torso simulator the earbud 300 is positioned within proximity of. As shown in FIG. 6B, in some measurements where there is excessive air pressure leakage at low frequencies, sound pressure at the DRP is lower than sound pressure at the NFM—this results in an underestimation of sound pressure at the DRP and an insufficient level of air pressure leakage compensation at low frequencies when applying PEQ.

FIG. 6C illustrates example graph plots 1020-1140 of measurements for 13 of the 14 inserts, in one or more embodiments. A horizontal axis of each graph plot 1020-1140 represents frequency expressed in Hz. A vertical axis of each graph plot 1020-1140 represents sound pressure expressed in dB. Each graph plot 1020-1140 corresponds to one of the 13 inserts, and includes: (1) a first curve (“NFM”) representing sound pressure at the NFM for the corresponding insert, (2) a second curve (“DRP”) representing sound pressure at the DRP for the corresponding insert, and (3) a third curve (“G”) representing a measured individual transfer function G (i.e., G=DRP-NFM) for the corresponding insert.

Each graph plot 1020-1140 further indicates a leak ratio (i.e., an amount of air pressure leakage due to insufficient coupling) for a corresponding insert, wherein the leak ratio is based on a NFM ratio for the corresponding insert between 40 Hz and 300 Hz. For example, the graph plot 1020 corresponding to a first insert indicates a leak ratio of −3.4 dB, the graph plot 1030 corresponding to a second insert indicates a leak ratio of −2.1 dB, the graph plot 1040 corresponding to a third insert indicates a leak ratio of −3.2 dB, the graph plot 1050 corresponding to a fourth insert indicates a leak ratio of −17.3 dB, the graph plot 1060 corresponding to a fifth insert indicates a leak ratio of −16.3 dB, the graph plot 1070 corresponding to a sixth insert indicates a leak ratio of −2.8 dB, the graph plot 1080 corresponding to a seventh insert indicates a leak ratio of −9.4 dB, the graph plot 1090 corresponding to an eighth insert indicates a leak ratio of −2.6 dB, the graph plot 1100 corresponding to a ninth insert indicates a leak ratio of −15 dB, the graph plot 1110 corresponding to a tenth insert indicates a leak ratio of −9.1 dB, the graph plot 1120 corresponding to an eleventh insert indicates a leak ratio of −13 dB, the graph plot 1130 corresponding to a twelfth insert indicates a leak ratio of −2.6 dB, and the graph plot 1140 corresponding to a thirteenth insert indicates a leak ratio of −3.2 dB.

Estimation of sound pressure at an eardrum 420 may be determined using DRP-ERP. Specifically, a measured individual transfer function G at low frequencies may be determined in accordance with equation (3) provided below:

G
=

DRP
-

ERP
.

(
3
)

FIG. 6D illustrates an example graph plot 1150 of measured individual transfer functions G for the 13 inserts, in one or more embodiments. A horizontal axis of the graph plot 1150 represents frequency expressed in Hz. A vertical axis of the graph plot 1150 represents sound pressure difference expressed in dB. The graph plot 1150 includes a first set of curves (“G”) representing measured individual transfer functions G (i.e., G=DRP−ERP) for the 13 inserts. As shown in FIG. 6D, at low frequencies, some of the measured individual transfer functions G show air pressure leakage due to insufficient coupling.

Let GLF gain generally denote a gain in a measured individual transfer function G at low frequencies. At low frequencies, the gain GLF gain relates to an underestimation in the measured individual transfer function G to predict sound pressure at the DRP. Table 1 below provides, for each of the measured individual transfer functions G in FIG. 6D, a corresponding average level of GLF gain in dB in the frequency range of 40 Hz to 100 Hz.

TABLE 1

GLF gain (in units of dB)

−0.0204

−0.0042

−0.1236

−4.3649

−4.0310

−0.0831

−1.1236

−0.0751

−3.5158

−1.0193

−2.2900

−0.0130

−0.1751

FIG. 6E illustrates an example graph plot 1160 of a fitted model, in one or more embodiments. A horizontal axis of the graph plot 1160 represents NFM ratio between 40 Hz and 300 Hz. A vertical axis of the graph plot 1160 represents GLF gain expressed in dB in the frequency range of 40 Hz to 100 Hz. The graph plot 1160 includes a fitted quadratic polynomial curve (“fitted model”) that fits data points representing the average levels of GLF gain in Table 1 provided above.

For example, in one embodiment, the fitted model is represented in accordance with equation (4) provided below:

val
⁡
(
x
)

=

p
1

*

x
2

+

p
2

*
x

+

p
3

,

(
4
)

wherein p₁, p₂, and p₃are coefficients with 95% confidence bounds as follows: p₁=−0.01823 (−0.02161,−0.01485), p₂=−0.06016 (−0.1233, 0.002995), and p₃=−0.08705 (−0.2867, 0.1126).

In one embodiment, the PEQ system 600 is configured for individualization of an individual transfer function G at low frequencies (e.g., via the inference unit 630). In one embodiment, the PEQ system 600 adapts an individual transfer function G at low frequencies using the fitted model by applying a low shelving filter LSHV to G_HATS. A gain g of the low shelving filter LSHV corresponds to a gain GLF gain in a measured individual transfer function G (i.e., G=DRP-NFM). An optimal center frequency f_cand an optimal Q of the low shelving filter LSHV are determined using non-linear optimization in which the sum of root mean square (RMS) errors between an estimated DRP and an actual DRP is minimized. For example, in one embodiment, f_c=1493.3 Hz, Q=0.2457, and [b, a]=biquad (f_c, Q, g, f_s, LSHV), wherein f_sis a sampling frequency of the low shelving filter LSHV.

For example, in one embodiment, the PEQ system 600 determines an individual transfer function G_newat low frequencies in accordance with equations (5)-(7) provided below:

G
new

=

G
HATS

+
LSHV

,

(
5
)

H
DRPnew

=

H
NFM

+

G
new

,
and

(
6
)

e
=

∑

1
n

⁢

∑

i

(

H
DRPnew

-

H
DRP

)

i
2

,

(
7
)

wherein n is 14 inserts, and i is frequency bins 30 Hz to 2000 Hz.

By using the fitted model and the low shelving filter LSHV, a transfer function G can be personalized to allow more precise prediction of sound pressure at low frequencies even on bad inserts with a high amount of air pressure leakage, thereby providing air pressure leakage compensation.

FIG. 6F illustrates example graph plot 1170 of an estimated DRP using G_HATS, in one or more embodiments. A horizontal axis of the graph plot 1170 represents frequency expressed in Hz. A vertical axis of the graph plot 1170 represents sound pressure expressed in dB. The graph plot 1170 includes: (1) a first curve (“G_HATS”) representing G_HATS, (2) a second curve (“estimated DRP”) representing an estimated sound pressure at the DRP using G_HATS, (3) a third curve (“G_measured”) representing an individual transfer function G_measuredthat is measured, and (4) a fourth curve (“measured DRP”) representing a sound pressure at the DRP that is measured using G_measured. Estimating sound pressure at the DRP using G_HATSproduces a wrong estimation of sound pressure at an eardrum 420, resulting in an insufficient level of air pressure leakage compensation at low frequencies when applying PEQ.

FIG. 6G illustrates example graph plot 1180 of an estimated DRP using G_MODEL, in one or more embodiments. A horizontal axis of the graph plot 1180 represents frequency expressed in Hz. A vertical axis of the graph plot 1180 represents sound pressure expressed in dB. The graph plot 1180 includes: (1) a first curve (“NFM”) representing sound pressure at the NFM, (2) a second curve (“estimated DRP”) representing an estimated sound pressure at the DRP using G_MODEL, and (3) a third curve (“G_MODEL”) representing a modeled individual transfer function G_MODEL, wherein G_MODEL=DRP-NFM.

Compared to using G_HATS, estimating sound pressure at the DRP using G_MODELproduces a much better estimation of sound pressure at an eardrum 420, resulting in a good level of air pressure leakage compensation at low frequencies when applying PEQ.

FIG. 6H illustrates example graph plot 1190 comparing the estimated DRP using G_MODELagainst an actual DRP, in one or more embodiments. A horizontal axis of the graph plot 1190 represents frequency expressed in Hz. A first vertical axis of the graph plot 1190 represents sound pressure expressed in dB. A second vertical axis of the graph plot 1190 represents error. The graph plot 1190 includes: (1) a first curve (“estimated DRP”) representing an estimated sound pressure at the DRP using G_MODEL, (2) a second curve (“actual DRP”) representing an actual sound pressure at the DRP, and (3) a third curve (“error”) representing a difference between the estimated DRP and the actual DRP.

FIG. 6I illustrates an example graph plot 1200 of modeled individual transfer functions G_MODELfor the 13 inserts, in one or more embodiments. A horizontal axis of the graph plot 1200 represents frequency expressed in Hz. A vertical axis of the graph plot 1200 represents sound pressure difference expressed in dB. The graph plot 1200 includes a first set of curves (“G”) representing modeled individual transfer functions G_MODEL(i.e., G_MODEL=DRP-NFM) for the 13 inserts. Compared to FIG. 6D, at low frequencies, the modeled individual transfer functions G_MODELfor the 13 inserts provide air pressure leakage compensation.

FIG. 7 is a flowchart of an example process 2000 for implementing PEQ, in one or more embodiments. Process block 2001 includes obtaining, via a microphone of a hearable device, one or more measurements of a first individual transfer function from a transducer of the hearable device to a first sound pressure at the microphone, wherein at least a portion of the hearable device is within proximity of an ear canal of an individual ear (e.g., inserted within the ear canal). Process block 2002 includes determining, based on the one or more measurements of the first individual transfer function, a second individual transfer function from the first sound pressure to a second sound pressure at an eardrum within the ear canal. Process block 2003 includes applying, based in part on the second individual transfer function, PEQ within the audio full range (low, mid and high frequencies) to an audio signal for reproduction via the hearable device.

In one embodiment, process blocks 2001-2003 may be performed by one or more components of the system 300 and/or the system 600.

FIG. 8 is a flowchart of an example process 2100 for air pressure leakage compensation at low frequencies, in one or more embodiments. Process block 2101 includes obtaining one or more measurements of a first sound pressure at a NF microphone of a hearable device, wherein at least a portion of the hearable device is within proximity of an ear simulator (e.g., a head and torso simulator). Process block 2102 includes obtaining one or more additional measurements of a second sound pressure at a drum reference point of the ear simulator. Process block 2103 includes personalizing a first individual transfer function (e.g., G_MODELor G_new) at low frequencies for an individual ear based on the one or more measurements of the first sound pressure, the one or more additional measurements of the second sound pressure, a fitted model, and a low shelving filter, wherein the first individual transfer function is used to estimate sound pressure at an eardrum within an ear canal of the individual ear when at least a portion of the hearable device is within proximity of the ear canal, and, at the low frequencies, the first individual transfer function compensates for air pressure leakage resulting from a lack of coupling between the hearable device and the ear canal.