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Homomorphic Systems and Cepstrum Analysis of Speech

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Book cover Springer Handbook of Speech Processing

Part of the book series: Springer Handbooks ((SHB))

Abstract

In 1963, Bogert, Healy, and Tukey published a chapter with one of the most unusual titles to be found in the literature of science and engineering [9.1]. In this chapter, they observed that the logarithm of the power spectrum of a signal plus its echo (delayed and scaled replica) consists of the logarithm of the signal spectrum plus a periodic component due to the echo. They suggested that further spectrum analysis of the log spectrum could highlight the periodic component in the log spectrum and thus lead to a new indicator of the occurrence of an echo. Specifically they made the following observation:

In general, we find ourselves operating on the frequency side in ways customary on the time side and vice versa.

As an aid in formalizing this new point of view, they introduced a number of paraphrased words. For example, they defined the cepstrum of a signal as the power spectrum of the logarithm of the power spectrum of a signal. (In fact, they used discrete-time spectrum estimates based on the discrete Fourier transform.) Similarly, the term quefrency was introduced for the independent variable of the cepstrum [9.1].

In this chapter we will explore why the cepstrum has emerged as a central concept in digital speech processing. We will start with definitions appropriate for discrete-time signal processing and develop some of the general properties and computational approaches for the cepstrum of speech. Using this basis, we will explore the many ways that the cepstrum has been used in speech processing applications.

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Abbreviations

ASR:

automatic speech recognition

CELP:

code-excited linear prediction

DCT:

discrete cosine transform

DFT:

discrete Fourier transform

DTFT:

discrete-time Fourier transform

DoD:

Department of Defense

FFT:

fast Fourier transform

FIR:

finite impulse response

IDTFT:

inverse discrete-time Fourier transform

LPC:

linear prediction coefficients

LPC:

linear predictive coding

MFCC:

mel-filter cepstral coefficient

VQ:

vector quantization

References

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Authors and Affiliations

  1. Hewlett-Packard Laboratories, 1501 Page Mill Road, 94304, Palo Alto, CA, USA

    Ronald W. Schafer Prof.

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  1. Ronald W. Schafer Prof.
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Correspondence to Ronald W. Schafer Prof. .

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Editors and Affiliations

  1. INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, H5A 1K6, Montreal, Quebec, Canada

    Jacob Benesty Dr.

  2. Avayalabs Research, 233 Mount Airy Road, 07920, Basking Ridge, NJ, USA

    M. Mohan Sondhi Ph.D.

  3. Alcatel-Lucent, Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ, USA

    Yiteng Arden Huang Dr.

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© 2008 Springer-Verlag Berlin Heidelberg

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Schafer, R.W. (2008). Homomorphic Systems and Cepstrum Analysis of Speech. In: Benesty, J., Sondhi, M.M., Huang, Y.A. (eds) Springer Handbook of Speech Processing. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49127-9_9

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  • DOI: https://doi.org/10.1007/978-3-540-49127-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49125-5

  • Online ISBN: 978-3-540-49127-9

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