MASTER
Modeling the sensation of fluctuation strength
García León, R.
Award date:
2015
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Modeling the Sensation of Fluctuation Strength
by Rodrigo García León
0867877
in partial fulfilment of the requirements for the degree of
Master of Science
in Human-Technology Interaction
Department of Industrial Engineering & Innovation Sciences Eindhoven University of Technology
Supervisors:
Prof. Dr. A.G. Kohlrausch IE and IS, Eindhoven University of Technology Dr. Ir. R.H. Cuijpers IE and IS, Eindhoven University of Technology A.A. Osses Vecchi BSc IE and IS, Eindhoven University of Technology
Fluctuation Strength, Perceptual Attributes, Sound Perception, Psychoacoustics, Roughness, Magnitude Estimation, Modeling
Perceptual attributes are discernible dimensions into which auditory events can be decomposed.
They allow to understand the perceptual and cognitive effects caused by sound signals. Among these perceptual attributes is the attribute of fluctuation strength, which corresponds to a fluctuation or circulation sensation that certain sounds (e.g., ambulance sirens) give.
Fluctuation strength has been related to several cognitive and perceptual processes, such as speech production and comprehension, cognitive performance, perceived sound quality, among others. However, the attribute itself has not been studied as deeply as other perceptual attributes.
Additionally, there is not a publicly available model that reflects its characteristics. Furthermore, recent studies have run into problems when trying to reproduce the findings reported in the available literature. The present study addressed all these problems related to the research of fluctuation strength, limiting its scope to amplitude-modulated (AM) and frequency-modulated (FM) tones.
In order to deal with possible methodological issues, a new experimental procedure was devised aimed at correcting possible biases. The procedure included the use of a training phase to familiarize subjects with the sensation of fluctuation strength. Moreover, subjective data that assessed the dependencies of fluctuation strength on several key parameters were obtained, using a magnitude estimation procedure. Twenty-four subjects in total participated in this study. In general, the training phase helped participants understand better the concept of fluctuation strength. Furthermore, the obtained subjective data and the data found in the literature were deemed as qualitatively similar.
Using the obtained subjective data, a model adjusted to it was developed. The proposed model was based on a model for the perceptual attribute of roughness. Similarities between the physical phenomena related to both perceptual attributes made it possible to use this model as the basis of the proposed model. The proposed model was able to produce qualitatively similar results to those present in the obtained subjective data. However, the model adapts better for AM tones than to FM tones.
Overall, even though some differences exists between the obtained data and the data from the literature, the proposed experimental procedure was considered to be adequate in order to obtain perceptual data regarding the attribute of fluctuation strength. Along the same lines, although the proposed model presented some important limitations to consider, it was possible to obtain similar results from it when compared to the obtained data. As so, the model was deemed to be adequate in modeling the obtained data.
List of Abbreviations ix
1. Introduction 1
2. Theoretical Background 3
2.1. Perceptual Attributes . . . 3
2.2. Fluctuation Strength . . . 3
2.2.1. Dependencies of Fluctuation Strength . . . 4
2.2.2. Models of Fluctuation Strength . . . 9
2.2.3. Related Studies . . . 11
3. General Methods 13 3.1. Equipment . . . 13
3.2. Stimuli . . . 13
3.3. Procedure . . . 14
3.4. Results . . . 15
4. Pilot Experiment Design and Results 19 4.1. Initial Design . . . 19
4.1.1. Subjects . . . 19
4.1.2. Stimuli . . . 19
4.1.3. Procedure . . . 19
4.2. Iterative Improvements . . . 21
4.3. Results . . . 22
4.4. Conclusions . . . 23
5. Experimental Design and Results 27 5.1. Design . . . 27
5.1.1. Subjects . . . 27
5.1.2. Stimuli . . . 27
5.1.3. Procedure . . . 27
5.2. Results . . . 30
6. Model Development 39 6.1. Roughness Model . . . 39
6.1.1. Peripheral Stage . . . 39
6.1.2. Modulation Depth Extraction Stage . . . 42
6.1.3. Specific Roughness Stage . . . 43
6.2. Procedure . . . 45
6.3. Results . . . 45
7. Discussion 51 7.1. Experiment . . . 51
7.1.1. Methods . . . 51
7.1.2. Results . . . 52
7.2. Model . . . 54
7.2.1. Results . . . 54
7.2.2. Limitations . . . 54
7.3. Conclusions . . . 54
Bibliography 57 A. Experimental Protocol 59 A.1. Procedure . . . 59
A.1.1. Before . . . 59
A.1.2. During . . . 59
A.1.3. After . . . 60
A.2. Prompts . . . 60
A.2.1. Training Phase . . . 60
A.2.2. Before Rough Tones . . . 60
A.2.3. After Rough Tones . . . 61
A.2.4. Long Stimuli . . . 61
A.2.5. Test Trials . . . 61
A.2.6. Before Sections . . . 62
B. TU/e Code of Scientific Conduct 63
AM amplitude-modulated 1, 4, 6, 11, 13–15, 17, 20, 21, 23, 24, 27–33, 45, 52–54
BBN broad-band noise 1, 4, 54
df frequency deviation 14, 28, 53
fc center frequency 14, 21, 28
fm modulation frequency 8, 14, 21, 28
FM frequency-modulated 1, 6, 7, 9, 13, 14, 17, 21, 25–31, 34, 35, 45, 52–54
I/O input/output 13
IFFT inverse fast Fourier transform 41 IIR infinite impulse response 43
IQR interquartile range 31, 52
ISE irrelevant sound effect 12
md modulation depth 14, 28, 53
PCM pulse-code modulation 13
RMS root mean square 10, 43
SNR signal-to-noise ratio 13
SPL sound pressure level 4, 14, 28, 45
The auditory sensation of fluctuation strength is the sensation that arises due to fluctuating or circulating patterns present in certain stimuli. For instance, ambulance sirens and the sounds of working washing machines have this quality, as their sounds have a certain movement, rotation or circulation associated to it. Fluctuation strength is part of a group of perceptual attributes in the body of knowledge of the psychoacoustic discipline. These components allow to understand from a perceptual point of view sound events, quantifying phenomena that develop themselves within the human mind.
Fluctuation strength [9, pp. 247] relates to several cognitive processes that mediate important human phenomena [14]. A possible relation with the speech system has been suggested, and could prove to be an important indicator for it [5]. Furthermore, it is known that fluctuation strength plays an important role when it comes to the perceived “pleasantness” of given sounds [8].
There are several knowledge gaps when it comes to fluctuation strength in the available literature. First, methodological issues in past studies have resulted in inability to reproduce reported findings. Second, to our knowledge, there is no publicly available source when it comes to modeling the sensation of fluctuation strength.
Taking the preceding points into account, the objective of this research is twofold:
1. Formulate a clear methodological procedure to eliminate the problems found in past studies 2. Propose a fluctuation strength model based on existing roughness models, adjusted to the
collected experimental data
Furthermore, this study will focus on two types of stimuli, amplitude-modulated (AM) tones and frequency-modulated (FM) tones, leaving AM broad-band noise (BBN) stimuli aside due to time constraints.
Chapter 2 lays down the theoretical underpinnings that support the knowledge regarding the sensation of fluctuation strength. An introduction to the topic of perceptual attributes is given, followed by a thorough description of the sensation of fluctuation strength. Then, literature concerning the modeling of fluctuation strength is reviewed. Afterwards, related studies investigating fluctuation strength are presented.
Chapter 3 presents the general methods used to obtain subjective data from participants, used both in the pilot and the main experiments. The equipment and the stimuli used are described, and then the magnitude estimation process used to obtain participants data is detailed.
Chapters 4 and 5 deal with the process of designing and carrying out the experiments of this study. First, the pilot experiments used to shape the initial design are presented, with
their results and conclusions given afterwards. Following this, the final form of experiment is described, and the results are reported along with the data already existing in the literature.
Chapter 6 documents the process of developing a model for the obtained experimental data, based on an existing model intended for the sensation of roughness. The procedure used to modify and adjust the roughness model is detailed. Afterwards, a comparison between the model output and the experimental data is presented.
Chapter 7 presents a discussion regarding the results of both the experimental and modeling stages of this research, finalizing in a series of conclusions and limitation to be taken into account for future work.
In this chapter the theoretical background for the sensation of fluctuation strength is presented.
First, an introduction to the topic of perceptual attributes is given. Afterwards, the sensation of fluctuation strength is addressed, exploring its dependencies on stimulus parameters; most of this information comes out from the work done by Fastl and Zwicker [9]. Next, literature concerning the modeling of fluctuation strength is given. Finally, several studies expanding upon the basic concepts of fluctuation strength are presented.
2.1. Perceptual Attributes
Perceptual attributes are discernible dimensions in which an auditory event can be decomposed.
They are derived from the physical characteristics of sounds. By using them the effects of incoming audio events can be understood from a perceptual point of view. A short overview of the perceptual processes and their associated perceptual quantities is presented in Table 2.1, which summarizes all the perceptual measures, along with their dominant physical stimuli. Most of the research on perceptual dimensions, except for density, comes from the “Munich school”
work of Fastl and Zwicker [9].
It is important to note that the human auditory system can generate these perceptual sensations independently of each other, although to understand the psychological impact of them, for instance the “pleasantness” of a given sound, a bigger context needs to be taken into account. As an example, the emotions of the listeners can have an important effect on the cognitive construal of a given sound.
2.2. Fluctuation Strength
Fluctuation strength corresponds to the sensation that arises when a sound has a slowly varying envelope (i.e., a modulation signal whose frequency is less than 20 Hz). Fluctuation strength is closely related to roughness, the difference between the two being the range of modulation frequencies where each sensation is predominant. In the case of roughness, this range corresponds to modulation frequency values greater than 20 Hz.
Fluctuation strength can have a significant effect on the pleasantness of sound, and a particu- larly clear example of this are alarms, which must have a sharp and distinctive sound.
The effect of fluctuation strength can be seen as a temporary masking pattern created by the original signal, in which the modulation depth is of utmost importance. This is also the case for
Dominant stimulus dimension Perceptual parameters Sound pressure level (dB) Loudness (sone)
Loudness level (phon)
Frequency (Hz) Critical band rate (Bark)
Ratio pitch (mel) Degree of modulation (%) Roughness (asper) Modulation frequency (Hz)
Frequency (Hz) Sharpness (acum)
Degree of modulation (%) Fluctuation strength (vacil) Modulation frequency (Hz)
Spectral components (Pa) Pitch strength Tonality (tu)
Impulse duration (s) Subjective duration of impetus (IU) Sound pressure level (dB) Density (dasy)
Frequency (Hz)
Table 2.1.: Stimuli and sensations [13, pp. 70]
roughness, which resembles fluctuation strength in this regard.
2.2.1. Dependencies of Fluctuation Strength
The unit used to quantify the sensation of fluctuation strength is the vacil. As a reference, 1 vacil is defined as the fluctuation strength created by a 1 kHz tone with a sound pressure level (SPL) of 60 dB, an AM envelope of 4 Hz and a modulation index of 1. The maximum value of fluctuation strength seems to occur for modulation rates around 4 Hz, regardless of the modulation technique used (Figure 2.1).
It seems that a relation between fluctuation strength and speech production exists, as the normal production rate of syllables during normal conversation speed is about 4 syllables/second.
This coincides with the frequency in which a maximum value of fluctuation strength occurs (4 Hz).
Figure 2.2 shows the relation between SPL and fluctuation strength for two different stimuli, tones and BBN, and two modulation techniques, amplitude modulation and frequency modulation.
An increase in SPL entails an increase of fluctuation strength.
Figure 2.1.: Fluctuation strength as a function of modulation frequency for (a) amplitude- modulated broad-band noises, (b) amplitude-modulated tones and (c) frequency- modulated tones [9, pp. 248]
Figure 2.2.: Fluctuation strength as a function of sound pressure level for (a) amplitude- modulated broad-band noises, (b) amplitude-modulated tones and (c) frequency- modulated tones; modulation frequency of 4 Hz [9, pp. 249]
Next the effect of modulation depth on fluctuation strength is analyzed, shown in Figure 2.3.
For AM tones the modulation depth is determined by the modulation index h. The modulation index is defined as the ratio between the modulating signal amplitude M and the carrier signal amplitude A,
xam = [1 + h · sin(2πfmt)] · A · sin(2πfct), (2.1) h = M
A. (2.2)
Modulation depth can also be expressed by using the modulation factor m, which corresponds to the modulation index expressed as a percentage. Furthermore, the modulation index can be expressed in dB units using the following equations:
h = m0d− 1
m0d+ 1, (2.3)
m0d= 10md20. (2.4)
where md correspond to the modulation depth expressed in dB.
It can be observed that, for values of modulation depth between 3 dB and 30 dB the relation between fluctuation strength and modulation depth is somewhat linear. After reaching a maximum value at around 30 dB, which corresponds to a modulation factor of 94%, fluctuation strength remains constant with further increments of modulation depth.
Figure 2.3.: Fluctuation strength as a function of modulation depth for (a) amplitude-modulated broad-band noises of 60 dB SPL and (b) amplitude-modulated tones of 70 dB SPL and 1 kHz frequency; both with a modulation frequency of 4 Hz [9, pp. 249].
the center frequency. For FM tones a clear dependence between both variables exists. For center frequencies below 1 kHz the fluctuation strength is almost constant; above 1 kHz it experiences a linear decrease until it fades away at around 8 kHz.
Figure 2.4.: Fluctuation strength as a function of center frequency for an amplitude-modulated tone of 70 dB SPL, 4 Hz modulation frequency and 40 dB modulation depth (a), and a frequency-modulated tone with 70 dB SPL, 4 Hz modulation frequency and
±200 Hz frequency deviation [9, pp. 250].
To understand why this change of fluctuation strength occurs in the case of the FM tones, it is necessary to take into account the excitation patterns that the modulated sounds cause. The auditory filters are a series of overlapping bandpass filters that model the frequency selective response of the auditory system. The excitation pattern refers to the pattern that results as the outcome of all the precedent stages of the hearing process, being the outer ear transmission, middle ear transmission, and the auditory filters themselves.
In the case of fluctuation strength, for an FM tone with center frequency of 0.5 kHz and frequency deviation of 200 Hz, the frequency would vary between 300 and 700 Hz. This corresponds to a 3.5 Bark interval. For a tone with center frequency of 8 kHz and frequency deviation of also 200 Hz these values would be 7.8 kHz and 8.2 kHz, leading to a 0.2 Bark interval. For both FM tones the range of frequency is constant on a Hertz scale, i.e. 400 Hz.
The proportion between these two Bark intervals (i.e., 3.5 and 0.2 Bark) is 17.5, which seems to be also the proportion between the relative fluctuation strength for these two frequencies.
Thus, this leads to the idea that fluctuation strength can be explained in terms of the excitation patterns that present themselves across the auditory filters.
Figure 2.5 shows the relation between fluctuation strength and frequency deviation (∆f ). For FM tones, frequency deviation is defined as the amplitude of the modulating signal. This is shown in Equation (2.5), where A corresponds to the carrier signal amplitude.
xf m= A · sin[2πfct + ∆f · sin(2πfmt)]. (2.5) It can be seen that, for frequencies above 20 Hz, there is a linear increase of fluctuation
strength with frequency deviation.
Figure 2.5.: Fluctuation strength as a function of frequency deviation for a tone with 70 dB SPL, 1.5 kHz center frequency and a modulation frequency of 4 Hz [9, pp. 251].
Figure 2.6 compares the fluctuation strength of several sounds, whose physical characteristics are described in Table 2.2. The sounds that present the largest values of fluctuation strength (sounds 1 and 2) excite a large range of frequencies and therefore more than one auditory filter.
As so, it can be said that fluctuation strength combines across critical bands.
Figure 2.6.: Fluctuation strength of sounds 1–5 as described in Table 2.2 [9, pp. 252].
Sound 1 2 3 4 5
Abbreviation FM AM AM FM
SIN BBN SIN SIN NBN
Frequency [Hz] 1500 — 2000 1500 1000
Level [dB] 70 60 70 70 70
Modulation frequency [Hz] 4 4 4 4 —
Modulation depth [dB] — 40 40 — —
Frequency deviation [Hz] 700 — — 32 —
Bandwidth [Hz] — 16000 — — 10
Table 2.2.: Physical data of sounds 1–5 [9, pp. 253].
2.2.2. Models of Fluctuation Strength
A basic model for fluctuation strength (proposed by Fastl and Zwicker [9, pp. 254]) based on the temporal variation of the masking pattern of the sound to analyze is shown in Figure 2.7, where the temporal variation of the amplitude of the masking pattern, also called temporal masking depth, is denoted by the magnitude ∆L. The inverse of the time difference between peaks corresponds to the modulation frequency (fm).
Figure 2.7.: Model of fluctuation strength [9, pp. 254].
Equation (2.6) shows the equivalence relationship (represented by ∼) between fluctuation strength F , temporal masking depth ∆L and modulation frequency fm (expressed in Hz), where the importance of the 4 Hz frequency is emphasized.
F ∼ ∆L
(fm/4) + (4/fm) (2.6)
It should be noted that there is a dependency between the temporal masking depth ∆L and the frequency. In the case of amplitude and frequency modulated tones, these two variables are dependent on each other, due to the nonlinearity of the upper slope in the masking pattern.
This effect being the strongest for FM stimuli. In order to address this, when modeling the fluctuation strength for these tones not a single ∆L value is taken, but instead it is integrated
across the critical-band rate scale.
The resulting temporal masking pattern for several values of modulation frequency is shown in Figure 2.8. It can be seen that, as the modulation frequency increases, the temporal masking depth decreases. This leads to the idea that, although fluctuation strength presents a bandpass response with respect to modulation frequency, the temporal masking reveals a low pass characteristic. It can be considered that the temporal masking depth decreases proportionally with modulation frequency, as shown on Figure 2.8.
Figure 2.8.: Temporal masking pattern for an amplitude-modulated broad-band noise [9, pp.
255].
The modeling based on the temporal masking property, proposed by Fastl and Zwicker, poses difficulties when its implementation details are addressed. Furthermore, to our knowledge, there is not a publicly available implementation for any given model of fluctuation strength up to this date. There are, however, implementation models when it comes to roughness, a sensation that it was already mentioned as being similar to fluctuation strength regarding its physical characteristics. The most prominent of these models is the one developed by Daniel and Weber [3], which is based on the dependency of roughness on modulation depth, shown in Equation (2.7),
R ∼ (md)p, (2.7)
where R corresponds to the total roughness, md to the modulation depth and p is a constant, set at 2 for the model of Daniel and Weber.
In order to obtain a roughness value from a given sound, the model first decomposes the incoming signal into excitation patterns, using a critical filterbank composed of 47 channels.
Each excitation pattern is then band-pass filtered, to account for the dependence of roughness on modulation frequency. After this, an estimate of the modulation depth present in the signal is calculated, using a generalized modulation depth function Equation (2.8).
mi∗= ˜hBP,i(t)/h0,i (2.8)
where ˜hBP,i(t) is the root mean square (RMS) value of the band-pass filtered signal and h0,i is the absolute value of the mean value of the signal. Afterwards, a specific roughness value (i.e., a roughness value per filterbank channel) is obtained from the extracted modulation depth of each channel. Finally, a total overall roughness value is obtained as a result of adding all the specific roughness values. A more in-depth explanation of the model is given in Chapter 6.
Given the similarity in physical terms that fluctuation strength and roughness possess, a model for the sensation of fluctuation strength could be elaborated taking as a base Daniel and Weber’s model. In this regard, Sontacchi [16] has already formulated a model whose structure is similar to that of the roughness model. However, no subjective comparison of the model outcome with participants judgments was presented as part of his work. The present work expands on this point, including a subjective evaluation of the model with the experimental data collected.
2.2.3. Related Studies
Although the work by Fastl and Zwicker is the most extensive reference for the fluctuation strength sensation, other studies have been carried out to further investigate the phenomenon.
Accolti and Miyara [1] conducted a study where they used stimuli composed of two mixed AM sources. They implemented a fluctuations strength model based on the extraction of temporal masking patterns within the stimuli. Afterwards, they compared the model outcome with perceived values of fluctuation strength using 5 participants. They used a modified magnitude estimation procedure, where 10 references with known and equidistant values of fluctuation strength were made available to participants for them to compare before giving an answer. The minimum and maximum of this set of references corresponded to stimuli with modulation indexes of 0.1 and 1, respectively. They found that their model could not properly characterize this type of stimulus. However, the most remarkable part of their study is the inclusion of a training phase before the actual experiment. They decided to include such a phase based on results from a preliminary test, which showed that results were strongly variable among subjects. One possible explanation given [1, pp. 17] is that that individuals are not familiar with the concept of fluctuation strength and that a confusion between roughness and fluctuation strength can often arise between the two sensations.
Building upon this last point, Wickelmaier and Ellermeier [19] carried out a three-part experiment that came out with similar results in that sense. First, a full-factorial design with 54 pairs of stimuli, with nine modulation frequencies and six modulation depths, and a magnitude estimation test was run. The results differ from those reported by Fastl and Zwicker, since
they do not show the characteristic band-pass response as a function of modulation rate. The second experiment tried to assess the contribution of the two factors used in the past experiment (modulation frequency and modulation depth) separately, by varying one while leaving the other constant. It was found that the variation of the modulation depth is similar to the data by Fastl and Zwicker, while the variation of the modulation frequency was not.
In the last experiment they tried to assess whether the perceived fluctuation can be represented by an additive combination of modulation frequency and modulation depth. To test this they used the Thomsen condition [6], which for their study was stated as follows:
Let a, b, c be three values of fm(∆f ) and x, y, z three values of ∆f (fm). The Thomsen condition holds, iff
ay ∼ bz, bx ∼ cy =⇒ ax ∼ c0z (2.9)
A adaptive forced-choice procedure (1-up/1-down) using 16 repetitions was used to calculate the matches (∼) stated in Equation (2.9). Their results show that only for one participant out of seven the Thomsen condition proved to be true, suggesting this that listeners do not integrate modulation frequency and modulation depth as an unidimensional percept when it comes to the sensation of fluctuation strength. Wickelmaier and Ellermeier’s conclusions are that the data by Fastl and Zwicker do not conform properly to their data, and that the status of fluctuation strength as a basic auditory perceptual attribute could be debated. The discrepancy between the two data sets could also be attributed to the lack of understanding of participants, as Accolti and Miyara had stated.
Expanding upon possible applications of the sensation of fluctuation strength, Schlittmeier et al. [14] investigated fluctuation strength as a predictor for irrelevant sound effect (ISE). ISE refers to the phenomenon that occurs when background sounds with distinctive temporal-spectral variations significantly reduce short-term memory. This negatively affects individuals cognitive performance. The changing-state features required from sounds to cause this mental interference are the following:
1. Segmentability from a temporal-spectral perspective 2. Different successive auditory-perceptive tokens
The first feature resembles the phenomenon that occurs when the sensation of fluctuation strength arises, and as so Schlittmeier et al. devised an algorithm that predicts ISE using fluctuation strength values. Using the algorithm, they were able to predict accurately performance changes in individuals from 63 out of 70 types of sounds. Although the complete characterization of ISE cannot be achieved by the use of fluctuation strength alone, it paves the way for future works regarding the understanding of ISE.
This chapter describes the general methods used in the pilot and the main experiments. First, the equipment and the stimuli used during the experiments are described. Then the magnitude estimation procedure used to assess the various dependencies of fluctuation strength is detailed.
Finally, the manner in which the results were treated is reported.
3.1. Equipment
A personal computer with a M-Audio Transit USB audio interface [12] and a set of Sennheiser HD 265 Linear headphones [15] were used to conduct the experiment. The audio interface had a specified dynamic range output of 104 dB and a signal-to-noise ratio (SNR) of 104 dB. The interface itself was configured to use a 16-bit Linear pulse-code modulation (PCM) input/output (I/O) audio data format. The headphones had an specified frequency response of −3 dB over the 10 Hz - 30,000 Hz frequency range. Furthermore, the headphones provided a diffuse-field loudness equalization to the reproduced sounds. The experiments were conducted inside a sound isolation booth. The experiment itself was programmed using the APEX software platform [10]
and Windows batch files.
3.2. Stimuli
All the sounds presented during the experiment consisted of diotic stimuli, where a monaural stimulus is reproduced to both ears simultaneously. Two types of stimuli were considered: AM tones defined in Equation (3.1), and FM tones defined in Equation (3.4),
xam = [1 − h · cos(2πfmt)] · Ac· sin(2πfct), (3.1) where
h = m0d− 1
m0d+ 1, (3.2)
m0d= 10md20. (3.3)
xf m= Ac· sin{2π[fc− df · cos(2πfmt)]t}. (3.4) In both equations the variable Accorresponds to the amplitude of the carrier signal. Moreover,
a phase shift of −π2 was introduced to the modulating signal for both tones in order to start the corresponding modulation at its lowest point. This phase shift is needed to avoid pops and clicks due to an abrupt onset when presenting the sounds to the participants. Additionally, a cosine ramp with attack and release times of 25 ms was applied to the stimuli to further prevent this phenomenon.
The duration of the stimuli was specified such that it presented at least three periods of the modulating signal, within a range of values between 2 and 4 seconds. Therefore, stimuli with long periods (e.g., fm = 0.25 Hz) were truncated to 4 seconds and stimuli with short periods (e.g., fm = 32 Hz) were generated to reach a 2 sec duration. This was done to maintain a similar duration among stimuli while keeping the whole experiment duration to an acceptable value.
Furthermore, the stimuli were generated such that a level of 100 dB SPL value corresponds to a 0 dBFS value. The sampling rate was set to 44.1 kHz.
3.3. Procedure
The experiment was divided into two phases:
1. Training phase 2. Experimental phase
The training phase will be discussed subsequently in Chapters 4 and 5, as it varied significantly from the pilot experiments to the final experiment. The experimental phase will be discussed as follows.
Experimental Phase The objective of the experiment was to evaluate the dependence of fluctuation strength on the parameters of the AM and FM tones, namely:
• Modulation frequency (fm)
• Center frequency (fc)
• Sound pressure level (SPL)
• Modulation depth (md) for AM tones; frequency deviation (df) for FM tones
In order to obtain subjective data regarding these dependencies, a magnitude estimation procedure was used. In a magnitude estimation procedure [9, pp. 9], individuals are asked to estimate a value for an attribute of a stimulus, taking as a reference an anchor value. The anchor value is usually called the standard. Hence, the standard is assigned to an specific value, and the participant must state according to this reference value which would be the value for the presented stimulus. For example, in case that a value of 10 is assigned to the standard, an answer value of 60 would indicate that the stimulus value is 6 times larger than the reference
the dependency of fluctuation strength on the parameter of the section. For each experimental section a stimuli set was defined by the variation of parameter of the section, thus specifying the stimuli to use during the magnitude estimation procedure.
Every magnitude estimation procedure presented pairs of sounds, composed of one of two possible standards (Table 3.1) and a stimulus from the stimulus set of the section. The standard and the stimulus were separated by 800 ms silence. There were four repetitions per pair, and hence eight per stimulus (four per standard). The selection of the standard and the stimulus used was randomized. After each pair presentation, the participant had to indicate how much did the second sound fluctuate with respect to the first one. A screenshot of the computer interface used in the final experiment design is shown in Figure 3.1.
After each experimental section, participants were given the opportunity to take a break away from the computer for a short while, or to continue directly with the rest of the experimental sections.
Section1 Parameters
fm [Hz] fc [kHz] SPL [dB] md [dB] df [Hz]
AM-fm 4 1 70 40 —
0.25 1 70 40 —
AM-fc 4 1 70 40 —
4 0.25 70 40 —
AM-SPL 4 1 70 40 —
4 1 50 40 —
AM-md 4 1 70 40 —
4 1 70 4 —
FM-fm 4 1.5 70 — 700
0.5 1.5 70 — 700
FM-fc 4 6 70 — 200
4 0.5 70 — 200
FM-SPL 4 1.5 60 — 700
4 1.5 40 — 700
FM-df 4 1.5 70 — 700
4 1.5 70 — 32
Table 3.1.: Description of the standards used per experiment section
3.4. Results
From the data obtained from the magnitude estimation procedures, it was possible to plot the relative fluctuation strength as a function of each varying parameter. An example of these plots
1Each experimental section is designated with the type of stimuli followed by the parameter varied. Therefore, AM-fm represents the fluctuation strength as a function of modulation frequency experiment for AM tones.
Figure 3.1.: Screenshot of the computer interface used in the final experiment design
is shown in Figure 3.2. The actual plot pertaining the experiments will be shown in Chapters 4 and 5.
In order to combine the data points from the two standards, a correction factor had to be applied to the data that used the second standard as a reference. The correction factor was obtained taking into account the data where the second stimulus in the pairs corresponded to the value of the first standard. The correction factor was calculated such that the median of the values that used the second standard was the same as the median of the values that used the first standard. An example of this can be seen in Figure 3.2 panel (b), where the value of the first standard corresponds to a modulation frequency of 4 Hz.
Finally, another correction factor was applied to all the data points, in order to normalize the maximum mean value of the medians of the standards to 100%. The curve of the mean values correspond to the black line shown in Figure 3.2.
Modulation frequency [Hz]
0.25 0.5 1 2 4 8 16 32
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140 160
Standard 1 Standard 2 Combined
(a)
Modulation frequency [Hz]
0.25 0.5 1 2 4 8 16 32
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140 160
Standard 1 Standard 2 Combined
(b)
Figure 3.2.: Relative fluctuation strength as a function of modulation frequency (adapted from [9, pp.248]). The two standards had modulation frequencies of 4 and 0.5 Hz. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data for AM tones with center frequency of 1 kHz, sound pressure level of 70 dB and modulation depth of 40 dB. Panel (b): data for FM tones with center frequency of 1.5 kHz, sound pressure level of 70 dB and frequency deviation of 700 Hz
This chapter describes the experimental design for the evaluation of the fluctuation strength attribute. First, the initial design (as in [7]) is presented. Then, the iterative process of the pilots execution is detailed, stating the progressive changes made to the initial design. Finally, a series of conclusions that lead to the final experimental design are presented.
4.1. Initial Design
4.1.1. Subjects
In total 9 subjects participated in the pilot experiments. Participants were between 20 and 30 years old. All of them had self-reported normal hearing.
4.1.2. Stimuli
Table 4.1 presents all the stimuli used for the different experimental sections, stating which parameters were fixed and which were varied.
4.1.3. Procedure
The pilot experiment was divided in two phases, the training phase and experimental phase, as stated earlier in Chapter 3. The experimental phase remained the same as explained before, using the stimuli set defined in Table 4.1. The training phase for the pilot experiment is described as follows.
4.1.3.1. Training Phase
The objective of this phase was to make the concept of fluctuation strength clear to the participants and to familiarize them with the range of stimuli. Past studies [1] have pointed out the need of such a phase to familiarize subjects with the sensation. However, this must be approached with caution, as the intention of the training phase is to show participants what the sensation is, not teach them how to answer to specific questions regarding the stimuli.
Stimulus Comparison First, a subset of AM tones (Table 4.2) was presented to the participants sequentially according to their ID in pairs (i.e., first stimuli 1 and 2, then 2 and 3, etc.). After
Section Parameters
Fixed Varied
AM-fm fc = 1 [kHz]
SPL = 70 [dB]
md = 40 [dB]
fm = {0, 0.25, 0.5, 1, 2, 4, 8, 16, 32} [Hz]
AM-fc fm = 4 [Hz]
SPL = 70 [dB]
md = 40 [dB]
fc = {0.125, 0.25, 0.5, 1, 2, 4, 8} [kHz]
AM-SPL fm = 4 [Hz]
fc = 1 [kHz]
md = 40 [dB]
SPL = {50, 60, 70, 80, 90} [dB]
AM-md fm = 4 [Hz]
fc = 1 [kHz]
SPL = 70 [dB]
md= {1, 2, 4, 10, 20, 40} [dB]
FM-fm fc = 1.5 [kHz]
SPL = 70 [dB]
df = 700 [Hz]
fm = {0, 0.25, 0.5, 1, 2, 4, 8, 16, 32} [Hz]
FM-fc fm = 4 [Hz]
SPL = 70 [dB]
df = 200 [Hz]
fc = {0.5, 1, 1.5, 2, 3, 4, 6, 8} [kHz]
FM-SPL fm = 4 [Hz]
fc = 1.5 [kHz]
df = 700 [Hz]
SPL = {40, 50, 60, 70, 80} [Hz]
FM-df fm = 4 [Hz]
fc = 1.5 [kHz]
SPL = 70 [dB]
df = {16, 32, 100, 300, 700} [Hz]
Table 4.1.: Description of initial set of stimuli used per experiment section
each pair presentation, participants were asked whether a difference in the fluctuation strength among stimuli was detected. In the case of a negative answer the pair was repeated until a positive answer was obtained.
ID fm [Hz] fc [kHz] SPL [dB] md [dB]
1 0 1 70 40
2 0.5 1 70 40
3 4 1 70 40
4 32 1 70 40
Table 4.2.: Initial subset of AM stimuli for training phase
Long Interval Afterwards, a long interval was presented to the participants. The long interval
Presentation
fm [Hz] fc [kHz] SPL [dB] md [dB]
order
1 8 1 70 40
2 0.5 1 70 40
3 0 1 70 40
4 2 1 70 40
5 32 1 70 40
6 4 1 70 40
7 16 1 70 40
8 1 1 70 40
9 0.25 1 70 40
Table 4.3.: Initial long interval composed of AM stimuli for training phase
4.2. Iterative Improvements
Not all participants were subjected to the same experimental conditions, and not all of them used the same version of the experiments. Table 4.4 presents the conditions and in which one of them the subjects participated.
Participant AM FM Version
1 All All 1
2 All None 1
3 All None 1
4 All None 1
5 fm None 2
6 fm None 3
7 None fm, fc 3
8 None All 3
9 None All 4
Table 4.4.: Participants experimental conditions and versions
The experimental procedure was varied during the pilot experiment to accommodate perceived errors during the realization of them. The first version of the experiment yielded unsatisfactory results with regard to the relation between fluctuation strength and modulation frequency (participants 2, 3 and 4). The procedure was then modified, adding two more AM tones with modulation frequencies of 64 and 128 Hz. The idea behind the addition of these two tones was that, if the participants had stimuli that give a distinguishing roughness sensation, it would be easier for them to distinguish between a fluctuating and a rough tone. Additionally, FM tones were included in the training, since up to this point only AM tones were used in the training phase. This constitutes the second version of the experiment.
Participant 5 was the only participant that was subjected to version 2 of the experiment.
The results did not show any significant improvements with regard to the confusion between fluctuation strength and roughness. However, by talking to the participants it was discovered that the training phase was not able to make the concept of fluctuation strength clear. Participants
were only asked to tell whether there was a difference of fluctuation among the presented stimuli, without explaning what fluctuation strength actually was. As such, several participants associated the rate of change of the stimuli (modulation frequency in this case) with a bigger fluctuation in the presented sounds. Hence, they tended to deem as highly fluctuating the sounds that had a high modulation frequency. Participants 4 and 5 explicitly stated that they were counting the number of cycles in the stimuli, due to confusion on what to answer.
Taking all these comments as feedback, version 3 of the experiment was elaborated. In this version, explicit instructions regarding the rough tones were given. It was indicated that the sensation of fluctuation was unrelated to the apparent ‘speed’ of the stimuli, and that the answers should be intuitive, based on the arising sensation and not rationalizing any judgment about it (for instance by counting cycles). Using this approach participants were able to understand better the fluctuation strength concept, some of them even coming with analogies to the sensation itself (the sound of an ambulance alarm, the sound of a washing machine). The actual instructions used in the final experiment can be found in the prompts of the experimental protocol (Appendix A).
The final version, number 4, of the experiment added a small test experiment before starting the actual experimental sections. This was added as a suggestion from participant 8, who indicated that although the training phase was effective in making the fluctuation strength concept clear, it did not show the participant how to do the expected judgments using the magnitude estimation procedure. Moreover, a latin square randomization approach was used, rotating the order of the experimental sections for each participant. The purpose of this was to distribute possible learning effects of participants among the experimental conditions. Finally, the modulation frequency sections (AM-fm and FM-fm) were split into two separate sections, each one with 2 repetitions per pairs instead of 4. Therefore, two smaller sections for the AM-fm and FM-fm were used in the final experiment. This was done due to the longer duration of the modulation frequency sections when compared to the other sections. By keeping all the sections relatively short (around 6 minutes each) it was expected that participants attention and focus would be retained from one section to another.
4.3. Results
The following figures show the results of the pilot experiments, together with the results reported by Fastl and Zwicker [9]. Comparing the two plots per experimental condition, it can be concluded that both graphs are similar from a qualitative point of view. Therefore, the pilot experiment was deemed as successful in obtaining the relevant subjective data from participants.
A more detailed description of the particularities of each experimental condition curve will be given in Chapter 5.
Modulation frequency [Hz]
0.25 0.5 1 2 4 8 16 32
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140 160
Standard 1 Standard 2 Combined
(a)
Modulation frequency [Hz]
0 0.25 0.5 1 2 4 8 16 32 64 128
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140 160
Standard 1 Standard 2 Combined
(b)
Figure 4.1.: Relative fluctuation strength as a function of modulation frequency for AM tones with center frequency of 1 kHz, sound pressure level of 70 dB and modulation depth of 40 dB. The two standards had modulation frequencies of 4 and 0.5 Hz. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.248]. Panel (b): own results
Center frequency [Hz]
125 250 500 1000 2000 4000 8000
Relative fluctuation strength [%]
40 50 60 70 80 90 100 110 120 130 140
Standard 1 Standard 2 Combined
(a)
Center frequency [Hz]
125 250 500 1000 2000 4000 8000
Relative fluctuation strength [%]
40 50 60 70 80 90 100 110 120 130 140
Standard 1 Standard 2 Combined
(b)
Figure 4.2.: Relative fluctuation strength as a function of center frequency for AM tones with modulation frequency of 4 Hz, sound pressure level of 70 dB and modulation depth of 40 dB. The two standards had center frequencies of 1 and 0.25 kHz. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.250]. Panel (b): own results
4.4. Conclusions
From the obtained data it can be concluded that the main problem when dealing with the perceptual attribute of fluctuation strength is its ambiguity and confusion with the perceptual attribute of roughness. The proposed training phase was effective in clarifying the concept to participants, by adding stimuli with a clear rough sensation, and by clearly instructing them on what the sensation is about. It should be noted that only with regard to modulation frequency this confusion arises, the other parameters do not present this particularity and as so it was not necessary to adapt the experimental procedure with them.
Sound pressure level [dB]
50 60 70 80 90
Relative fluctuation strength [%]
20 30 40 50 60 70 80 90 100 110
(a) 120
Sound pressure level [dB]
50 60 70 80 90
Relative fluctuation strength [%]
20 30 40 50 60 70 80 90 100 110 120
Standard 1 Standard 2 Combined
(b)
Figure 4.3.: Relative fluctuation strength as a function of sound pressure level for AM tones with modulation frequency of 4 Hz, center frequency of 1 kHz and modulation depth of 40 dB. The two standards had sound pressure levels of 70 and 50 dB. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.249]. Panel (b): own results
Modulation depth [dB]
1 2 4 8 20 40
Relative fluctuation strength [%]
0 20 40 60 80 100
(a) 120
Modulation depth [dB]
1 2 4 10 20 40
Relative fluctuation strength [%]
0 20 40 60 80 100 120
Standard 1 Standard 2 Combined
(b)
Figure 4.4.: Relative fluctuation strength as a function of modulation depth for AM tones with modulation frequency of 4 Hz, center frequency of 1 kHz and sound pressure level of 70 dB. The two standards had modulation depths of 40 and 4 dB. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.249]. Panel (b): own results
Modulation frequency [Hz]
0.25 0.5 1 2 4 8 16 32
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140 160
Standard 1 Standard 2 Combined
(a)
Modulation frequency [Hz]
0 0.25 0.5 1 2 4 8 16 32 64 128
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140 160
Standard 1 Standard 2 Combined
(b)
Figure 4.5.: Relative fluctuation strength as a function of modulation frequency for FM tones with center frequency of 1.5 kHz, sound pressure level of 70 dB and frequency deviation of 700 Hz. The two standards had modulation frequencies of 4 and 0.5 Hz.
The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.248]. Panel (b): own results
Center frequency [Hz]
500 1000 1500 2000 3000 4000 6000 8000
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140
Standard 1 Standard 2 Combined
(a)
Center frequency [Hz]
500 1000 1500 2000 3000 4000 6000 8000
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140
Standard 1 Standard 2 Combined
(b)
Figure 4.6.: Relative fluctuation strength as a function of center frequency for FM tones with modulation frequency of 4 Hz, sound pressure level of 70 dB and frequency deviation of 200 Hz. The two standards had center frequencies of 6 and 0.5 kHz. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.250]. Panel (b): own results
Sound pressure level [dB]
40 50 60 70 80
Relative fluctuation strength [%]
20 30 40 50 60 70 80 90 100 110
(a) 120
Sound pressure level [dB]
40 50 60 70 80
Relative fluctuation strength [%]
20 30 40 50 60 70 80 90 100 110 120
Standard 1 Standard 2 Combined
(b)
Figure 4.7.: Relative fluctuation strength as a function of sound pressure level for FM tones with modulation frequency of 4 Hz, center frequency of 1.5 kHz and frequency deviation of 700 Hz. The two standards had sound pressure levels of 60 and 40 dB. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.249]. Panel (b): own results
Frequency deviation [Hz]
16 32 100 300 700
Relative fluctuation strength [%]
0 20 40 60 80 100 120
(a) 140
Frequency deviation [Hz]
16 32 100 300 700
Relative fluctuation strength [%]
0 20 40 60 80 100 120 140
Standard 1 Standard 2 Combined
(b)
Figure 4.8.: Relative fluctuation strength as a function of modulation depth for FM tones with modulation frequency of 4 Hz, center frequency of 1.5 kHz and sound pressure level of 70 dB. The two standards had frequency deviations of 700 and 32 Hz. The data points show the median and interquartile ranges per standard. The black line represents the mean values of the medians of each standard. Panel (a): data adapted from [9, pp.251]. Panel (b): own results
In this chapter the final experimental design and results for the evaluation of the fluctuation strength attribute are presented.
5.1. Design
5.1.1. Subjects
Twenty-four participants were recruited from the JF Schouten database of the Eindhoven University of Technology. Participants were between 19 and 31 years old. There were in total six females and eighteen males. All of them reported to have normal hearing, however this was not confirmed in any way. Subjects were paid for their participation.
5.1.2. Stimuli
The stimuli used in the final experiment have the same characteristics as the ones used in the pilot experiments (Section 4.1.2). Table 5.1 shows the stimuli used in the final experiments.
5.1.3. Procedure
Participants were assigned either to AM tones or to FM tones, both conditions having 12 participants. Furthermore, the presentation order of the experimental sections was varied, using a latin square design. The order of the parameters used is presented in Table 5.2.
The whole experiment had an approximate duration of 60 minutes. The experimental protocol followed during the experiment can be found in the appendix of this document (Appendix A).
The experimental phase of the experiment remained the same as the one of the last pilot experiment. The only sensible change compared to the procedure described in Chapter 3 is the split of the modulation frequency sections into two separate sections. The training phase had some changes, described below.
5.1.3.1. Training Phase
Adding all the improvements postulated in the pilot experiment section, the training phase was expanded and became a 3-part phase, described below.
Section Parameters
Fixed Varied
AM-fm fc = 1 [kHz]
SPL = 70 [dB]
md = 40 [dB]
fm = {0, 0.25, 0.5, 1, 2, 4, 8, 16, 32, 64, 128} [Hz]
AM-fc fm = 4 [Hz]
SPL = 70 [dB]
md = 40 [dB]
fc = {0.125, 0.25, 0.5, 1, 2, 4, 8} [kHz]
AM-SPL fm = 4 [Hz]
fc = 1 [kHz]
md = 40 [dB]
SPL = {50, 60, 70, 80, 90} [dB]
AM-md fm = 4 [Hz]
fc = 1 [kHz]
SPL = 70 [dB]
md= {1, 2, 4, 10, 20, 40} [dB]
FM-fm fc = 1.5 [kHz]
SPL = 70 [dB]
df = 700 [Hz]
fm = {0, 0.25, 0.5, 1, 2, 4, 8, 16, 32, 64, 128} [Hz]
FM-fc fm = 4 [Hz]
SPL = 70 [dB]
df = 200 [Hz]
fc = {0.5, 1, 1.5, 2, 3, 4, 6, 8} [kHz]
FM-SPL fm = 4 [Hz]
fc = 1.5 [kHz]
df = 700 [Hz]
SPL = {40, 50, 60, 70, 80} [Hz]
FM-df fm = 4 [Hz]
fc = 1.5 [kHz]
SPL = 70 [dB]
df = {16, 32, 100, 300, 700} [Hz]
Table 5.1.: Description of stimuli used per experiment section
Order1 Parameters
1 fm, fc, {md or df}, fm, SPL
2 fc, {md or df}, fm, SPL, fm
3 {mdor df}, fm, SPL, fm, fc
4 SPL, fm, fc, {mdor df}, fm
Table 5.2.: Presentation order of parameters
Stimulus Comparison As in the pilot experiments, the initial part of the training phase consisted of comparison between stimuli. An additional stimulus was added (fm = 128 Hz) and a subset of FM stimuli was also added to complement the AM tones.
The stimuli presented in Tables 5.3 and 5.4 were reproduced in groups, according to their ID values. First, stimuli with ID values of 1 and 2 were reproduced. This pair presented the
values of fluctuation strength. Finally, stimuli with ID values of 3, 4 and 5 were reproduced.
This last group presented the difference between fluctuating and rough tones. After each group presentation, participants were asked whether the specific difference of sensation of the group was acknowledged. In case of a negative answer, the stimuli of the group were once again reproduced.
ID fm [Hz] fc [kHz] SPL [dB] md [dB]
1 0 1 70 40
2 0.5 1 70 40
3 4 1 70 40
4 32 1 70 40
5 128 1 70 40
Table 5.3.: Subset of AM stimuli for training phase
ID fm [Hz] fc [kHz] SPL [dB] df [Hz]
1 0 1 70 700
2 0.5 1 70 700
3 4 1 70 700
4 32 1 70 700
4 128 1 70 700
Table 5.4.: Subset of FM stimuli for training phase
Long Interval This part of the training phase presented participants with long intervals, which consisted of stimuli separated by 800 ms of silence. Two long intervals were reproduced, composed of AM and FM tones, respectively. These two intervals are described in Tables 5.5 and 5.6.
Presentation
fm [Hz] fc [kHz] SPL [dB] md [dB]
order
1 0.5 1 70 40
2 32 1 70 40
3 2 1 70 40
4 16 1 70 40
5 4 1 70 40
6 1 1 70 40
7 0 1 70 40
8 64 1 70 40
9 0.25 1 70 40
10 128 1 70 40
11 8 1 70 40
Table 5.5.: Long interval composed of AM stimuli for training phase
Test Section In order to familiarize participants with the interface used during the experiment and with the magnitude estimation procedure, a small test section was added at the end of the
Presentation
fm [Hz] fc [kHz] SPL [dB] df [Hz]
order
1 0.25 1 70 700
2 64 1 70 700
3 32 1 70 700
4 2 1 70 700
5 1 1 70 700
6 0 1 70 700
7 8 1 70 700
8 4 1 70 700
9 0.5 1 70 700
10 128 1 70 700
11 16 1 70 700
Table 5.6.: Long interval composed of FM stimuli for training phase
training phase. This section consisted of four pairs (Table 5.7), which were presented to the participants in randomized order.
Pair Parameters
fm [Hz] fc [kHz] SPL [dB] md [dB] df [Hz]
1 4 1 70 40 —
32 1 70 40 —
2 4 6 70 — 200
4 6 70 — 200
3 4 1 70 40 —
0 1 70 40 —
4 4 1.5 60 — 700
4 1.5 80 — 700
Table 5.7.: Pairs used in training phase test section
5.2. Results
The following section presents the results of the experiments, compared to the data published by Fastl and Zwicker [9]. Overall the obtained data is qualitatively similar to the data by Fastl and Zwicker, although some differences do exist. Most notably, in the modulation depth response curve for AM tones and in the center frequency and frequency deviations curves for FM tones.
In the following paragraphs the obtained curves will be described, focusing on similarities and discrepancies with the literature data. Possible causes of this discrepancies will be discussed in Chapter 7.
modulation frequency below 4 Hz on average higher values of fluctuation were obtained. This leads to the fact that the response from the obtained data has a wider bandwidth than the data from the literature. Also, more variability seems to exist with the use of the first standard, evidenced by the difference of length between the larger interquartile range (IQR)s of the first standard and the smaller IQRs of the second standard.
Figure 5.2 shows the dependency of fluctuation strength on center frequency from AM tones.
In this case both responses present a similar flat response with large IQRs. Figure 5.2 shows the dependency of fluctuation strength on center frequency from FM tones. Here the difference is more dramatic, the data from the literature decreases monotonically with the increase of center frequency, whereas the data from this study remain mostly flat.
Figures 5.3 and 5.7 show the dependency of fluctuation strength on sound pressure level for AM and FM tones. Although the curves from the obtained data are not as linear as the data from the literature, in both cases fluctuation strength increases with sound pressure level.
Figure 5.4 shows the dependency of fluctuation strength on modulation depth from AM tones.
Here a difference exists between the obtained data and the literature data. Both response curves show an increase of fluctuation strength with the increase of modulation depth. However, the obtained data increases more quickly with modulation depth than the data from the literature.
Figure 5.8 shows the dependency of fluctuation strength on frequency deviation from FM tones. In this case a clear difference exists between the obtained data and the literature data.
For the obtained data, for small values of frequency deviation a significant fluctuation strength (around 50%) does exist. This causes that the curve presents a less steep slope when compared to the literature data. Both curves present an increase in fluctuation strength with an increase in frequency deviation.
Finally, to summarize Figures 5.9 and 5.10 compared the mean of the values of the two standard for each experimental condition. The discrepancies between obtained data and literature data can be further observed in these figures.
