Psychoacoustic study on active control system for kitchen hoods noise

Abstract

This study introduces a real-time shaping noise control approach for kitchen hoods using the filtered-E least mean square (FELMS) algorithm-based active noise control (ANC) system. The goal is to not only lower the noise effectively but also make the remaining sound more pleasant to human ears. Two existing noise control methods, including the filtered-X LMS (FxLMS) based, and the output-error filtered-U recursive LMS (OE-FURLMS) based ANC systems were compared. Both the amount of noise reduction and the sound quality measurement using five key factors: loudness, sharpness, roughness, tonality, and overall pleasantness were measured to evaluate performance. The test results show that the proposed system reduces kitchen hood noise effectively, spreads the noise reduction more evenly across different frequencies, and creates a sound that people find more pleasant compared to the traditional methods.

Keywords

active noise control centrifugal fan noise kitchen hood noise psychoacoustic analysis residual noise shaping

Introduction

Kitchen hoods are common appliances found in homes. They play an important role in improving indoor air quality and ventilation.^1,2 However, using noisy appliances like kitchen hoods for long periods can lead to unsafe noise levels that may harm health. These effects include hearing problems, sleep disturbances, reduced concentration, and even heart-related issues.^3,4 According to ref. 5, even short-term exposure to loud noise can affect mental well-being. In ref. 6, a study focused on kitchen workers showed that those with longer work experience had more problems with concentration, sleep, anxiety, and hearing. These show that it is crucial to reduce noise in kitchen environments.

Previous research has explored different ways to lower kitchen hood noise, mostly by changing the structure of the hood or using passive materials that absorb sound. For example, Maggiorana et al.⁷ used computer models to suggest structural changes that could lower kitchen hood noise. Ozturk and Erol⁸ created a model to reduce noise from the hood’s structure. Paramasivam et al.⁹ managed to reduce a specific type of noise by switching from diffuser vanes to guide vanes. Other studies also tried using sound-absorbing materials like micro-perforated panels,¹⁰ metal foams,¹¹ and special materials placed at the air inlet.¹² More recently, researchers have looked into ANC. Regala et al.¹³ used an ANC technique with the FxLMS algorithm on a kitchen hood and reduced the noise from 60.7 dBA to 54.3 dBA at the highest fan speed. While this method works well to reduce overall noise, it does not always make the sound more pleasant to human ears. In some cases, the remaining sound can still feel uncomfortable or may even hide important safety-related sounds.^14,15

To improve this, a shaping noise method with FELMS algorithm was developed. It uses special filters to shape the sound in a way that matches how humans hear, allowing for more pleasant and safer noise reduction.^16,17 This is especially useful for household appliances like kitchen hoods, where both effective noise reduction and user comfort are important.¹⁸ In addition to lowering the sound pressure level (SPL), researchers have also studied sound quality, which is how pleasant people perceive different types of noise. For example, with dishwashers, loudness was the main factor causing annoyance, followed by roughness and tonality.¹⁹ For washing machines, various sound features like sharpness, tonality, and fluctuation strength also played an important role in how the noise was judged.²⁰ In the case of kitchen hoods,²¹ found that loudness, tonal sounds, and sharpness were key to how people rated the noise. These studies use psychoacoustic models, which measure sound in a way that reflects human hearing and perception.^18,22,23

Recent studies have advanced robust ANC through improved adaptive algorithms. One approach proposed a nonlinear active function-based filtered-x recursive least squares (FxRLS) algorithm using thresholding and gain adaptation to enhance stability against impulsive noise.²⁴ Hermont et al. developed an FxLMS algorithm employing a hyperbolic tangent exponential kernel M-estimator to down-weight large errors and improve convergence under non-Gaussian conditions.²⁵ A further method introduced an algorithm editing method that combines multiple adaptive algorithms across iteration stages to accelerate convergence and improve steady-state performance.²⁶ Collectively, these works strengthen ANC robustness, efficiency, and adaptability in challenging acoustic environments.

Some researchers have already started combining ANC with psychoacoustic models. They used A-weighted filters to improve how the noise feels to listeners.^27–31 These studies showed that even if the overall SPL did not drop much, listeners still found the noise more pleasant. The FELMS-based systems were also tested in different settings, such as in factories or with MRI machine sounds.

This study aims to use the FELMS algorithm along with an adaptive filter to reduce kitchen hood noise in a way that considers how people actually hear sound. Along with the usual SPL and frequency measurements, we also look at psychoacoustic indicators such as loudness, sharpness, roughness, tonality, and overall pleasantness to judge how well the system works.

This paper is organized as follows. Section II explains the ANC methods and the proposed psychoacoustic system based on the FxLMS, FELMS and OE-FURLMS algorithms. Section III introduces the sound quality measures used in the study. Section IV presents the experiment setup, results, and analysis. Section V describes discussions for future works.

Feedforward ANC algorithms

Single-channel feedforward ANC (FFANC) system is composed of a reference sensor to capture the primary noise, a loudspeaker to output the anti-noise signal, and an error sensor to capture the residual signal. The anti-noise, with equal amplitude and 180° difference of the phase to the noise, is used to reduce the measured primary noise through the superposition theorem. Multiple sensors and loudspeakers can be also applied for multiple channels FFANC system.

FFANC with FXLMS algorithm

The fundamental structure for FFANC is the FxLMS algorithm with finite impulse response (FIR) control filter. The block diagram representation of the FxLMS algorithm is shown in Figure 1. The residual signal $e (n)$ can be calculated as follows:

e (n) = d (n) - y^{'} (n)

(1)

where

y^{'} (n) = y (n) * S (z)

represents the anti-noise signal,

d (n)

represents the primary disturbance, which is the primary noise

v (n)

filtered by the unknown acoustic path

P (z)

existing between the reference and the error sensors.

S (z)

and

F (z)

denote the secondary and acoustic feedback paths,

\hat{S} (z)

and

\hat{F} (z)

(acoustic feedback neutralization (AFN)) filters are their estimates obtained offline in advance. The reference sensor is applied to have

x (n)

, and the control filter

W (z)

is updated using the filtered reference and the error signals,

w (n + 1) = w (n) + μ x^{'} (n) e (n)

(2)

where

w (n) = {[w_{0} (n), w_{1} (n), \dots, w_{L - 1} (n)]}^{T}

is the weight vector of

W (z)

at time n,

μ

is the step size, and

x^{'} (n)

is the filtered input signal that can be computed as follows:

x^{'} (n) = \hat{s} (n) * x (n)

(3)

\hat{s} (n)

is the impulse response of

\hat{S} (z)

Figure 1.

Block diagram of FFANC with FxLMS algorithm.

The z-transform of (1) considering the presence of the acoustic feedback path $F (z)$ can be expressed as the equation below:

E (z) = P (z) V (z) - \frac{S (z) W (z) V (z)}{1 - F (z) W (z)}

(4)

Assuming that the paths $P (z)$ , $S (z)$ , and $F (z)$ are time-invariant and the ANC system has already converged, the error $E (z)$ can be equated to zero. Solving for the optimal control filter $W_{o p t} (z)$ yields³²:

W_{o p t} (z) = \frac{P (z)}{\hat{S} (z) + P (z) \hat{F} (z)}

(5)

In this study, the real-time performance of the FFANC with FxLMS algorithm is used as the baseline performance for comparison with the other algorithms due to its established stability, broad adoption for broadband noise sources.

FFANC with FELMS algorithm

The FELMS algorithm has been developed for the purpose of shaping the residual signal spectrum in ANC systems, providing a more customized response. Its block diagram is shown in Figure 2. Comparing it with the FxLMS algorithm, the key difference is the addition of the shaping filter $C (z)$ at the input signal path and at the residual signal path. The filtered input signal vector $x_{f i l t}^{'} (n)$ and the filtered residual signal $e_{f i l t} (n)$ can be calculated as follows:

x_{f i l t}^{'} (n) = x^{'} (n) * c (n)

(6)

e_{f i l t} (n) = e (n) * c (n)

(7)

where

c (n)

is the impulse response of

C (z)

, and

x^{'} (n)

can be calculated similarly to (3). The weight update equation for the FELMS algorithm becomes:

w (n + 1) = w (n) + μ x_{f i l t}^{'} (n) e_{f i l t} (n)

(8)

Figure 2.

Block diagram of FFANC with FELMS algorithm.

The frequency response of the shaping filter $C (z)$ can be designed according to the evaluation of the psychoacoustic models. So that the estimated error signal $e_{f i l t} (n)$ can be restrained to zero.

OE-FURLMS algorithm

The OE-FURLMS algorithm uses IIR-based control filter in the ANC system. The main advantage of an IIR filter over an FIR filter is its ability to provide better performance with less computational complexity.^32,33 The OE based ANC with FURLMS algorithm is shown in Figure 3.

Figure 3.

Block diagram of OE-FURLMS algorithm.

Assuming the control filter $w (n)$ of the OE-FURLMS algorithm-based ANC system can be expressed as follows:

w (n) = [\begin{array}{l} b (n) \\ a (n) \end{array}]

(9)

where

b (n)

and

a (n)

are the weight vectors of

B (z)

and

A (z)

at time

n

, and the reference signal

v^{'} (n)

can be expressed as the vector:

v^{'} (n) = [\begin{array}{l} x (n) \\ y (n - 1) \end{array}]

(10)

where

x (n)

is the input signal for the adaptive control filter

B (z)

, and

y (n - 1)

is the output signal vector serving as the input for the adaptive control filter

A (z)

. The OE-FURLMS algorithm can be calculated as follows:

b (n + 1) = b (n) + μ x^{'} (n) e (n)

(11)

a (n + 1) = a (n) + μ y^{\hat{'}}

(12)

where

x^{'} (n)

is the filtered signal, and the signal

y^{\hat{'}}

can be calculated as follows:

y^{\hat{\hat{'}}}

(13)

The anti-noise signal $y (n)$ , combining the output of the recursive adaptive control filters $B (z)$ and $A (z)$ , can be calculated as follows:

y (n) = b^{T} (n) x (n) + a^{T} (n) y (n - 1)

(14)

Performance metrics

The frequency-domain plot of the residual error signal is typically used to analyze the performance of the ANC system. Another common metric is the noise reduction measured using a SPL meter at the target quiet zone. Although these metrics help assess the ANC performance, when considering the human hearing sensitivity, the psychoacoustic models can provide better sound evaluation as follows.

Loudness

Loudness is the intensity sensation that corresponds to how louder or softer a sound is relative to a standard signal.²² From previous literature in sound quality investigation and psychoacoustic ANC in refs. 27–31 and 34, loudness is the most used metric in psychoacoustics. The total loudness, usually denoted as N but here referred to as $L$ so as not to confuse with the number of samples, can be computed using the equation below:

L = \int_{0}^{24 B a r k} L^{'} d ρ

(15)

wherein the total loudness

L

is taken as the integral of specific loudness

L^{'}

taken over the first 24 critical bands of hearing known as the Bark scale, represented by

ρ

²².

The specific loudness is referred to as

L^{'} = 0.08 {(\frac{E_{T Q}}{E_{0}})}^{0.23} [{(0.5 + 0.5 \frac{E}{E_{T Q}})}^{0.23} - 1] \frac{s o n e_{G}}{B a r k}

(16)

where

E

is the excitation signal,

E_{T Q}

is the excitation at threshold in quiet, and

E_{0}

is the excitation that corresponds to the reference intensity (also known as the threshold of hearing),

1 \times 1 0^{- 12}

Watts per square meters. The subscript G at the unit “sone” is to indicate that the loudness here is produced using the critical-band levels. A 1 kHz tone with 40 dB SPL generates loudness of 1 sone. The unit of measurement for specific loudness is sone/Bark.

Sharpness

The sharpness of narrowband sounds is primarily influenced by their spectral content and center frequency. Although the noise of the kitchen hood prototype in this study is a broadband signal, the residual noise resulting from ANC may affect the sharpness measurement. A reference sound that produces 1 acum, the unit of sharpness, is a narrowband noise with a width of one critical band, centered at a 60-dB 1 kHz signal.

The narrowband noise of 1 kHz measured sharpness increases from 1 to 2.5 acum when more noise is included at the higher frequencies, yielding a spectral width of 1 to 10 kHz.²² However, the sharpness decreases when the cut-off frequency is set to 1 kHz and the noise bandwidth is extended in the lower frequency spectrum producing a spectral width of 200 Hz to 1 kHz. From this, it can be deduced that the sharpness of a sound can be diminished by adding signals at the lower frequencies.

From the perspective of ANC, it can be interpreted as contradictory at first. However, sounds with lower frequencies can be perceived as softer than sounds with higher frequencies in their response. It is also to be noted that there are other psychoacoustic factors that influence sensory pleasantness aside from sharpness. The sharpness of a sound $S$ , can be calculated as follows:

S = 0.11 \frac{\int_{0}^{24 B a r k} L^{'} g (ρ) ρ d ρ}{\int_{0}^{24 B a r k} L^{'} d ρ}

(17)

In equation (17), the specific loudness is denoted by $L^{'}$ , $ρ$ is the critical-band rate or the Bark scale from 0 to 24, and $g (ρ)$ is a weighting factor dependent on the critical-band rate which is represented by the graph in Figure 4. It increases from unity to a value of 4 for a critical-band rate greater than 16 Bark. This can be expressed as the following equation²⁹:

g (ρ) = {\begin{cases} 1, & ρ \leq 16 \\ 0.066 e^{0.171 ρ}, & ρ > 16 \end{cases}

(18)

Figure 4.

The weighting factor for sharpness.²²

The response of the weighting factor considers the phenomenon where there is an increase in sharpness measurement of narrowband noises at high center frequencies.

Roughness

Another psychoacoustic model affecting the overall pleasantness of a sound is roughness. The human hearing response is limited to detecting changes in specific loudness along the critical-band rate. A roughness of 1 asper corresponds to a 1 kHz reference tone with a level of 60 dB, has 100% amplitude modulation, and modulation frequency 70 Hz. The model for roughness

R = 0.3 {f (\int_{0}^{24 B a r k} Δ L_{E} (ρ) d ρ)}_{\mod}

(19)

is based on the temporal resolution differences of human hearing and can be computed as a function of the degree of signal modulation, where the modulation frequency is denoted by

f_{\mod}

, and

Δ L_{E}

is the perceived modulation depth, quantifying how strongly amplitude (or frequency) modulation is perceived by the human auditory system.

Tonality

Tonality is another psychoacoustic metric that influences the quantitative measurement of sensory pleasantness. In computing the tonality, the spectral flatness measure (SFM) can be used to determine the tone-like characteristic of the signal.³⁴ The SFM can be calculated as follows:

S F M_{d B} = 10 \log_{10} \frac{G_{m}}{A_{m}}

(20)

where

G_{m}

is the geometric and

A_{m}

is arithmetic means of a signal of the power spectrum. The tonality coefficient

T

can be computed:

T = \min (\frac{S F M_{d B}}{S F M_{d B, \max}} ())

(21)

An entirely tone-like signal has the value of −60 dB while an SFM of 0 dB indicates a noise-like characteristic.

Pleasantness

In evaluating the ANC performance using psychoacoustic metrics, loudness, sharpness, roughness, and tonality are applied. In quantifying the overall human hearing perception, the model of sensory pleasantness

P

³⁵ can be expressed as follows:

P = e^{- 0.55 R} e^{- 0.113 S} (1.24 - e^{- 2.2 T}) e^{- {(0.023 L)}^{2}}

(22)

which considers the measurement of roughness

R

, sharpness

S

, tonality

T

, and loudness

L

listed in Table 1. Higher perceived pleasantness signifies a higher pleasant sound. A strong correlation exists between high pleasantness value and increased tonality, as the latter distinguishes tonal components from noise. Conversely, high pleasantness value is typically associated with lower levels of perceived loudness, roughness, and sharpness, indicating that these psychoacoustic attributes contribute negatively to the overall subjective evaluation of sounds.

Table 1.

Absolute values for the reference sounds in the psychoacoustic measurements.

Psychoacoustic metrics	Parameters of the reference sounds
Roughness, $R$	High-pass noise with lower limit of 2 kHz, $f_{\mod}$
	Hz with 100% modulation
	$L = 14$ sone
Sharpness, $S$	8 kHz sine tone
Sharpness, $S$	$L = 14$ sone
Tonality, $T$	500 Hz sine tone
Tonality, $T$	$L = 14$ sone
Loudness, $L$	1 kHz sine tone with a 40-dB level

Psychoacoustic models have a broad range of application scopes across engineering, audio technology, and perceptual research. These models aim to describe how humans perceive sound, rather than just its physical properties, and they are applied wherever perceived sound quality matters.

Considering the human hearing sensitivity in the ANC performance evaluation will give more insight into the effect of ANC application, particularly for consumer products such as the kitchen hood.

Experiments

This section shows the experimental setups, design considerations, and experimental results.

Experimental setups

The kitchen hood prototype, depicted in Figure 5, is modeled from commercialized kitchen hood, features four distinct sections (A, B, C, D) measuring 600 mm, 290 mm, 410 mm, and 100 mm, respectively. Section A is typically the hidden part when kitchen hoods are installed in a real environment. Section B houses the centrifugal fan, while Section C contains the anti-noise speaker sockets, and lastly, Section D is the air inlet of the kitchen hood, positioned directly above the user in practical installations. It is also to be noted that less than half of Section B to Section C is the only window for adjustment for placing the sensors and actuators, making the kitchen hood ANC as a short duct problem. The kitchen hood prototype has sound-absorbing materials installed in the linings of the duct frame and are represented by the hatched lines in Figure 5, for high frequencies noise reduction.

Figure 5.

Kitchen hood prototype.

The anti-noise speakers (Visaton B-80) are placed on the sides of Section C of the kitchen hood at a 45° orientation, facing downstream the error microphones. This orientation is done to lessen the acoustic feedback at the reference microphones. Several reference microphone configurations were investigated. In setup 1, five reference microphones were employed, as illustrated in Figure 6(a). Setup 2 utilized three reference microphones positioned on top of the removable middle PNC, as shown in Figure 6(b). These microphones were placed as close as possible to the centrifugal fan of the kitchen hood and connected in parallel to form a single-channel reference input. To minimize contamination of the reference signal, direct exposure to air turbulence from the fan was carefully avoided. All the reference and error microphones were covered by using nonwoven fabric. Besides, the error microphones are placed at the end of Section D, as it is the main noise source when kitchen hood is installed in a practical setting exposed directly above the user. The first setup for the error microphones is shown in Figure 6(c). Four microphones at the left and right opening outlets are connected in parallel to be the left and right error signals. The second setup is similar, but five error microphones are applied at left and right sides, revealed in Figure 6(d).

Figure 6.

Placements of (a) reference microphones setup 1, (b) reference microphones setup 2, (c) error microphones setup 1, and (d) error microphones setup 2.

The maximum noise reduction in feedforward ANC systems is also dependent on the coherence measurement between the reference and the error signals. Its relationship can be expressed as the equation below³²:

{N R l o g}_{10 (d x m a x}

(23)

where the maximum noise reduction is denoted as

{N R}_{\max}

, and the coherence value is denoted as follows:

C_{d x} (ω) = \frac{{| S_{d x} (ω) |}^{2}}{S_{d d} (ω) S_{x x} (ω)}

(24)

which ranges from 0 to 1. Besides,

S_{x x} (ω)

and

S_{d d} (ω)

are auto-power spectrum of signals measured at reference and error microphones, and

S_{d x} (ω)

is their cross-power spectrum. The higher the value of the coherence is, the lower the residual noise. For example, if the coherence

C_{d x} (ω)

can be up to 0.99, the expected noise reduction can reach 20 dB.

Four coherence measurements between different reference and error microphones setups are tested. By activating the kitchen hood with highest operating speed, the results are shown in Table 2. Comparing the coherence measurement of the various microphone setups, C₄ has the highest coherence, shown in Figure 7. Listed in Table 2 below are the average values of the measured coherence and estimated maximum reduction from (23). From Table 2, the developed setup C₄, yields a higher averaged coherence during frequency range from about 100 Hz to 1400 Hz, and has higher maximum noise reduction than the other setups. The noise of the kitchen hood without ANC is 60.5 dBA. The SPL measurement points for the kitchen hood are placed 8 cm away from the removable middle noise-absorbing material.

Table 2.

Coherence measurement.

Coherence	Microphones setup	Average coherence	Average theoretical maximum reduction in dB
C₁	Ref. Mic. Setup 1/Err. Mic. Setup 1	0.8422	8.0189
C₂	Ref. Mic. Setup 2/Err. Mic. Setup 2	0.8779	9.1328
C₃	Ref. Mic. Setup 2/Err. Mic. Setup 1	0.8779	9.1328
C₄	Ref. Mic. Setup 1/Err. Mic. Setup 2	0.8922	9.6738

Figure 7.

Coherence comparison.

Shaping filters design considerations

Three types of shaping filters are used for implementing the FELMS algorithm. They are (a) peaking filters, (b) Butterworth bandpass filter (BPF) based on A-weighting, and (c) an A-weighted digital IIR filter of 6th order. Peaking filters are used as shaping filters in this study as it is one of the most common digital filters used for equalization.³⁷ Since peaking filters introduce gain at the specified frequency, this will let the adaptive control filter see increased magnitude at the specified frequencies resulting to an increased ANC performance within those ranges.

The cascaded combination of shaping filters $H_{1} (z)$ and $H_{2} (z)$ , shown in Figure 8(a) will be used in the subsequent experiments, wherein the peak frequencies of 200 Hz and 1200 Hz for both shaping filters were retained, as well as the quality factor which affects the bandwidth of the shaping filter. The filter order for both the shaping filters $H_{1} (z)$ and $H_{2} (z)$ were 4^th order, and the gain for the shaping filter $H_{2} (z)$ was 40 dB. The use of a higher gain for the shaping filter targets further improvement in the ANC performance from 800 Hz frequency range. However, recognizing the increase in computational complexity and electrical delay when implementing cascaded filters, a single-peak filter $H_{3} (z)$ with peak frequency at 1200 Hz was also investigated in this study. The design parameters of the peaking filters are listed in Table 3. Other shaping filters studied in this paper include the digital A-weighted (6^th order) filter and the Butterworth BPF (2^nd order) with passband frequencies of 400 Hz to 8 kHz and gain 30 dB, shown in Figure 8(b). While A-weighting inherently attenuates lower frequencies, its incorporation into the BPF design allows for exploration of its impact on ANC performance, given that the kitchen hood noise has significant levels in the lower frequency ranges.

Figure 8.

Magnitude response of (a) peak shaping filters and (b) digital A-weighted filter and BPF with 30 dB gain.

Table 3.

Parameters for peaking filters used as shaping filters.

Parameters	$H_{1} (z)$	$H_{2} (z)$	$H_{3} (z)$
Peak frequency, $f_{o}$	200 Hz	1200 Hz	1200 Hz
Quality factor, Q	$10$	$0.25$	$1.5$
Filter order	4	4	2
Gain, G	25 dB	40 dB	45 dB

Results

The filter order significantly affects the performance of the ANC system. For the FELMS algorithm employing cascaded shaping filters, the maximum stable FIR control filter length is 250 taps, while for non-cascaded shaping filters (including the single-peak, bandpass, and A-weighted digital filters), the maximum stable length is 320 taps. In the case of the FELMS algorithm utilizing an IIR control filter, the maximum stable lengths are 160 and 190 for the cascaded and non-cascaded shaping filter implementations, respectively. The initial weights of the FIR and IIR control filters are pre-trained using Matlab. The detailed parameters are listed in Table 4.

Table 4.

Summary of parameters for ANC implementation.

Algorithm	Filter length	Step size
FxLMS with AFN	450	$2 \times 10^{- 7}$
OE-FURLMS	260	$2 \times 10^{- 7}$
FELMS using FIR control filter (with cascaded shaping filters)	250	$1 \times 10^{- 10}$
FELMS using IIR control filter (with cascaded shaping filters)	160	$4 \times 10^{- 10}$
FELMS using FIR control filter (with non-cascaded shaping filters)	320	$1 \times 10^{- 10}$
FELMS using IIR control filter (with non-cascaded shaping filters)	190	$2 \times 10^{- 9}$

In Figure 9, the horizontal axis represents frequency, while the left vertical axis shows the magnitude of the kitchen hood noise. The right vertical axis corresponds to the coherence values. The coherence curve (gray line) in Figure 9 indicates that the experimental setup C₄ provides sufficient coherence within the frequency range of 100–800 Hz, which corresponds to the main power region of the kitchen hood noise.

Figure 9.

Coherence (gray line) and comparison of traditional FxLMS and OE-FURLMS ANC systems with FELMS ANC using adaptive (a) FIR and (b) IIR filter.

As seen from Figure 9(a), the ANC with FELMS using adaptive FIR control filter has improved performance starting from 530 Hz to 1600 Hz, except for the one with single-peak shaping filter, wherein its improved performance is only from 800 Hz to 1600 Hz. The trade-off in its performance at 800 Hz below is also higher than that of the other shaping filters. The region in which a trade-off in performance can be seen for the other shaping filters is in the 150 Hz to 350 Hz frequency range. On the other hand, the performance of FELMS using adaptive IIR control filter, shown in Figure 9(b), has a greater reduction at 400 Hz to 1600 Hz frequency range except for the FELMS using cascade combination of shaping filters whose improved performance starts at 500 Hz. From these observations from the frequency response of the ANC ON conditions, the implementation shows better results for adaptive IIR control filter. This can be attributed to the inherent capability of an adaptive IIR filter to model the complete feedback path, and ability to model more complicated paths. While the traditional ANC with FxLMS and OE-FURLMS have the advantage in performance the lower frequencies ranging from 150 Hz to 400 Hz, the bandwidth of improved performance particularly for the FELMS using adaptive IIR filter is larger than that of the traditional algorithms. A summary of the SPL measurements in dBA, recorded with the TES-1358 Class-1 sound level meter, is presented in Table 5.

Table 5.

Summary of SPL measurement.

ANC algorithm	SPL in dBA (reduction)
ANC OFF	60.4
FxLMS w/AFN	55.1 (5.3)
OE-FURLMS w/o AFN	53.7 (6.7)

Shaping filter variation	SPL in dBA
Shaping filter variation	FIR filter	IIR filter
Cascaded combination	58.3 (2.1)	56.5 (3.9)
Single-peak filter (1200 kHz, G = 45 dB, Q = 1.5)	57.7 (2.7)	55.5 (4.9)
Digital A-weighted IIR filter (G = 30 dB)	57.2 (3.2)	56.7 (3.7)
BPF (G = 30 dB)	57.4 (3)	55.9 (4.5)

To further evaluate the performance of the FFANC algorithm various conditions are recorded at the SPL measurement point. The measurements for the psychoacoustic models: loudness, sharpness, roughness, tonality, and overall pleasantness were calculated for each recorded file.

By examining the psychoacoustic models, the results are depicted in Table 6. It shows that the OE-FURLMS algorithm demonstrates the highest performance in terms of psychoacoustic loudness measurements, exhibiting an average difference of 2 sones compared to other FFANC algorithms and 6.3 sones compared to the ANC OFF. The sharpness value remains the lowest, due to the uneven frequency response introduced by ANC compared to the spread of the response of a broadband noise. In the meantime, FELMS algorithm with the control filter by IIR structure shows the similar pleasantness measurement with the OE-FURLMS algorithm.

Table 6.

Summary of psychoacoustic measurement value.

	Loudness (sones)	Sharpness (acum)	Roughness (aspers)	Tonality	Pleasantness
ANC OFF	23.0229	1.2630	0.0957	0.4498	0.5396
FXLMS	18.7591	1.4483	0.0917	0.4276	0.5694
OE-FURLMS	16.7243	1.4925	0.0751	0.4491	0.6066
FELMS FIR (cascaded)	22.1816	1.2540	0.0715	0.1277	0.4506
FELMS IIR (cascaded)	18.6829	1.4057	0.0791	0.4373	0.5826
FELMS FIR (single peak, 1200 Hz)	19.3302	1.3692	0.0789	0.0013	0.4417
FELMS IIR (single peak, 1200 Hz)	19.0718	1.4185	0.0810	0.4314	0.5733
FELMS FIR (A-weighted, G = 30 dB)	19.0467	1.3672	0.0875	0.0014	0.4449
FELMS IIR (A-weighted, G = 30 dB)	18.1456	1.4125	0.0619	0.4417	0.5964
FELMS FIR (BPF, G = 30 dB)	19.8266	1.3308	0.0958	0.0017	0.4450
FELMS IIR (BPF, G = 30 dB)	18.4638	1.3936	0.0823	0.4402	0.5865

Comparing the FELMS implementations, the utilization of an IIR control filter shows overall better performance than an FIR control filter. In terms of overall pleasantness, the OE-FURLMS algorithm and the FELMS system using an IIR control filter with A-weighted digital shaping filter of 30 dB gain achieve the highest value. The difference in pleasantness between these two systems is only 0.0102. By the way, the computational complexity of OE-FURLMS is higher than FELMS IIR. This means OE-FURLMS may be not suitable to be realized in practical implementation because of the causality constraint.

To evaluate the global noise reduction and analyze the distribution of ANC performance across the target quiet zone, multiple recordings were conducted for both ANC OFF and ON conditions for the FxLMS algorithm, the OE-FURLMS algorithm, and the FELMS system utilizing an adaptive IIR control filter with an A-weighted digital filter. The plots illustrate the reduction in sound levels of the recorded audio in dB. The equation used to calculate the power in dB is below:

P_{o w e r} = 10 \log_{10} [\frac{1}{N} \sum_{n = 1}^{N} y^{2} (n)]

(25)

where

P_{o w e r}

is the power in dB, N is the number of samples, and

y (n)

is the recorded signal. The recording points are illustrated in Figure 10. The quiet zone measurements of FxLMS, OE-FURLMS and OE-FELMS algorithms are plotted in Figure 11(a)–(c), respectively.

Figure 10.

Quiet zone recording points.

Figure 11.

Global noise reduction (dBA) plots of (a) FxLMS algorithm, (b) OE-FURLMS algorithm, and (c) FELMS using adaptive IIR filter (digital A-weighted filter as shaping filter) algorithm.

Obviously, the FELMS algorithm (Figure 11(c)) shows the most even distribution of noise reduction. While the overall global noise reduction for the FELMS is approximately 3–5 dBA, its even distribution of noise reduction and high perceived pleasantness value of 0.5964—only 0.0102 less than the highest value achieved by the traditional OE-FURLMS—indicate that the FELMS, utilizing an adaptive IIR control filter with an A-weighted digital filter, represents the most balanced ANC application for the broadband kitchen hood noise.

Discussions

The experimental results clearly demonstrate the effectiveness of the proposed FELMS-based psychoacoustic ANC system in mitigating broadband kitchen hood noise while improving perceptual sound quality. Across all tested configurations, the FELMS algorithm, particularly when implemented with an adaptive IIR control filter and an A-weighted digital shaping filter, exhibited the most balanced performance in terms of both objective noise reduction and subjective pleasantness.

From the SPL measurements, the traditional FxLMS and OE-FURLMS algorithms achieved reductions of 5.3 dBA and 6.7 dBA, respectively, confirming their established efficiency in active noise control applications. However, while OE-FURLMS achieved the highest absolute reduction, the FELMS system using the IIR control filter achieved a comparable 4.9 dBA reduction with a more uniform spatial distribution of attenuation, as revealed by the quiet zone plots. This even distribution indicates better robustness of the FELMS system to spatial variations in the noise field—an important consideration for practical kitchen hood installations where users are positioned directly below the air inlet.

In terms of psychoacoustic metrics, the FELMS algorithms delivered favorable results. The FELMS using the IIR control filter with the A-weighted shaping filter achieved a pleasantness value of 0.5964, which is only 0.0102 lower than the OE-FURLMS algorithm, despite slightly lower SPL reduction. This demonstrates that the FELMS system achieves a superior perceptual outcome relative to its physical attenuation level. The FELMS system also maintained relatively low sharpness (≈1.41 acum) and roughness (≈0.06–0.08 asper), both of which are desirable for pleasant residual sound. In contrast, the FxLMS algorithm produced a higher sharpness and less perceptually balanced residual noise. These results confirm that incorporating psychoacoustic weighting through shaping filters effectively improves not only the quantitative attenuation but also the qualitative listening experience.

Comparative analysis among different shaping filters further highlights the influence of psychoacoustic design on ANC performance. The A-weighted digital filter offered the best compromise between noise attenuation and sound pleasantness, while cascaded peaking filters achieved higher attenuation in specific frequency bands but introduced slight trade-offs in low-frequency performance. The FELMS system thus enables flexible control of frequency-dependent attenuation to target perceptually important regions, offering an adaptive way to shape the residual sound according to human hearing sensitivity.

Regarding coherence, the C₄ configuration (Reference Setup 1 + Error Setup 2) achieved the highest average coherence of 0.8922, corresponding to a theoretical maximum reduction of 9.67 dB. This result validates the chosen microphone placement strategy, showing that spatially distributed reference microphones effectively capture the broadband fan noise with minimal turbulence interference. The high coherence across 100–1400 Hz correlates well with the observed broadband improvement in the FELMS frequency response.

Overall, the experiments verify that the FELMS algorithm with adaptive IIR control filter and A-weighted shaping filter provides the most balanced trade-off between attenuation level, spectral evenness, and perceived pleasantness, outperforming traditional FxLMS and approaching the performance of OE-FURLMS but with lower computational complexity and better robustness to spatial variations. These findings suggest that the FELMS-based system offers a practical and perceptually optimized ANC solution for real-world kitchen hood applications.³⁶

Conclusions

Among the algorithms used, the OE-FURLMS exhibited the highest reduction of 6.7 dBA. However, based on the quiet zone plots, the OE-FURLMS algorithm exhibited uneven global noise reduction and dead-spot regions where no reduction was measured. The global noise reduction plot of the FELMS, utilizing an adaptive IIR control filter with an A-weighted digital filter of 30 dB gain, exhibited the most even distribution of noise reduction compared to the FxLMS and OE-FURLMS algorithms. The FELMS also achieved a high perceived loudness and pleasantness value, closely matching that of the OE-FURLMS, while maintaining a more balanced noise reduction profile.

Footnotes

ORCID iD

Cheng-Yuan Chang

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Gao

, et al. A pilot study on characterization of air pollutants from typical Chinese cooking with clean fuels without and with range hood usage. Atmos Pollut Res 2022; 13(9): 101537.

Sun

Wallace

. Residential cooking and use of kitchen ventilation: the impact on exposure. J Air Waste Manag Assoc 2021; 71(7): 830–843.

Pretzsch

Seidler

Hegewald

. Health effects of occupational noise. Curr Pollution Rep 2021; 7(3): 344–358.

World Health Organization . Compendium of WHO and other UN guidance on health and environment. WHO/HEP/ECH/EHD, 2022. https://www.who.int/tools/compendium-on-health-and-environment/environmental-noise/#:∼:text=Excessive-noise-can-cause-annoyance%3B-in-addition-research,as-adverse-birth-outcomes-and-mental-health-problems

Tao

Chai

Kou

, et al. Understanding noise exposure, noise annoyance, and psychological stress: incorporating individual mobility and the temporality of the exposure-effect relationship. Appl Geogr 2020; 125: 102283.

Bilge

. Effects of occupational noise pollution on kitchen workers. An underestimated environmental health issue. Global Journal on Advances in Pure & Applied Sciences. 2013; 1(1): 271–274.

Maggiorana

Rossi

Morettini

, et al. Measurement and modelling techniques to approach the problem of noise reduction of domestic range hood. In: Euronoise. Naples, Italy, May, 2003, p. 1. 19–21.

Öztürk

Erol

. Numerical and experimental studies on the structure-borne noise control on a residential kitchen hood. Int J Acoust Vib 2013; 18(1): 3–6.

Paramasivam

Rajoo

Romagnoli

. Suppression of tonal noise in a centrifugal fan using guide vanes. J Sound Vib 2015; 357: 95–106.

10.

Wang

Mai

, et al. Structure design of low-frequency broadband sound-absorbing volute for a multi-blade centrifugal fan. Appl Acoust 2020; 165: 107315.

11.

Mao

. Experimental investigation of metal foam for controlling centrifugal fan noise. Appl Acoust 2016; 104: 182–192.

12.

Huang

Zhang

, et al. Numerical simulation of aerodynamic noise and noise reduction of range hood. Appl Acoust 2021; 175: 107806.

13.

Regala

Chang

C-Y

Mei

M-C

. Active noise control for kitchen hood. In: INTER-NOISE and NOISE-CON congress and conference proceedings, institute of noise control engineering, 20-23 Aug, Tokyo, Japan, 2023, pp. 1397–1404.

14.

Kuo

Yang

. Broadband adaptive noise equalizer. IEEE Signal Process Lett 1996; 3(8): 234–235.

15.

Kuo

. Principle and application of adaptive noise equalizer. IEEE Trans Circuits Syst II 1994; 41(7): 471–474.

16.

Kajikawa

Gan

W-S

Kuo

. Recent advances on active noise control: open issues and innovative applications. APSIPA Trans Signal Inf Process. 2012; 1(1): 1–21.

17.

Kuo

Tsai

. Residual noise shaping technique for active noise control systems. J Acoust Soc Am 1994; 95(3): 1665–1668.

18.

Fastl

. Psychoacoustic basis of sound quality evaluation and sound engineering. In: The thirteenth international congress on sound and vibration, 2-6 July, Vienna, Austria, 2006.

19.

Atamer

Ercan Altinsoy

. Sound quality of dishwashers: annoyance perception. Appl Acoust 2021; 180: 108099.

20.

Moravec

Ižaríková

Liptai

, et al. Development of psychoacoustic model based on the correlation of the subjective and objective sound quality assessment of automatic washing machines. Appl Acoust 2018; 140: 178–182.

21.

Wang

Chen

Cheng

, et al. Specific psychacoustic metrics and their application to range hoods. Appl Acoust 2021; 179: 108079.

22.

Zwicker

Fastl

. Psychoacoustics: facts and models. 3rd. ed. [Repr.]. in Springer series in information sciences, no. 22. Springer, 2010.

23.

Fastl

. The psychoacoustics of sound-quality evaluation. Acustica 1997; 83(5): 754–764.

24.

Turpati

Roy

Swamy

KCT

, et al.

Robust non-linear active function-based FxRLS for impulsive active noise control

IEEE Access 2024; 12: 43222–43234.

25.

Hermont

IKDS

Flores

De Lamare

. Robust adaptive filtering with the hyperbolic tangent exponential Kernel M-Estimator function for active noise control. IEEE Access 2025; 13: 148522–148532.

26.

Song

Dong

Yang

, et al. Research and application of the algorithm editing method for improving active noise control performance. Journal of Low Frequency Noise, Vibration and Active Control 2025; 44(3): 1855–1875.

27.

Wang

Gan

Chong

. Psychoacoustic hybrid active noise control system. In: 2012 IEEE international conference on acoustics, speech and signal processing (ICASSP), 25-30 March, Kyoto, Japan, 2012. IEEE, pp. 321–324.

28.

Bao

Panahi

. Using A-weighting for psychoacoustic active noise control. In: 2009 annual international conference of the IEEE engineering in medicine and biology society, 3-6 Sept., Minneapolis, MN, USA, 2009. IEEE, 2009, pp. 5701–5704.

29.

Bao

Panahi

. Psychoacoustic active noise control with ITU-R 468 noise weighting and its sound quality analysis. In: 2010 annual international conference of the IEEE engineering in medicine and biology, 31 Aug.-4 Sept., Buenos Aires, Argentina, 2010. IEEE, 2010, pp. 4323–4326.

30.

Bao

. A perceptually motivated active noise control design and its psychoacoustic analysis. ETRI J 2013; 35(5): 859–868.

31.

Bao

Panahi

. A novel feedforward active noise control structure with spectrum-tuning for residual noise. IEEE Trans Consum Electron 2010; 56(4): 2093–2097.

32.

Kuo

Morgan

. Active noise control systems: Algorithms and DSP implementations. John Wiley & Sons, Inc., 1996.

33.

Johnston

. Transform coding of audio signals using perceptual noise criteria. IEEE J Sel Area Commun 1988; 6(2): 314–323.

34.

Wang

Ren

. Convergence analysis of the filtered-U algorithm for active noise control. Signal Process 1999; 73(3): 255–266.

35.

Aures

. Berechnungsverfahren fur den sensorischen Wohlklan beliebiger Schallsignale (A procedure for calculating sensory pleasantness of various sounds). Acta Acustica united Acustica 1985; 59(2): 130–141.

36.

Kuo

Tsai

. Acoustical mechanisms and performance of various active duct noise control systems. Appl Acoust 1994; 41(1): 81–91.

37.

Orfanidis

. High-order digital parametric equalizer design. J Audio Eng Soc. 2005; 53(11): 1026–1046.