Section 1 Signal Denoising

#### **Chapter 1**

## Introductory Chapter: Signal and Image Denoising

*Mourad Talbi*

#### **1. Introduction**

Both signal and image are unfortunately degraded by different factors that affect as noise during acquisition or transmission. Those noisy effects decrease the performance of visual and computerized analysis. It is clear that cancelling the noise from the signal facilitates its processing. The denoising process can be described as to cancel the noise while retaining and not distorting the quality of processed signal or image [1–4]. The conventional manner of denoising for noise cancelling consists in applying a band/low-pass filter with cut-off frequencies. Though conventional filtering methods are capable to suppress a relevant of the noise, they are not able when the noise is located in the band of the signal to be processed. Consequently, numerous denoising techniques were introduced in order to overcome this problem. The algorithms and processing approaches employed for signals can be also used for images and this is due to fact that an image is viewed as a two-dimensional signal. Consequently, the signal processing methods for one-dimensional signals can be adapted for processing two-dimensional images. Due to the fact that the origin and non-stationarity of the noise corrupt the signal, it is not easy to model it. Nevertheless, when the noise can be considered as stationary, an empirically recorded signal that is degraded by an additive noise is formulated as follows [1]:

$$\mathbf{y}(j) = \mathbf{x}(j) + \sigma \cdot \varepsilon(j), j = \mathbf{0}, \mathbf{1}, \dots, n - \mathbf{1} \tag{1}$$

With *y j*ð Þ is the noisy signal, *x j*ð Þ is the clean signal and εð Þ*j* are independently normal random variables and σ designates the level noise corrupting ð Þ*j* . The noise can be modeled as stationary independent zero-mean white Gaussian variables [5, 6]. If this model is employed, the objective of noise cancellation consists in reconstructing *x j*ð Þ from a finite set of *y j*ð Þ values without considering a particular structure for the signal. The commonly used approach for noise cancellation models noise as a high frequency signal corrupting in additive manner, the clean signal. These high frequencies can be bringing out employing Fourier transform, ultimately cancelling them by an adequate filtering. This noise cancelling method is conceptually clear and efficient since it is depending only on computing DFT (Discrete Fourier Transform) [7]. However, there is some issue that should be considered. The most important having same frequency since the noise owns important information in the original signal. Filtering out these frequency components introduces noticeable information loss of the desired signal. It is clear that a technique is strongly needed for preserving the prominent part of the signal having relatively high frequencies as the noise has. As an example, the wavelet-based noise removal approaches have provided this prominent part conservation. De-noising of natural images degraded by Gaussian Noise employing wavelet based denoising techniques are very efficient due to the fact that it is able to capture the energy of a signal in few energy transform values. The wavelet de-noising scheme thresholds the wavelet coefficients arising from the standard discrete wavelet transform [8]. In Ref. [8], it was introduced to investigate the suitability of different wavelet bases and the size of different neighborhood on the performance of image denoising techniques in term of peak signal-to-noise ratio (PSNR) [8].

In Ref. [9], Di Liu and Xiyuan Chen introduced an image denoising technique applying an ameliorated bidimensional empirical mode decomposition (BEMD) and using soft interval thresholding. At first step, a noise compressed image is constructed. After that, this noise compressed image is decomposed by applying BEMD into a series of intrinsic mode functions (IMFs), which are separated into signal-dominant IMFs and noise-dominant IMFs employing a similarity measure based on ℓ2-norm and a probability density function, and a soft interval thresholding is employed in adaptive manner for cancelling the noise inherent in noise-dominant IMFs. The denoised image is finally obtained *via* the combination of the signal dominant IMFs and the denoised noise dominant IMFs. The performance of this image denoising technique [1] was applied to multiple images with different sorts of noise, and the results obtained from the application of this technique [1] were compared to those obtained from the application the some traditional techniques in different noisy environments. Simulation results in terms of peak signal-to-noise ratio, mean square error, and energy of the first IMF, proved that this denoising technique [9] outperforms the other denoising techniques.

Hybridization of the BEMD with denoising approaches has been introduced in the literature as an efficient image denoising technique.

In Ref. [10], Student's probability density function was proposed in the calculation of the Mean Envelope of the data during the BEMD sifting process for making it robust to values that are far from the mean. The obtained BEMD was named tBEMD. To prove the efficiency of the tBEMD, many image denoising approaches were used in the tBEMD field. Among these approaches, we can mention the discrete wavelet transform (DWT), fourth-order partial differential equation (PDE), linear complex diffusion process (LCDP), and nonlinear complex diffusion process (NLCDP). For experiments, a standard digital image and two biomedical images are considered. The original images are degraded by additive Gaussian Noise with three diverse levels. Based on PSNR (peak signal-to-noise ratio), the obtained results show that DWT, PDE, LCDP, and NLCDP, all perform better in the tBEMD domain compared to the conventional BEMD domain. Moreover, the tBEMD is faster than conventional BEMD in case where the noise level is low. However, in case where it is high, the calculation cost in terms of processing time is similar. The efficiency of the presented approach makes it promising for clinical applications.

This book is intended for engineers and researchers in the fields of signal and image processing. Indeed, this book deal with a large number of signal and image denoising techniques. These techniques include an innovative image denoising approaches.

#### **2. Examples of signal and image denoinsing**

In this section, we will give some examples of signal and image denoising obtained from the application of the discrete wavelet transform (DWT).

*Introductory Chapter: Signal and Image Denoising DOI: http://dx.doi.org/10.5772/intechopen.112689*

#### **Figure 1.**

*An example of PCG denoising using DWT [1]: (a) clean PCG signal, (b) noisy PCG signal, (c) denoised PCG signal, (d) difference between the original and the denoised signal.*

#### **2.1 Phonocardiogram denoising**

The acoustical vibrations records from the heart, acquired through microphones from human chest, named phonocardiogram (PCG), consist of both the murmurs and the heart sounds. Those records of acoustic signals are unfortunately corrupted by diverse factors which effecting as noise. Those effects cause the decreasing of the performance of visual and computerized analysis [1, 11, 12].

**Figure 1** illustrates an example of PCG denoising using DWT.

According to **Figure 1**, the noise is considerably reduced and the waveform of the original signal is conserved because the difference between the original and the denoised signals is very small. Consequently, the denoising technique based on thresholding in DWT domain and applied in Ref. [1], shows its performance in noise reduction while conserving the information contained in the original PCG signal.

**Figure 2.**

*An example of medical image denoising by applying thresholding in the DWT domain: (a) a noisy medical image with PSNR* ¼ 62 *dB, (b) denoised image obtained from the application of a denoising technique based on thresholding in the DWT domain.*

#### **2.2 Image denoising**

All digital images are degraded by different types of noise during their acquisition and transmission. As an example of these images, the medical one is likely disturbed by a complex sort of addition noise depending on the devices that are employed for capturing or storing it. There are no medical imaging devices that are noise free. The most commonly employed medical images are produced from MRI and CT equipment [1]. The additive noise corrupting medical image causes the reducing of the visual quality that complicates diagnosis and treatment.

**Figure 2** illustrates an example of a medical image denoising using DWT.

A noise-added medical image and its denoised one obtained from employing a wavelet denoising technique are illustrated in **Figure 2**. The added noise has Gaussian distribution, and symlet 6, decomposition level of two, hard thresholding were used as the parameters for the application the wavelet-based denoising technique [1].

#### **3. Conclusion**

In this chapter, we deal with a number of signal and image denoising techniques existing in the literature. We also give two examples of signal and image denoising by applying the denoising techniques based on thresholding in the Discrete Wavelet Transform domain. Those examples show the performance of these denoising techniques.

#### **Author details**

Mourad Talbi Laboratory of Nanomaterials and Systems for Renewable Energies (LaNSER), Center of Researches and Technologies of Energy (CRTEn), Tunis, Tunisia

\*Address all correspondence to: mouradtalbi196@yahoo.fr

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Ergen B. Signal and image denoising using wavelet transform. In: Advances in Wavelet Theory and their Applications in Engineering, Physics and Technology. London, UK: InTech; 2012

[2] Chen G, Bui T. Multiwavelets denoising using neighboring coefficients. IEEE Signal Processing Letters. 2003; **10**(7):211-214

[3] Portilla J, Strela V, et al. Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Transactions on Image Processing. 2003; **12**(11):1338-1351

[4] Buades A, Coll B, et al. A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation. 2006;**4**(2):490-530

[5] Moulin P, Liu J. Analysis of multiresolution image denoising schemes using generalized Gaussian and complexity priors. IEEE Transactions on Information Theory. 1999;**45**(3):909-919

[6] Alfaouri M, Daqrouq K. ECG signal denoising by wavelet transform thresholding. American Journal of Applied Sciences. 2008;**5**(3):276-281

[7] Wachowiak MP, Rash GS, et al. Wavelet-based noise removal for biomechanical signals: A comparative study. IEEE Transactions on Biomedical Engineering. 2000;**47**(3):360-368

[8] Kother Mohideen S, Perumal SA, Sathik MM. Image de-noising using discrete wavelet transform. IJCSNS International Journal of Computer Science and Network Security. 2008;**8**(1):2

[9] Liu D, Chen X. Image denoising based on improved bidimensional empirical mode decomposition thresholding

technology. Multimedia Tools and Applications. 2019;**78**:7381-7417. DOI: 10.1007/s11042-018-6503-6

[10] Lahmiri S. Image denoising in bidimensional empirical mode decomposition domain: The role of Student's probability distribution function. Healthcare Technology Letters. 2016;**3**(1):67-71

[11] Akay M, Semmlow J, et al. Detection of coronary occlusions using autoregressive modeling of diastolic heart sounds. IEEE Transactions on Biomedical Engineering. 1990;**37**(4): 366-373

[12] Ergen B, Tatar Y, et al. Timefrequency analysis of phonocardiogram signals using wavelet transform: A comparative study. Computer Methods in Biomechanics and Biomedical Engineering. 2010;**99999**(1):1-1

#### **Chapter 2**

## Sound Absorption Measurement: Alpha Cabin and Impedance Tube

*Pavel Němeček*

#### **Abstract**

The stage of development of absorbent materials, when necessary to verify their properties in relation to established requirements, plays one of the key challenges in current research. Nowadays, experimentation represents the only reliable way to quantify sound absorption. Thus, the determined sound absorption coefficient is used to compare individual development variants, and also, it is used in a selection of material from the commercial offer. Therefore, the main part of research is devoted to measurements in the impedance tube and in the alpha cabin, because these procedures play one of the most challenging roles in practice. All used experimental methods are based on the theory about transformation of sound energy into other forms of energy in the material. Nevertheless, the physical nature of sound absorption and individual measurement principles are not covered in this chapter, nor are any sound insulation measurements. It deals solely with the sound absorption and determination of the sound absorption coefficient. As a results, this chapter further summarizes basic information on a sound absorption measurement, and mainly, focuses on practical recommendations as well as applicability of results. First and foremost, these individual procedures may represent a considerable international overlap in the field.

**Keywords:** sound absorption coefficient, impedance tube, alpha cabin, sound absorption measurement, reverberation time

#### **1. Introduction**

Sound absorption measurement serves as an activity associated with the design, verification and application of suitable materials for solving an acoustic situation of enclosed spaces. These materials have a specific composition, may be applied to large surfaces, and their properties must typically meet many requirements (thermal insulation, mechanical resistance, low dirtiness, compactness, etc.). Absorbent materials are used in building acoustics, the automotive industry and everywhere where humans and noise sources are in a confined space.

This chapter covers the experimental determination of the sound absorption coefficient of industrially produced materials or samples in the stage of development, which are intended for the reduction, or regulation of noise in closed spaces. The chapter also contains a brief description of basic comparison methods and a more

detailed description of two laboratory methods, i.e. the measurement of sound absorption in an impedance tube and in an alpha cabin. The goal is to provide a basic description of experimental methods, their comparison, evaluation and determination of accuracy.

In practice:


### **2. Basics of measuring sound absorption**

Sound absorption is the ability of a material environment to absorb coming sound. It is a process in which sound energy falling on a sample of material is transformed into another form, mainly thermal energy. In the ideal case, the sound energy that encounters the sample (WINBOUND) is partly reflected (WREFLECTION), partly transmitted through the sample (WTRANSMISSION) and partly absorbed into the sample (WABSORPTION). Applies to:

WINBOUND = WREFLECTION + WABSORPTION + WTRANSMISSION.

When experimentally investigating absorption, certain conditions need to be met so the equation above can be applied. The conditions are:


There are additional requirements for experimental methods:


To the methods used, it should also be mentioned:


#### **3. Physical and metrological basis of sound absorption measurement**

A measurement can be considered as the only objective option to determine the sound absorption coefficient α. Other options, such as simulations and modeling in a virtual environment, face problems with an accurate determination of the boundary conditions and with the definition of the internal structure of the material. Validation of materials intended to solve a sound situation in closed spaces requires a determination of the sound absorption factor by experiment, therefore on a real part by objective methods. Requirements are set, for example, by the automotive industry or the building materials industry. Knowledge of the sound absorption coefficient makes it possible to model sound propagation in closed spaces using special software.

Measuring the sound absorption coefficient is a topic mainly for:

1. Independent testing laboratories,


In the next part of the text, 4 measurement methods are described. Two of them are very simple and serve more for a comparison to the reference sample, the other two ones are the most used in practice. A method, which is used mainly by independent testing laboratories and complies the international standards be briefly mentioned.

The following points apply to all described methods:


#### **3.1 Approximate and comparative methods of measuring sound absorption**

In this chapter are described simple methods of sound absorption measurement. Their description serves rather to complement the technical and historical context of sound absorption measurements. It is based on conditions where it is not possible or preferred to use more advanced methods. These methods:


These methods cannot be characterized as laboratory methods for an objective determination of sound absorption. They only serve as quick comparison tests in the optimization of the composition of absorbing layers and can be used directly at the place of application.

#### *3.1.1 Tone burst method*

This method is currently used very rarely. However, in the available literary sources, it is still found in various methodological variants [1–3], it is popular with students who use it in a case when sound absorption is only one of the properties they investigate on materials.

This is a simple method based on the idea that when a sound wave strikes a sample at a certain angle, a reflected wave propagates at the same angle with energy reduced by the absorbed energy. The calculation is based on processing the ratio of incident energy and reflected energy.

The measurement takes place in a space that is as anechoic as possible, ideally using a directional microphone and a directional speaker.

1.Measurement step: a signal with sufficient energy and bandwidth is applied to the speaker and the sound pressure level Lp,d (its frequency spectrum) is measured at the distance A between the speaker and the microphone.

2.Measurement step: a testing object of sufficient dimensions is placed on the reflective pad. The distances from the microphone to the point of reflection of the sound waves and the distance of the loudspeaker from the point of reflection of the waves are identically A/2. The identical signal emitted by the speaker is partially absorbed in the absorbing wave, the rest is reflected to the microphone. The measurement takes place according to the diagram below, the important thing is the same angle of incidence/reflection φ. The frequency spectrum of the sound pressure level Lp,r is evaluated at the microphone.

3. Step 3: at individual frequencies (1/3 octave), the sound absorption coefficient α(φ;f) is estimated according to the formula:

$$a(\varphi; f) = \mathbf{1} - \mathbf{10}^{\frac{\binom{\mathcal{L}\_{p, \mathcal{d}}(\varphi; f) - \mathcal{L}\_{p, \mathcal{r}}(\varphi; f)}{\cdot \otimes}}} \tag{1}$$

Method Notes:


#### *3.1.2 Sound intensity measurement method*

This approximate method requires the use of a measuring system with a sound intensity probe.

In an open field, the reflective surface is covered with a sufficiently large sample of the measured material. A sound source is placed at a sufficient distance from the surface of the sample. At a close distance from the sample (approx. 0.2 distance between the surface of the sample and the speaker), the average sound pressure level Lp and the average sound intensity level LI reflected from the sample are measured. The sound absorption coefficient is then calculated by the formula:

$$a(f) = \frac{4}{1 + 10^{\frac{L\_p(f) - L\_I(f)}{10}}} \tag{2}$$

The incident energy is proportional to the sound pressure level, the reflected energy is identified as a component of the sound intensity vector. Both quantities are identified by the sound intensity probe.

Advantages of the Sound Intensity Measurement Method may be:


The disadvantages of the Sound Intensity Measurement Method may be:

• Lower accuracy,

• The impossibility of relating the result only to the absorbent material sample. It is not possible to separate the absorption of the sample and the absorption of the substrate on which it is placed.

#### **3.2 Accurate methods of measuring the sound absorption coefficient**

#### *3.2.1 Standard ISO 354*

This international standard [4] defines the basic laboratory procedure for determining the sound absorption coefficient in a reverberation space. The procedure can be considered the most accurate procedure leading to the determination of the sound absorption coefficient. The method determines the sound absorption coefficient for diffusing the sound impact and can be used to measure materials with distinct shape structures in the straight and perpendicular direction. It is described in great detail in the standard and is especially suitable for specialized laboratories. The standard places strict requirements on the reverberation space, its dimensions and above all on the dimensions of the sample. The declared frequency range is from 100 Hz to 5000 Hz. The principle of indirect measurement of the sound absorption coefficient is based on Sabin's formula [5]:

A formula developed by Wallace Clement Sabine that allows designers to plan reverberation time in a room in advance of construction and occupancy. Defined and improved empirically the Sabine Formula [5] is.

$$T(\mathbf{60}) = \mathbf{0}.\mathbf{161} \cdot \frac{V}{A} |\mathbf{s}|,\tag{3}$$

Where:

T(60) = reverberation time or time required (for sound to decay 60 dB after source has stopped) |s|,

V = Volume of room |m<sup>3</sup> |,

A = the equivalent absorption surface |m<sup>2</sup> |.

In the test room, the reverberation time is measured with and without the mounted test sample. The reverberation time is the time during which the sound pressure level decreases by 60 dB after the sound source is turned off. This means that the original acoustic energy drops to 1/1000000 of its original size. In the test room, the reason for the decrease is the sound absorption and then the reverberation time is its measure. The equivalent surface is a hypothetical surface of a perfectly absorbing sample that has the same properties as a real sample. The equivalent area is the basis for calculating the sound absorption coefficient.

Advantages of determining the sound absorption coefficient according to ISO 354:


Disadvantages of determining the sound absorption coefficient according to ISO 354:


Above all, the requirement for a size of a sample is a problem of using this basic method in the sample development phase, when many possible variants are experimentally verified with subsequent optimization. It is practically impossible for manufacturers of absorbent materials and research organizations that are not directly oriented towards this research to acquire such expensive laboratory facilities.

Specific information on the measurement and calculation procedure is contained in the mentioned standard and it is not the aim of this chapter to discuss them in more detail.

#### *3.2.2 Measurement in an impedance tube*

An impedance tube is the most common device used today to estimate sound absorption. In the professional literature, this method is currently mentioned most often. There are more concrete technical versions of the tube, from the own construction of a research workplace to commercially offered versions. As an example, **Figure 1** shows the assembly from Brüel & Kjær Impedance Tube Kit 4206 (4206-A), which is described in the following text.

The impedance tube principle is based on the creation of a combination of direct and reflected waves in a rigid closed tube with an internal smooth and reflective surface. The skeleton of the tube must be as soundproof as possible. One end of the tube covers a sample that is being measured, on the other end of the tube there is placed a speaker that excites by broadband noise the inner volume of the tube. A plane wave is created between the speaker and the sample, which is a combination of incident and reflected waves. The energy of the reflected wave is reduced by the energy absorbed in the sample. The resulting wave is sampled in the tube and an estimate of the sound absorption coefficient is determined by evaluating the data obtained. The sound wave strikes the sample perpendicularly.

Basic characteristics of impedance tube measurement:


*Sound Absorption Measurement: Alpha Cabin and Impedance Tube DOI: http://dx.doi.org/10.5772/intechopen.110410*

**Figure 1.** *Impedance tube and absorptive material samples (author's archive).*

the methods in the diffusion field according to ISO 354 [4] and in the alpha cabin [7, 8].


#### *3.2.2.1 Method using standing Wawa ratio*

This method determines the sound absorption coefficient of acoustic materials when the sound is incident perpendicularly. The specific procedure for determining the sound absorption coefficient is described in [9]. The absorbing sample is fixed at one end of the tube. An incident plane sine wave pi is excited by a speaker at the opposite end of the tube. By superposition p = pi + pr of the pressures of the incident wave pi and the reflected wave pr from the test sample, a standing wave is created in the tube. The course of the sound pressure level of this standing wave is measured by an adjustable microphone, which is moved along the axis of the tube through the hole in the center of the speaker. The evaluation of sound absorption is based on the difference in sound pressure levels ΔL between the pressure maximum and minimum in the tube.

$$a = \frac{4 \cdot 10^{\Delta l\_{\text{20}}}}{\left(10^{\Delta l\_{\text{20}}} + 1\right)^2} \tag{4}$$

Moving the microphone and accurately identifying the maximum and minimum sound pressure level reduces the speed of the sound absorption coefficient measurement. Impedance tubes for this evaluation method are more often an individual product of test laboratories, which allows adaptation to the desired frequency band and the way of moving the microphone and evaluating the absorption.

#### *3.2.2.2 Transfer-function method*

This test method is similar to the previous method in that it uses the same experimental scheme with a sound source at one end and a sample fixed in an impedance tube at the other end. The procedure is described in detail in [10, 11]. In this test method, plane waves in the tube are excited by a noise source and the sound pressure is measured by microphones located at two fixed points (or by one microphone moved in the tube) and by subsequent calculation of the complex transfer function at a perpendicular incidence of sound waves. The test method is overall much faster than the measurement procedure described in the previous chapter.

The test sample is fixed to one end of a straight, rigid, smooth and sealed impedance tube. Plane waves are excited in the tube by a sound source (noise) and the sound pressure is measured by microphones at two locations near the sample. A complex transfer function is determined from the measured signals, which is used to calculate the sound absorption coefficient. The frequency range of the measurement depends on the dimensions of the tube and the distance between the positions of the microphones. In order to determine the sound absorption coefficient in a wider frequency range, measurements are made on an assembly that contains tubes of two different diameters. **Figure 1** shows a measuring set-up that allows determining the sound absorption coefficient for a sample diameter of 100 mm in the frequency range of 50 Hz to 6.4 kHz (for a sample thickness of 440 mm maximum [6]) and for a sample diameter of 29 mm in the frequency range of 100 Hz to 3.2 kHz (for a sample thickness of 200 mm maximum [6]).

Measurements can be done:


Procedure 1 is quick, accurate and easier to do. It is widespread in practice and much more published.

Procedure 2 requires a specialized excitation signal, has more demanding requirements for processing the measured signals, and is more time-consuming. It better eliminates phase mismatch between microphones and allows optimal selection of microphone locations for each measured frequency. According to [10], this procedure is recommended for evaluating of tuned resonators.

Advantages of measuring in an impedance tube:


Disadvantages of measuring in an impedance tube:


#### *3.2.3 Measurements in the alpha cabin*

The Alpha cabin [7, 8, 12, 13] is an internationally acknowledged measurement platform for determining the sound absorption coefficient at the omnidirectional impact of sound waves. It is therefore close to measurements according to ISO 354, it is based on the requirements of this standard, it respects the methodology as much as possible, but removes the disadvantage of the need for large samples.

The Alpha cabin is a platform that is scaled 1:3.2 to the echo chamber parameters of the Swiss Material Testing and Testing Laboratory (EMPA) in Dübendorf. **Figure 2** shows an example of the latest design of the alpha cabin. It is a reverberant space sound-isolated from the outside environment with non-parallel walls.

The main technical data of the alpha cabin are:


**Figure 2.** *Alpha cabin - Technical University of Liberec (author's archive).*

The formula [7] is used to determine the sound absorption coefficient:

$$a\_{\mathcal{S}} = \frac{0,966}{\mathcal{S}} \left( \frac{1}{T\_1} - \frac{1}{T\_0} \right) \tag{5}$$

Where the measured quantities are:

S = sample area |m<sup>2</sup> |.

T1 = reverberation time in the sample booth |s|,

T0 = reverberation time in the cabin without sample |s|.

The ratios in the diffusion field of the alpha cabin (**Figure 3**) are practically the same as in the large reverberation chamber, but for three times shorter wavelengths (three times higher frequencies). The Alpha cabin therefore provides comparable results on much smaller sample areas than required by ISO 354. However, the proportional changes in cabin conditions run into one problem. The thickness of the sample is the only geometric quantity that cannot be reduced in a ratio of 1:3, and thus the absorbing surface corresponding to the edges of the sample appears three times larger in proportion to its surface. The problem must be eliminated by edging the side surface of the sample with soundproof material. As standard, it is solved by a metal bounding frame with the dimensions of a standard sample, which is higher than the usual thicknesses of the developed materials. In the case of larger thicknesses, it is recommended to manufacture your own frame and validate it using a reference sample. The importance of sample edging can be shown on the measurement results of the same sample with a thickness of 20 mm with and without a bounding frame in **Figure 4**. The course shows that the error of determining the sound absorption coefficient increases with increasing frequency (**Figure 5**).

*Sound Absorption Measurement: Alpha Cabin and Impedance Tube DOI: http://dx.doi.org/10.5772/intechopen.110410*

**Figure 3.** *Alpha cabin with embedded and framed sample (author's archive).*

The Alpha cabin measurement procedure generally requires two measurements.


The sound absorption coefficient is then calculated according to formula (5).

**Figure 4.** *Results of measurements with and without a border frame.*

**Figure 5.** *Frames for delimiting samples (author's archive).*

The Alpha cabin has one more function, which is the evaluation of absorbing objects. These are shaped parts that absorb sound, but the absorbing surface cannot be determined. A typical example is the seat of a passenger car [12], which significantly affects the noise in the closed space of the cabin due to its absorption, but it is not possible to clearly determine the absorbing surface, or to create a sample of standardized dimensions from the seat. In Eq. (5) it is not possible to substitute the absorbing surface S, and thus the measurement result is equal to the equivalent absorbing surface A:

*Sound Absorption Measurement: Alpha Cabin and Impedance Tube DOI: http://dx.doi.org/10.5772/intechopen.110410*

$$A = 0, 966 \cdot \left(\frac{1}{T\_1} - \frac{1}{T\_0}\right) \qquad |m^2| \tag{6}$$

The equivalent absorptive surface corresponds to the absolute absorptive surface (α<sup>S</sup> = 1), which has the same absorptive capacity as the shaped part. Therefore, the larger the equivalent surface area, the more the shaped part is able to absorb more sound energy. An example of the result of measuring the equivalent absorbing surface for a shaped part in the construction of a passenger car is shown in **Figure 6**.

The equivalent absorptive surface of shaped parts is primarily a comparative parameter when developing or selecting a part for a protected space. However, it can be used in the calculations of the total absorption, because according to Eq. (5):

$$A = \mathbb{S} \cdot a\_{\mathbb{S}} \tag{7}$$

Advantages of measuring sound absorption in the alpha cabin:



Disadvantages of measuring sound absorption in the alpha cabin:


#### **4. Conclusion**

Measurement is still the most accurate and fastest procedure for determining the sound absorption coefficient. The practical use of absorbing materials in practice requires an objective determination of absorption for the purpose of optimizing the acoustic properties of enclosed spaces.

The current development of absorbent materials is predominantly still using fibers or porous raw materials with an emphasis on other important properties, such as ecology, usability of waste and recyclable resources, esthetics, non-flammability, etc. For products designed in this way (mats, panels, absorbent elements) the main principle of absorption is the conversion of sound energy into heat by friction of the internal structure of the absorbing element. In general, the elements then have optimal efficiency starting from the frequency that is determined by following equation:

$$f = \frac{\text{86000}}{H} \left| \text{Hz} \right| \tag{8}$$

Where:

H = the thickness of the absorbing element |mm|,

f = frequency |Hz|.

The optimal thickness equals to a quarter of the wavelength of a perpendicular incident wave, so it can be considered the minimum value at which the material is able to use its full potential to absorb sound. With omnidirectional impact, it can be assumed that the optimal bandwidth will shift to lower frequencies. **Figure 7** shows an example of the measurement result in the Alpha cabin of a sample of absorbent material with a reference thickness of 22 mm. A frequency of 3.9 kHz (4 kHz 1/3 octave) corresponds to a thickness of 22 mm. Due to the omnidirectional impact of sound waves, the maximum absorption value is maintained even at lower frequencies (2 kHz).

There is an inverse proportional relationship between the optimal frequency and the thickness of the material. When considering declared frequency ranges of individual measurement methods, **Figure 8** provides a comprehensive overview of the methods and their practical use for materials testing.

It is clear from **Figure 8** that the lowest declared measurement frequency achievable in the impedance tube is at frequency of 50 Hz. This would correspond to the

*Sound Absorption Measurement: Alpha Cabin and Impedance Tube DOI: http://dx.doi.org/10.5772/intechopen.110410*

**Figure 7.** *Sound absorption of a sample with a thickness of 22 mm - measured in the alpha cabin.*

#### **Figure 8.**

*Measurement methods in relation to the optimization of the thickness of the absorbent material.*

optimal absorption of materials with a thickness of approx. 1700 mm, which is technically impossible. An impedance tube of such dimensions is not used in practice, but a sufficiently wide frequency band is available for an objective assessment of

commonly used materials. The Alpha cabin starts at a frequency of 400 Hz, which corresponds to roughly 200 mm of material thickness when optimally used. This thickness is usable for the Alpha cabin. The ISO 354 standard declares a minimum frequency of 100 Hz, which corresponds to 860 mm of optimal thickness, which is also acceptable given the dimensions of the space and the area of the sample. It should be emphasized that the measurement according to the ISO 354 standard and in the Alpha cabin is based on the omnidirectional impact of sound waves, the impedance tube is based on only a perpendicular impact.

From the **Figure 8**, an uncovered bandwidth of sound absorption measurements up to 100 Hz can be seen in the case of omnidirectional impact of sound waves. It should be emphasized that physical and technical obstacles to the use of independent methods are encountered here. The optimal thickness of the materials is greater than 860 mm and ends at 4.3 m for 20 Hz, which is the lowest frequency of the audible band. However, this range of thicknesses of absorbing materials is difficult to use in the real world for practical reasons. The exception is specialized anechoic chambers with high volumes. Here, the effectiveness of absorbing materials is assessed by measuring the reverberation time directly during implementation.

If the commercially usual area of absorbent materials (up to a maximum thickness of 200 mm) were to be evaluated, it can be seen from **Figure 9** that the optimal platform is the alpha cabin.

#### **Recommendations for the design and experimental verification of the properties of absorbent materials**

If the absorbing material is to fulfill the expectations, its structure must be properly designed. This is a matter of material development respecting other requirements (legislative requirements, esthetic requirements, applicability in specific conditions,

#### **Figure 9.** *Measurement methods in relation to thickness optimization of conventional absorbent material | author's archive |.*

other specific customer requirements). An objective assessment of sound absorption can only be achieved by measuring on an existing sample. Below is the basic procedure for determining the sound absorption coefficient by experiment.

1.To perform the measurement, a sample must be taken that clearly states:


Lower accuracy methods:


Higher accuracy methods:


#### **5. Discussion**

This chapter summarizes experimental methods for determining the sound absorption coefficient α. The chapter addresses the user (researcher, customer, project solvers) who are tasked with designing (developing) absorbing material and need to verify it during the development stage or after application. Available approximate and exact methods, their starting points, limitations, advantages and disadvantages and usability in practice are described. The solver can thus choose a suitable method for

#### *Denoising – New Insights*

the individual stages of the project solution or correctly formulate requirements for external laboratories. The chapter further helps to understand the measurement results in relation to the application to a specific space and guides the project solver to be aware of possible limitations and problems.

Recommendation:


### **Author details**

Pavel Němeček Technical University of Liberec, Liberec, Czech Republic

\*Address all correspondence to: pavel.nemecek@tul.cz

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Sound Absorption Measurement: Alpha Cabin and Impedance Tube DOI: http://dx.doi.org/10.5772/intechopen.110410*

### **References**

[1] Brüel & Kjær. Measurements in Building Acoustic [Internet]. 1988. Available from: https://www.academia. edu/17353265/Measurementsin\_Build ing\_Acoustics?email\_work\_card=viewpaper

[2] Bérengier M, Garai M. A State-of-the-Art of in situ Measurement of the Sound Absorption Coefficient of Road Pavements. Available from: https:// www.academia.edu/34047160/ MEASUREMENT\_METHODS\_OF\_ ACOUSTICAL\_PROPERTIES\_OF\_ MATERIALS\_SESSIONS\_A\_state\_of\_ the\_art\_of\_in\_situ\_measurement\_of\_ the\_sound\_absorption\_coefficient\_of\_ road\_pavements

[3] Quintero-Rincón A. Measurement of the Sound-Absorption Coefficient in situ in Eggs Cartons using the Tone Burst Method. Available from: https://www. academia.edu/12996142/Measurement\_ of\_the\_sound\_absorption\_coefficient\_ in\_situ\_in\_eggs\_cartons\_using\_the\_ Tone\_Burst\_Method?email\_work\_card= title

[4] ISO 354, Acoustic - Measurement of Sound Absorption in a Reverberation Room. Switzerland; International Organization for Standardization; 2003

[5] Reverberation Time and Sabine's Formula. Available from: https://www. acousticlab.com/en/reverberation-timeand-sabines-formula/

[6] Product Data. Impedance Tube Kit (50 Hz – 6.4 kHz) Type 4206, Impedance Tube Kit (100 Hz – 3.2 kHz) Type 4206-A, Transmission Loss Tube Kit (50 Hz – 6.4 kHz) Type 4206. Available from: https://www.bksv.com/ media/doc/bp1039.pdf

[7] Alpha Cabin. A Global Standard for Acoustic Absorption Measurements. Available from: https://www.autoneum. com/alpha-cabin-ii/

[8] Alpha Cabin. Available from: http:// www.cttm-lemans.com/en/acoustics-vib rations/produits/alpha-cabin.html

[9] ISO 10534-1, Acoustics - Determination of Sound Absorption Coefficient and Impedance in Impedance Tubes - Part 1: Method using Standing Wave Ratio. Switzerland: International Organization for Standardization; 1996

[10] ISO 10534-2, Acoustics – Determination of Sound Absorption Coefficient and Impedance in Impedance Tubes – Part 2: Transfer-Function Method. Switzerland: International Organization for Standardization; 1998

[11] Yaochi Tang Y, Chuang X-J. Tuning of Estimated Sound Absorption Coefficient of Materials of Reverberation Room Method. 2022. Available from: https://www.hindawi.com/journals/sv/ 2022/5192984/

[12] Megasorber, Alpha Cabin. Acoustic Performance, Sound Absorption Test Chamber. Available from: https:// megasorber.com/alpha-cabin/

[13] Nemecek P. Sound Absorption Measurement in Alpha Cabin. 2014. Available from: https://link.springer. com/chapter/10.1007/978-3-319- 05203-8\_52

Section 2
