Articulatory compensation for low-pass filtered formant-altered auditory feedback
Yasufumi Uezu,1 Sadao Hiroya,1 and Takemi Mochida1
NTT Communication Science Laboratories, Nippon Telegraph and Telephone
Corporation, 3-1, Morinosato-Wakamiya, Atsugi-shi, Kanagawa, 243-0198,
Japana)Copyright (2021) Acoustical Society of America. This article may be downloaded for
personal use only. Any other use requires prior permission of the author and the
Acoustical Society of America.
The following article appeared in
Yasufumi Uezu, Sadao Hiroya, Takemi Mochida; Articulatory compensation for
low-pass filtered formant-altered auditory feedback. J. Acoust. Soc. Am. 1 July 2021;
150 (1): 64–73.
and may be found at https://doi.org/10.1121/10.0004775 .

1

Low-pass filtered formant AAF
1

Auditory feedback while speaking plays an important role in stably controlling speech2articulation. Its importance has been verified in formant-altered auditory feedback

3(AAF) experiments where speakers utter while listening to speech with perturbed first4(F1) and second (F2) formant frequencies. However, the contribution of frequency

5components higher than F2 to the articulatory control under the perturbations of F1

6

and F2 has not yet been investigated. In this study, we conducted a formant AAF

7experiment where a low-pass filter was applied to speech. The experimental results

8

showed that the deviation in the compensatory response was significantly larger when9

a low-pass filter with a cutoff frequency of 3-kHz was used, compared to that of 4-10

and 8-kHz. We also found that the deviation in 3 kHz condition correlated with the11fundamental frequency and spectral tilt of the produced speech. Additional simu-

12

lation results using a neurocomputational model of speech production (SimpleDIVA

13model) and our experimental data showed that feedforward learning rate increased14

as the cutoff frequency decreased. These results suggest that high-frequency compo-

15

nents of the auditory feedback would be involved in the determination of corrective

16

motor commands from auditory errors.

uezu8223@gmail.coma)2

Low-pass filtered formant AAF
17

I.

INTRODUCTION

18

Sensory feedback is essential when humans are learning and performing complex move-19

ments. In speech production, auditory and somatosensory feedback plays an important role20in the coordination of speech organs, by which fluency in speaking is achieved (Perkell et al.,211997). Especially, the absence of auditory feedback significantly disrupts language acquisi-

22tion in infants and online correction of speech errors. The mechanism behind auditory-based

23

speech motor control is considered to be related to an auditory prediction associated with24

the speech motor command to be executed. Optimal speech motor coordination can be per-25

formed by evaluating and compensating the error between the predicted and actual auditory

26

consequences. This requires a function to transform auditory errors into corrective motor

27

commands.

28

Speech motor control has been investigated by exploring how speech production changes

29

when acoustic features of speech collected from a microphone are perturbed and returned

30

through headphones to the speaker. Some altered auditory feedback (AAF) experiments

31

have demonstrated compensatory responses to the perturbation of vowel formant frequencies,

32

where speakers’ vowel production changes in the direction of reducing the formant frequency

33

error between the intended target and the actual feedback (Houde and Jordan, 1998; Purcell

34

and Munhall, 2006; Villacorta et al., 2007). These studies have provided crucial evidence

35

that the brain is capable of estimating the correct amount of articulatory compensation to36

be made from the auditory error. We have also experimentally confirmed the importance of37

accurate formant manipulation for the correct compensatory response in AAF experiments3

Low-pass filtered formant AAF
38(Uezu et al., 2020). In parallel with these experimental developments, a neural network

39

model simulating brain function in speech production, called directions into velocities of40

articulators, or DIVA, has been proposed to investigate the neural mechanisms underlying

41

auditory feedback control during speech production (Guenther et al., 2006). The validity of42

the model has been verified by fitting of formant AAF experimental data (Villacorta et al.,432007) and by functional brain imaging (Tourville et al., 2008).

44

Speech sounds are composed of information in various frequency regions. In the study

45

of vowel production, F1 and F2 are considered to be goals of vowel production (Perkell

46

et al., 1997). In fact, many AAF experiments have perturbed F1 and F2 and investigated47

the compensatory responses. However, few vowel-production studies have focused on high-48

frequency components, although the shape of the vocal tract determines acoustic features49

such as F1 and F2 as well as high-frequency components. On the other hand, studies on

50vowel perception have investigated information in speech signals at different frequencies

51(Fig. 1). In general, lower-order formants such as F1 and F2 are parameters for determining52

the phonological properties of vowel sounds. Studies on vowel perception and classification

53

have also shown that intelligibility is improved by considering F3 as well (Hillenbrand and54

Gayvert, 1993; Miller, 1989; Schwartz and Escudier, 1989). Other studies have found that55

high-frequency components around F3 are associated with speaker individuality (Kitamura

56

and Akagi, 1995). Therefore, it is considered that the high-frequency components around57

F3 include phoneme-specific and speaker-specific information on vowel perception.

58

Conversion of auditory errors into corrective motor commands, which is specific to each59

speaker, is essential for compensation to occur, but it has a one-to-many mapping (Atal4

Low-pass filtered formant AAF
60

et al., 1978; Hiroya and Honda, 2004). Therefore, if a higher frequency component than61

F1 and F2 is not included in the speech in formant AAF experiments, it is considered62

difficult to accurately estimate the corrective motor commands from the error in F1 and F2

63

in narrowband auditory input. However, it is unclear whether the compensatory response to64

perturbations to F1 and F2 is affected by the presence or absence of frequency components

65higher than F1 and F2.

66

In this study, we examined how high-frequency components of speech affect the auditory-

67

motor control of vowel production by combining formant AAF and a low-pass filter. Speakers

68

were asked to produce a syllable containing the Japanese vowel /e/. F1 and F2 are simul-

69

taneously perturbed toward the vowel /a/. 3, 4 and 8 kHz were used as cutoff frequencies

70of the low-pass filter. We used a phase equalization-based autoregressive exogenous model

71(PEAR) (Oohashi et al., 2015) for its high formant estimation accuracy because the accuracy

72

in the low-frequency component is important. The analysis was based on the magnitude and73

deviation of the projection of the compensatory response to the perturbation in the F1-F2

74

plane (Daliri and Dittman, 2019; Niziolek and Guenther, 2013).

75

The purpose of this study is to investigate whether the presence or absence of frequency

76

components higher than F1 and F2 affect the one-to-many mapping in determining corrective

77

motor commands from auditory errors in F1 and F2 during vowel production, irrespective

78of phoneme-specific or speaker-specific properties on vowel perception. The effect should79

be observed as a difference in the magnitude and deviation of the compensatory response80

depending on the cutoff frequency. Furthermore, in order to investigate the neural mecha-

81

nism, formant AAF experimental data was fitted by a simplified version of the DIVA model5

Low-pass filtered formant AAF
82(SimpleDIVA model) (Kearney et al., 2020) and the feedforward and feedback parameters

83

were quantified. We also examined what specific features in the high-frequency components

84

contributed to the compensatory responses by calculating the correlation of the magnitude85

and deviation of response with F3, the fundamental frequency (f0 ) and spectral tilt.

86

II.

EXPERIMENTS

87

A.

Experimental procedure88

The participants were 29 native Japanese speakers (nineteen females and ten males;

89

average age, 37.9 years, standard deviation, 9.1, age range, 20-55 years). None of the90

speakers reported hearing or speech difficulties. All gave informed consent to participate in91

the study, which was approved by the NTT Communication Science Laboratories Research

92

Ethics Committee.

93

The experiment was performed in a soundproof room. Figure 2 shows a block diagram of94

the formant altered auditory feedback used in this study. The speakers sat 20-cm from the95

microphone (SONY ECM-678/9X) and wore headphones (SENNHEISER HD280 Pro). The

96

speech signal from the microphone was amplified (M-Audio DMP3), low-pass-filtered (MTT97

MS2319) at a cutoff frequency (Fc) of 8 kHz, A/D converted at 16 kHz, and transmitted to98

a real-time formant transformation system (Texas Instruments C66x) to generate formant-

99

shifted speech signals. The altered speech signals were D/A converted, low-pass-filtered100

at a cutoff frequency of 3, 4, or 8 kHz (NF P-86, -135 dB/oct rolloff), amplified (Audio-

101

Technica AT-MA 55), and presented via headphones with a delay of 16.5 ms. The uttered6

Low-pass filtered formant AAF
102

and altered speech was recorded on a PC using a DAQ device (National Instruments USB-

1036210). Speakers were encouraged to utter at a natural rate and level with timing controlled

104

by a prompt on a monitor and instructed to close their lips at the end of each trial. Each

105

prompt lasted 2 s, and the inter-trial interval was approximately 3.5 s.

106

Speakers were asked to produce the Japanese syllable /he/, which was shown on the107

monitor in hiragana (Japanese character) (Mitsuya et al., 2011). Figure 3 shows perturbation

108

patterns of F1 and F2 in a block including 140 utterance trials. A block consisted of four109

phases: Baseline (trials 1-20), Ramp (trials 21-70), Hold (trials 71-90), and Return (trials 91-

110140). In the Baseline phase, speakers produced utterances with no altered feedback. In the111

Ramp phase, the perturbation to the formant frequency increased linearly until reaching the112

maximum level of perturbation. In the Hold phase, speakers uttered while receiving speech

113

with formant frequencies altered at the maximum level of perturbation. In the Return phase,114

speakers produced utterances with normal feedback, which was the same as in the Baseline

115

phase. The maximum level of perturbation for formant frequencies was (F1, F2) = (+150,

116−300 Hz) (Martin et al., 2018). The cutoff frequency of 3, 4, or 8 kHz for the altered speech

117

was fixed within one block. All subjects participated under all experimental conditions.

118

The order of the three cutoff frequency conditions was counterbalanced among the subjects.

119

Masking noise was not used. The participants performed 30 trials for training. During these120

trials, calibration was performed so that the headphone output of the speech was 72 dBA

121

SPL (ACO TYPE6240 and TYPE2015).

122

Studies on speech production while speakers listen to speech whose frequency band is123

limited by the low-pass filter have been carried out in the past (Burzynski and Starr, 1985;
7

Low-pass filtered formant AAF
124

Garber and Moller, 1979; Garber et al., 1980, 1981; Peters, 1955). In those experiments

125

without the AAF system, when a low-pass filter with a cutoff frequency of less than 1 kHz126

was applied to the speech, the speech became clear and nasalization of speech subsided.

127

However, the cutoff frequencies were at most 1.8 kHz, and F2 may not have been included

128

for front vowels such as /i/ and /e/. Therefore, in this study, the cutoff frequency of the129

low-pass filter was set to at least 3 kHz to include F2. We set cutoff frequencies of 4 kHz

130

including F3 for all speakers and of 8 kHz, which is close to the frequency band of normal

131

speech.

132

Speech signals were pre-emphasized by a first-order high-pass filter. Then, a 16-ms Black-133

man window was applied, and LPC coefficients were obtained every 8 ms by using the PEAR

134

method. To estimate a time-stable spectrum, TANDEM windows were used (Oohashi et al.,1352015). The numbers of LPC coefficients (13 to 17) and taps of the phase equalization filter

136(9 to 28) for each of the speakers were determined by calibration (Uezu et al., 2020; Vallabha

137

and Tuller, 2004).

138

AAF experiments require formants to be estimated in real-time. Although linear pre-139

dictive coding (LPC) (Itakura and Saito, 1970) is widely used in such experiments (Purcell

140

and Munhall, 2006; Villacorta et al., 2007), the estimated formant frequency is prone to141errors (Oohashi et al., 2015). To improve estimation accuracy, we have proposed the PEAR

142

method (Oohashi et al., 2015). Our previous studies have shown that the compensatory

143

response to perturbations in PEAR is greater than that in LPC (Uezu et al., 2020) For this144

experiment, a system with a sampling frequency of 16 kHz was developed on the basis of the145

PEAR algorithm (Oohashi et al., 2015). In the conventional system (Oohashi et al., 2015),
8

Low-pass filtered formant AAF
146

the electroglottography (EGG) electrode is attached to the neck to extract the pitch mark147

corresponding to the glottal closure from the speech signal, whereas in the present system,

148

instead of EGG, the SEDREAMS algorithm was used to extract the pitch mark (Drugman

149

et al., 2012).

150

B.

Analysis151

The formant analysis of the speech was performed using the PEAR method offline, and152

the median value from 40 to 80% of the vowel interval was used as a representative value for

153

each trial. Compensatory responses in formant frequencies were determined by subtracting154

the value in the Baseline phase from that in the Hold phase. The Baseline and Hold values

155of the formant frequencies in each block were set by computing the mean value from Baseline156(11-20 trials) (Munhall et al., 2009) and Hold (71-90 trials) formants, respectively.

157

We not only evaluated the magnitude of the compensatory response of F1 and F2 inde-

158

pendently, but also used the projection of the compensatory response to the perturbation

159

in the F1-F2 plane (Daliri and Dittman, 2019; Niziolek and Guenther, 2013). Figure 4

160

shows a schematic diagram of the concept. The origin in the F1-F2 formant space is the161formant frequencies of the subject at the baseline. The vector from the baseline to the mean

162

value of the formant frequencies of the subject in the Hold phase is defined as the formant

163

−
→
response vector FR . A perturbation vector from the origin to the maximum perturbation

164(+150, −300 Hz) is considered, and its inverse vector is defined as an “ideal” compensatory

165

−
→
response vector FI . Here, the magnitude M was defined as the projection component from166

the response vector to the perturbation-compensation line, and the deviation response D
9

Low-pass filtered formant AAF
167(Daliri and Dittman, 2019) was defined as the value of the perpendicular component:−→ −→FI · FRM [Hz] = −
→
|FI |
q
−
→
D[Hz] = |FR |2 − M 2 .

(1)
(2)

168

A positive magnitude M means that compensation has been made for the perturbation,

169

and the larger the magnitude, the greater the compensation. The deviation D must be

170

greater than or equal to zero, and a larger deviation means that the compensation for the171

perturbation diverges from the ideal compensatory response vector. If the value of F 1/F 2

172

−
→
−
→
−
→
in FI matches that in FR , then M is |FR | and D is 0. Therefore, M and D are related

173

through the ratio of the change in F1 and F2.

174

An opposite direction of the effect, i.e., a following response to the AAF, has been re-

175

ported in recent studies (Vaughn and Nasir, 2015). While the compensatory response helps

176

to reduce the acoustic error between the intended and the actual speech, the mechanism

177

underlying the following response is not well understood. To statistically evaluate the fol-178

lowing response to the perturbation, we calculated the ratio A of the magnitude of the179

compensatory response to the absolute value of the formant response (Fig. 4):
M
A= −→ (−1 ≤ A ≤ 1).
|FR |

(3)

180

In the cosine formula, cos−1 (A) is the angle in radians. If A is positive, the response is181

considered compensatory; and if it is negative, the response is considered following. In

182

addition, if A is close to 1, the response is a more ideal compensatory response. This

183

index is expected to correctly evaluate the ratio of compensation and following responses,

184

independently of the magnitude of the compensatory response.
10

Low-pass filtered formant AAF
185

Although the DIVA model (Guenther et al., 2006) can simulate the data of formant AAF

186

experiments (Villacorta et al., 2007), it has many parameters. Recently, a simplified model

187

with only three parameters, SimpleDIVA (Kearney et al., 2020), has been proposed. Simple-

188

DIVA makes it possible to evaluate the reliance on auditory feedback by fitting experimental

189

data. The parameters are auditory feedback gain αA , somatosensory feedback gain αS , and190

feedforward learning rate λF F , and the model isyprod (n) = yF F (n) + ∆yF B (n)∆yF B (n) = αA × (yT (n) − yAF (n))+αS × (yT (n) − ySF (n))
yF F (n + 1) = yF F (n) + λF F × ∆yF B (n),191

where y is formant frequency and n is trial number. FF stands for feedforward, FB for

192

feedback, prod for production, AF for auditory feedback, SF for somatosensory feedback,193

and T for target. The parameters were estimated from the time-series subject-averaged

194

formant data of the AAF experiment for each cutoff frequency. Thus, data in the Baseline,

195

Ramp and Return phases were also considered.

196

III.

RESULTS

197

A.

Response to perturbation

198

Table I shows the mean and standard deviation of F1, F2, f0 , and vowel duration at the

199baseline. An ANOVA showed that there was no significant difference between the cutoff

200

frequencies for all of the feature values. This suggests that the cutoff frequency of the low11

Low-pass filtered formant AAF
201

pass filter used in this study does not affect speech production if the auditory feedback is

202

not perturbed.

203

Figure 5 shows the changes in the baseline of F1 and F2 in each trial, where the low-pass

204

filter cutoff frequency was 3, 4, or 8 kHz. Note that corrections have been made so that205

the baseline mean is zero. In all cases, compensation for the perturbation in Fig. 3 appears

206

in the Ramp and Hold phases, and it returns to zero in the Return phase (131-140 trials)

207

in all conditions for 3 kHz (t(28) = 0.98, p = 0.33 for F1 and t(28) = 1.70, p = 0.09 for

208

F2), 4 kHz (t(28) = 0.02, p = 0.98 for F1 and t(28) = 0.24, p = 0.80 for F2) and 8 kHz

209(t(28) = −0.38, p = 0.70 for F1 and t(28) = 1.51, p = 0.14 for F2).

210

−
→
Figure 6 shows response vectors FR for each participant for the cutoff frequency condition211

Fc = (3, 4, 8) kHz on the F1-F2 plane. If a participant produces formant compensations

212

in the ideal direction for the given perturbations, we would expect to see a response vector

213

in the upper left direction along the perturbation-compensation line, and many response

214

vectors indeed occurred in the upper left direction as expected. However, the magnitude215

and direction of the response vector were affected by individual differences. In addition, it

216

was found that the directions of the response vectors in the 3-kHz condition tended to be

217

more scattered compared with other cutoff frequency conditions.

218

Figures 7 and 8 show the compensatory responses for F1 and F2 for the cutoff frequency219

conditions. A one-sample t-test revealed that the absolute value of the compensatory re-220

sponse to baseline was significantly greater than 0 in all conditions for F1 (t(28) = −4.33

221

for 3 kHz, −5.45 for 4 kHz, −6.10 for 8 kHz, p < 0.01) and F2 (t(28) = 5.71 for 3 kHz,222

7.05 for 4 kHz, 7.56 for 8 kHz, p < 0.01). An ANOVA showed that there was no signif12

Low-pass filtered formant AAF
223

icant difference between the cutoff frequencies in F1 (F (2, 84) = 0.24, p = 0.78) and F2

224(F (2, 84) = 0.07, p = 0.92). Note that the dependent variable is the compensatory response225

of F1 or F2, the independent variable is the cutoff frequency, and repeated measure ANOVA226

was not used.

227

There was no difference between the cutoff frequencies when the compensatory responses

228

of F1 and F2 were evaluated independently. We also examined the magnitude and deviation229

of the compensatory response in the F1-F2 plane. Figures 9 and 10 show the magnitude

230

and the deviation of compensatory response for the cutoff frequency conditions, respectively.

231

Note that a Shapiro-Wilk test showed that the distribution of the deviation in the compen-232satory response did not satisfy normality. A Kruskal-Wallis test revealed that there was no233

significant difference in the magnitude of the compensatory response between the conditions234(χ2 (2) = 0.69, p = 0.70). However, the deviation in the compensatory response tended to235

decrease when the cutoff frequency was high. Another Kruskal-Wallis test revealed that there236

was a significant difference in the deviation in the compensatory response between the con-237

ditions (χ2 (2) = 7.86, p = 0.01). A two-tailed Mann-Whitney U test with Holm correction

238

revealed that there were significant differences between the 3- and 4-kHz conditions (effect239

size (r) = 0.46, p < 0.05) and between the 3- and 8-kHz conditions (r = 0.43, p < 0.05),

240

but not between the 4- and 8-kHz conditions (r = 0.14, p = 0.43). This indicates that the241

deviation in the compensatory response to the perturbation increased when the vowel was

242uttered while the participants listened to the speech through a low-pass filter having a cutoff

243

frequency of 3 kHz. Note that, in all cutoff conditions, the magnitude and deviation of the13

Low-pass filtered formant AAF
244

compensatory response did not show significant differences between genders, except for a

245

minor difference in the magnitude at 4 kHz (p < 0.05).

246

Figure 11 shows that the largest value of ratio A is at 8 kHz. A Shapiro-Wilk test

247

showed that the distribution of A did not satisfy normality. A Kruskal-Wallis test showed

248that there was a difference in A between cutoff frequencies (χ2 (2) = 7.30, p = 0.02). A

249

two-tailed Mann-Whitney U test with Holm correction revealed that there was a significant

250

difference between the 3 and 8 kHz conditions (r = 0.47, p < 0.05), but not between 4 and251

8 kHz (r = 0.24, p = 0.19) and between 3 and 4 kHz (r = 0.30, p = 0.19), although the252mean value was smaller for 4 kHz.

253

B.

SimpleDIVA simulation

254

Table II shows the results estimated using SimpleDIVA (Version 1.3). In the SimpleDIVA

255

study (Kearney et al., 2020), λF F , which was primarily affected by data in the Ramp phase,256

ranged between 0.11 and 0.15, which are reasonable values for 8 kHz, but the values for 3

257

and 4 kHz were extremely large. Moreover, the magnitudes of the feedback gains αA and258

αS for 3 and 4 kHz were smaller than those for 8 kHz. The variation in the ratio of αA and

259

αS , which determines the maximum amount of compensation in the Hold phase (Kearney260

et al., 2020), between the cutoff frequencies was smaller than that of λF F .

261

C.

Correlation with F3, f0 and spectral tilt

262

High-frequency component of speech at 3 kHz or higher include not only the third and263

fourth higher formant frequencies derived from the vocal tract but also the harmonic com14

Low-pass filtered formant AAF
264

ponents of the fundamental frequency and the spectral tilt characteristics derived from the265

glottal source. Therefore, eliminating the high-frequency components of the speech with266

a low-pass filter means that these pieces of source information are lost. We examined the267

correlation of the magnitude and deviation of the compensatory response at the cutoff fre-268

quency of 3 kHz with the values of F3, f0 , and the spectral tilt. The spectral tilt, which

269

represents the slope of the source, was obtained from linear prediction coefficients of the270

first order (Wakita, 1973): the larger the coefficient, the steeper the tilt. These values were271

obtained from speech at a sampling frequency of 16 kHz during calibration.

272

Figure 12 shows that the magnitude in the compensatory response at the cutoff frequency273

of 3 kHz was not significantly correlated with F3 (correlation coefficient (R) = 0.08, p =2740.67) or with f0 (R = −0.15, p = 0.46), but it was significantly correlated with spectral

275

tilt (R = −0.44 p < 0.05). Moreover, the figure shows that the deviation at 3 kHz was not276

significantly correlated with F3 (R = 0.00, p = 0.99), but it was marginally correlated with277

f0 (R = 0.33, p = 0.07) and significantly correlated with the spectral tilt (R = 0.47, p <2780.01). Note that the magnitude and deviation at 4 and 8 kHz were not correlated with these279

values, except for a correlation between the magnitude at 4 kHz and F3 (R = 0.37, p < 0.05),

280

and the magnitude and deviation in all cutoff conditions were not correlated with age, and281

there were significant differences in F3 and f0 between genders (p < 0.01), but not in spectral

282

tilt (p = 0.07).
15

Low-pass filtered formant AAF
283

IV.

DISCUSSION

284

We investigated the effect of using a low-pass filter to cut the high-frequency compo-

285

nents of speech on the compensatory response of formant AAF. The perturbations in this286

experiment were given to the F1 and F2 values, which were less than 3 kHz for all subjects.

287

When low-pass filters with cutoff frequencies of 3, 4, and 8 kHz were used, although the288

perturbations for F1 and F2 were the same between conditions, the frequency components

289

higher than F1 and F2 were not included in the 3 and 4 kHz conditions. The results of the290experiment indicated that the deviation in the compensatory response at 3 kHz was signifi-

291

cantly larger than that of 4 and 8 kHz, but that there was no significant difference between 4292

and 8 kHz, although the magnitude of the compensatory response did not differ among the293

cutoff frequencies. The fact that the magnitude of the compensatory response was almost294

the same, but the deviation differed between conditions suggests that the same magnitude of295

compensatory response can be generated from different corrective motor commands. This

296

corresponds to a redundancy in the acoustic-to-articulatory mapping (Atal et al., 1978).

297

Therefore, the absence of frequency components higher than 3 kHz increased the redun-

298

dancy in the determination of corrective motor commands from the auditory errors of F1

299

and F2, resulting in an increase in the deviation of compensatory response. These findings

300

suggest that the corrective motor commands for the magnitude of the auditory errors can be

301

determined precisely from only the errors contained in the auditory feedback regardless of302

the presence or absence of high-frequency components and that the difference in deviation

303

between conditions results from the redundancy in the determination of corrective motor
16

Low-pass filtered formant AAF
304

commands. In other words, compensation for the magnitude of perturbations is a task for305

auditory-motor control of vowel production.

306

SimpleDIVA modeling results showed that the feedforward learning rate increased with307

decreasing cutoff frequencies. This suggests that the change of feedforward control caused by308

low-pass filtering may affect the redundancy in the determination of corrective motor com-309

mands. Daliri and Dittman (2019) examined the effect of the reliance on auditory feedback on

310

the compensatory response by directly comparing compensatory responses to perturbations

311

of F1 and F2 for task-relevant errors under the formant shift condition with task-irrelevant

312

errors under the formant clamp condition. Our study is similar to Daliri and Dittman (2019)313

in that it varied the reliance on auditory feedback, but it differs from that study (Daliri and314

Dittman, 2019) in that the magnitude and deviation became smaller when the reliance on

315

auditory feedback was low. This is due to differences in the experimental methods: While

316

Daliri and Dittman (2019) varied the reliance on auditory feedback depending on whether

317

F1 and F2 was controlled, we changed it depending on whether or not there was a high-318

frequency component. We speculated that the difference in reliance on auditory feedback319

between the formant shift condition and the formant clamp condition of Daliri and Dittman

320(2019) was larger than that between our cutoff frequencies. Therefore, since the reliance on

321

auditory feedback was too low in Daliri and Dittman (2019), the dependence on feedforward322

control would increase, and there would be little compensatory response.

323

These results indicate that the absence of high-frequency components in the feedback

324

speech changed not only the redundancy in determining corrective motor commands but

325

also the reliance on auditory feedback. However, the relationship between the changes
17Low-pass filtered formant AAF
326

remains unclear. This is because SimpleDIVA, unlike full DIVA (Guenther et al., 2006), does327

not require F3 input and does not convert auditory errors into corrective motor commands,

328

which would be necessary to quantify the amount of redundancy. Also, the results indicating

329

that the deviation was different were obtained from the compensatory response in the Hold330

phase, while the results of SimpleDIVA were obtained from the formant data of all 140 trials.

331

We speculate that an increase in redundancy caused a decrease in the reliance on auditory332

feedback, but further investigation will be needed to confirm it.

333

From the experimental results, we speculated that there is a spectral feature of speech

334that changes the deviation in the compensatory response between 3 and 4 kHz. Although335

F3, which is considered to be related to speech intelligibility (Hillenbrand and Gayvert,

336

1993; Miller, 1989; Schwartz and Escudier, 1989) and speaker individuality (Kitamura and337

Akagi, 1995) on vowel perception, may be involved, it is unlikely to be responsible for the338

deviation, because about half of the subjects had F3 values less than 3 kHz and there was339

no significant correlation with F3. Therefore, this suggests that the increase in deviation

340

at the 3-kHz cutoff frequency is not related to the deterioration of vowel identification or

341

loss of speaker individuality on vowel perception due to the removal of F3, and that the342

deviation in the compensatory response is affected by the presence or absence of F4 or

343

higher features in the frequency band from 3 to 4 kHz. It has been reported that F4344

is related to the hypopharyngeal cavities of the speaker and that inter-speaker variation345

of the cavity is large, but intra-speaker variation is small (Kitamura et al., 2005). This346

suggests that speaker-specific information on vowel production may affect the reliance on

347

auditory feedback, but clarifying whether this is the case would entail experiments involving,18

Low-pass filtered formant AAF
348

e.g., direct manipulation of speaker-specific information (Toyomura and Omori, 2005; Zheng

349

et al., 2011).

350

The results in Sec. III C showed that the magnitude and deviation in the compensatory351

response at 3 kHz was correlated with f0 and spectral tilt. This indicates that the source

352

characteristics of the high-frequency components, which have been rarely considered in pre-353

vious studies, may play an important role in auditory feedback during speech production.

354

Perceptual experiments have shown that the vowel formant frequency discrimination355

threshold is reduced when the fundamental frequency is low (Kewley-Port et al., 1996)356

and that speech intelligibility increases in noisy environments as the spectral tilt becomes357

flatter (Simantiraki et al., 2020). This may be because lowering f0 increases the number of358

harmonics of f0 contained in the low-pass filtered speech and because decreasing the spectral

359

tilt increases the amplitude of the formant frequency of the high-frequency components.

360

Thus, those findings may be related to our results, but it will be necessary to directly

361

investigate the effect of source characteristics on auditory feedback because the harmonics

362

of f0 and the spectral tilt are also included below 3 kHz.

363

The results on the ratio A of the magnitude of the compensatory response to the absolute364

value of the formant response suggest that the lower the cutoff frequency is, the more likely it

365

is that the following response will occur. We speculate that lowering the reliance on auditory366

feedback may cause the following response. Recent f0 perturbation experiments claimed that367

the participants’ feeling of being “externally driven” is the cause of the following response

368(Franken et al., 2018, 2019b), but it remains to be seen whether they would feel that way

369

when the cutoff frequency is lowered.
19

Low-pass filtered formant AAF
370

SimpleDIVA has limitations making it hard to use it to model data from unexpected371

perturbations (Kearney et al., 2020) and following responses. Although the gradual pertur-372

bation was used as the AAF in this experiment, it is known that the feedforward command373

is unable to adapt when an unexpected perturbation is given (Franken et al., 2019a). The

374

effect of a cutoff frequency in the case of an unexpected perturbation remains to be studied.

375

Subjects may receive bone-conducted auditory feedback even if a low-pass filter was ap-

376

plied. However, if they were strongly affected by such an effect, they should have shown the377same compensatory responses across cutoff frequency conditions. Also, as with the 4 kHz

378

and 8 kHz conditions, there should be no correlation between deviation and spectral tilt un-379

der the 3 kHz condition. However, the experimental results in 3 kHz condition were different

380

from those in 4 and 8 kHz conditions. Therefore, we believe that the effect of bone-conducted381

auditory feedback was not so large as to change the experimental results.

382

As in this experiment, Daliri and Dittman (2019) changed the reliance on auditory feed-383

back in AAF experiments, but did not measure reliance itself directly. This is because the384

reliance on auditory feedback cannot be easily measured as intelligibility in speech percep-

385

tion. In other words, the reliance on auditory feedback is difficult to measure simply by

386

having participants passively listen to low-pass filtered sound. Note that passive listening is387

a passive input of speech to the auditory system. On the other hand, active listening means

388

monitoring one’s own voice while speaking. These differences are related to the presence or389

absence of prediction when listening to speech, and the reliance on auditory feedback can390

be evaluated by detecting the difference between predicted speech and actual feedback. The

391

mechanisms of passive and active listening are known to differ, and they are distinguished20

Low-pass filtered formant AAF
392

by differences in brain activity in speaking-induced auditory suppression (Curio et al., 2000)

393

and from classification of AAF data using convolutional neural networks to verify the im-394

portance of speech prediction (Taguchi et al., 2020). Therefore, quantifying reliance on

395

auditory feedback requires experiments with active listening, such as rating reliance during

396

AAF experiments and measuring physiological indices. However, attention should be paid397

to the possibility that doing so imposes a burden on the subject and may affect the formant

398

AAF experiment itself due to a dual task.

399

It is known that the elderly tend to lose the ability to hear high-frequency sounds (Cruick-400

shanks et al., 1998). In light of our results, it would be interesting to examine the relationship

401

between speech production and hearing in the elderly. Studies have shown that auditory

402

acuity can predict the compensatory response of AAF (Martin et al., 2018; Villacorta et al.,4032007), but they did not measure acuity under active listening conditions. A better under-

404

standing could be gained if the difficulties in conducting perceptual experiments in active

405

listening can be overcome in the future.

406

V.

CONCLUSION

407

We conducted a formant AAF experiment in which the high-frequency components of408

speech were removed by low-pass filtering. The experimental results showed that the de-409

viation in the compensatory response was significantly larger than that for 4 and 8 kHz

410

when a low-pass filter with a cutoff frequency of 3 kHz was used, but the magnitude did411

not differ between the cutoff frequencies. A simulation using a SimpleDIVA model found

412

that the feedforward control became dominant when the cutoff frequency decreased. These21

Low-pass filtered formant AAF
413

results indicate that increased redundancy in the determination of corrective motor com-414

mands from auditory errors and decreased reliance on auditory feedback due to the absence415

of high-frequency components affected the compensatory response of F1 and F2 in the AAF

416

experiment. Further analysis suggested that the presence or absence of F4 or higher in417

the 3 to 4 kHz frequency band, f0 , and the spectral tilt of the glottal source signal are418

responsible for the increasing deviations. In the future, it will be necessary to examine a419

method of measuring the reliance on auditory feedback simultaneously during formant AAF

420

experiments.

421

ACKNOWLEDGMENTS

422

423

We thank Dr. Shigeto Furukawa for his valuable comments on the manuscript and Jeffrey
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27

Low-pass filtered formant AAF

Fc (kHz) F1 (Hz)F2 (Hz)f0 (Hz) Duration (ms)3571 (107) 2239 (260) 206 (51)446 (275)4573 (99) 2235 (240) 208 (49)482 (296)8574 (99) 2249 (257) 207 (49)455 (289)

F(2,84)

0.00

0.02

0.00

0.12

p

0.99

0.97

0.99

0.88

TABLE I. Mean, standard deviation, F -value and p-value of F1, F2, f0 , and vowel duration atbaseline.

Fc (kHz) αA αS λF F αA /αSr

30.04 0.13 0.84

0.30 0.95

40.05 0.12 0.51

0.41 0.96

8

0.13 0.36 0.12

0.36 0.96

TABLE II. Results of parameter fitting to simple DIVA model. αA , αS , λF F and r are auditory
feedback gain, somatosensory feedback gain, feedforward learning rate, and Pearson’s correlation
coefficient, respectively.

28

Low-pass filtered formant AAF

FIG. 1. Spectrogram of vowel /e/ uttered by a female native Japanese speaker.

FIG. 2. Block diagram of altered auditory feedback in this study.

FIG. 3. Perturbation patterns of first and second formants in an experimental block. One blockcontains four phases: Baseline (trials 1-20), Ramp (trials 21-70), Hold (trials 71-90), and Return(trials 91-140).

FIG. 4. Formant response vector and its magnitude and error in F1-F2 plane.

FIG. 5. Patterns of formant frequency change for the baseline at each cutoff frequency condition.
(Top) F2. (Bottom) F1. Shaded regions denote the standard error.

FIG. 6. Formant response vectors for each participant on F1-F2 plane. The number written besideeach response vector indicates the ID of the participant, and the color of each response vector
indicates the condition of the cutoff frequency: red, Fc = 3 kHz; yellow, Fc = 4 kHz; blue, Fc = 8
kHz. The dotted line is a straight line through the origin and the maximum perturbation (+150,−300 Hz). The origin represents the baseline.

FIG. 7. Box-plot of compensatory responses for the first format frequency (F1) for cutoff frequency
conditions Fc = (3, 4, 8) kHz. Lower and upper error lines indicate minimum (Q1−1.5*IQR) andmaximum (Q3+1.5*IQR), respectively. Each circle above or below those top lines stands for an
outlier.

29

Low-pass filtered formant AAF

FIG. 8.

Box-plot of compensatory responses for the second format frequency (F2) for for cut-

off frequency conditions Fc = (3, 4, 8) kHz. Lower and upper error lines indicate minimum(Q1−1.5*IQR) and maximum (Q3+1.5*IQR), respectively. Each circle above or below those top
lines stands for an outlier.

FIG. 9.

Box-plot of magnitude M in compensatory response for cutoff frequency conditions Fc= (3, 4, 8) kHz. Lower and upper error lines indicate minimum (Q1−1.5*IQR) and maximum(Q3+1.5*IQR), respectively. Each circle above or below those top lines stands for an outlier.

FIG. 10.

Box-plot of deviation D in compensatory response for cutoff frequency conditions Fc= (3, 4, 8) kHz. Lower and upper error lines indicate minimum (Q1−1.5*IQR) and maximum(Q3+1.5*IQR), respectively. Each circle above or below those top lines stands for an outlier.

FIG. 11. Box-plot of ratio A of the magnitude of the compensatory response to the absolute valueof the formant response for cutoff frequency conditions Fc = (3, 4, 8) kHz. Lower and upper error
lines indicate minimum (Q1−1.5*IQR) and maximum (Q3+1.5*IQR), respectively. Each circle
above or below those top lines stands for an outlier.

FIG. 12. Correlation of magnitude and deviation in compensatory response at the cutoff frequencyof 3 kHz with F3, f0 , and spectral tilt.

30

Frequency [Hz]

8 kHz

4 kHz
F3
3 kHz
F2
F1
Time

DSP

LPF

(PEAR)

Fc = ( 3, 4, 8 ) kHz

Display

Head. Amp .

へ

Main PC• Parametersetting• Data recording

LPF
Fc = 8 kHz

Mic. Amp .

Sound proofroom

Perturbation magnitude [Hz]Baseline

Ramp

Hold

Return

F2

-300

+150

F1

1

20

70

Number of trials

90

140

Magnitude

Ideal compensatory
response vector FI

Deviation

Perturbation vector

Baseline

Angle

Formant response vector FR

Fc = 3 kHz

Fc = 4 kHz

120

100

80

80

80

40
20

F2 Change [Hz]

100

60

60
40
20

40
20

0

0

-20

-20

-20

-40
20

40

60

80

100

120

140

20

40

Number of trials

60

80

100

120

-40

140

20

30

20

20

20

10

10

10

0

0

0

-20
-30

F1 Change [Hz]

30

-10

-10
-20
-30

-50

-50

-50

Number of trials

100

120

140

140

100

120

140

-60

-60
80

120

-30
-40

60

100

-20

-40

40

80

-10

-40

-60

60

Number of trials

30

20

40

Number of trials

F1 Change [Hz]F1 Change [Hz]

60

0

-40

Fc = 8 kHz

120

100

F2 Change [Hz]F2 Change [Hz]

120

20

40

60

80

Number of trials

100

120

140

20

40

60

80

Number of trials

27
20

26

250

27

200

PERTURBATION
F1: +150 [Hz]F2: -300 [Hz]Fc CONDITIONS
3 kHz
4 kHz
8 kHz

27 23

16
14

7
13
1
16

150
15
2014
26
2
24
15
16
10
1
2 20
7
5
988
9 7
24
10
6
12
1

2

F2 Change [Hz]

13

100

50

9

8
5
310
143

0
4

28

17

17

17
19 5
13
18
19

25
12
6
18

25
3
23 1123 12
21
11
29
19
24
26
6
25
21 22
28
29
22
11
28
29
21
22
18

4

-50
15 4

-200

-150

-100

-50

F1 Change [Hz]

0

50

100

F1 change [Hz]

0

-50

-100

-150

3kHz

4kHz

Cutoff frequency conditions

8kHz

250

F2 change [Hz]

200

150

100

50
0

-50

3kHz

4kHz

Cutoff frequency conditions

8kHz

250

Magnitude [Hz]

200

150

100

50

0

3kHz

4kHz

Cutoff frequency conditions

8kHz

160

*

140

*
Deviation [Hz]

120
100
80
60
40
20
0
3kHz

4kHz

Cutoff frequency conditions

8kHz

*
1

Ratio A

0.5

0

-0.5

-1
3kHz

4kHz

Cutoff frequency conditions

8kHz

350

350

R = -0.15, p = 0.46
300

250

250

250

200

200

200

150
100

Magnitude [Hz]

300

150
100

150
100

50

50

50

0

0

0

-50
2000

2500

3000

3500

-50
100

4000

150

F3 [Hz]

200

250

-50
0.85

300

140

R = 0.00, p = 0.99

R = 0.33, p = 0.07

100

Deviation [Hz]100

Deviation [Hz]

100

80

60

60

40

40

20

20

20

3000

F3 [Hz]

3500

4000

0
100

1

80

40

2500

0.95

R = 0.47, p < 0.01
120

60

1

140

120

80

0.95

Spectral tilt

120

0
2000

0.9

f0 [Hz]140

Deviation [Hz]R = -0.44, p < 0.05

300

Magnitude [Hz]Magnitude [Hz]R = 0.08, p = 0.67

350

150

200

f0 [Hz]

250

300

0
0.85

0.9

Spectral tilt