Abstract
Psychologists have shown that most information about the mood and attitude of a speaker is carried by the lowest (fundamental) frequency. Because of this frequency’s importance, even when the corresponding Fourier component is weak, the human brain reconstruct this frequency based on higher harmonics. The problem is that many people lack this ability. To help them better understand moods and attitudes in social interaction, it is therefore desirable to come up with devices and algorithms that would reconstruct the fundamental frequency. In this paper, we show that ideas from soft computing and computational complexity can be used for this purpose.
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References
R. Belohlavek, J.W. Dauben, G.J. Klir, Fuzzy Logic and Mathematics: A Historical Perspective (Oxford University Press, New York, 2017)
A. Brown, Guide to the Fourier Transform and the Fast Fourier Transform (Cambridge Paperbacks, Cambridge, UK, 2019)
C.S. Burrus, M. Frigo, G.S. Johnson, Fast Fourier Transforms (Samurai Media Limited, Thames Ditton, UK, 2018)
Th.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms (MIT Press, Cambridge, MA, 2022)
S. Da Costa, W. van der Zwaag, L.M. Miller, S. Clarke, M. Saenz, Tuning in to sound: frequency-selective attentional filter in human primary auditory cortex. J. Neurosci. 33(5), 1858–1863 (2013)
J.L. deLyra, Fourier Transforms: Mathematical Methods for Physics and Engineering, by J.L. de Lyra (2019)
L.L.C. Frudensing, Freudensong: Unleashing the Human Voice. https://www.freudensong.com/
E. Freudenthal, R. Alvarez-Lopez, V. Kreinovich, B. Usevitch, D. Roundy, Work-in-progress: vocal intonation regeneration through heterodyne mixing of overtone series, in Abstracts of the 27th Joint NMSU/UTEP Workshop on Mathematics, Computer Science, and Computational Sciences, Las Cruces, New Mexico, 2 Apr. 2022
E. Freudenthal, V. Mueller, Summary of Vocal Intonation Boosting (VIB). https://www.freudensong.com/vib-white-paper
G. Klir, B. Yuan, Fuzzy Sets and Fuzzy Logic (Prentice Hall, Upper Saddle River, NJ, 1995)
N. Kuga, R. Abe, K. Takano, Y. Ikegaya, T. Sasaki, Prefrontal-amygdalar oscillations related to social behavior in mice. eLife, vol. 11, paper e78428 (2022)
J.M. Mendel, Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions (Springer, Cham, Switzerland, 2017)
D.F. Mix, Fourier, Laplace, and z Transforms: Unique Insight into Continuous-Time and Discrete-Time Transforms, Their Definition and Applications (2019). https://www.amazon.com
H.T. Nguyen, C.L. Walker, E.A. Walker, A First Course in Fuzzy Logic (Chapman and Hall/CRC, Boca Raton, FL, 2019)
V. Novák, I. Perfilieva, J. Močkoř, Mathematical Principles of Fuzzy Logic (Kluwer, Boston, Dordrecht, 1999)
B.G. Osgood, Lectures on the Fourier Transform and Its Applications (American Mathematical Society, Prividence, Rhode Island, 2019)
T. Pendlebury, How to Improve the Speech On Your TV to Make It More Understandable (2022). https://www.cnet.com/tech/home-entertainment/having-a-hard-time-hearing-the-tv-your-speaker-settings-may-be-the-culprit/
S.K. Reed, Cognition: Theories and Application (SAGE Publications, Thousand Oaks, CA, 2022)
J.V. Stone, The Fourier Transform: A Tutorial Introduction (Sebtel Press, Sheffield, UK, 2021)
L.A. Zadeh, Fuzzy sets. Information and Control 8, 338–353 (1965)
Acknowledgements
This work was supported in part by the National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science), and HRD-1834620 and HRD-2034030 (CAHSI Includes), and by the AT&T Fellowship in Information Technology.
It was also supported by the program of the development of the Scientific-Educational Mathematical Center of Volga Federal District No. 075-02-2020-1478, and by a grant from the Hungarian National Research, Development and Innovation Office (NRDI).
The authors are thankful to all the participants of the 27th Joint NMSU/UTEP Workshop on Mathematics, Computer Science, and Computational Sciences, Las Cruces, New Mexico, April 2, 2022 for valuable suggestions.
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Freudenthal, E., Kosheleva, O., Kreinovich, V. (2023). How to Detect the Fundamental Frequency: Approach Motivated by Soft Computing and Computational Complexity. In: Ceberio, M., Kreinovich, V. (eds) Uncertainty, Constraints, and Decision Making. Studies in Systems, Decision and Control, vol 484. Springer, Cham. https://doi.org/10.1007/978-3-031-36394-8_57
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DOI: https://doi.org/10.1007/978-3-031-36394-8_57
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