Abstract
Two new algorithms are proposed, which obtain pseudo complex cepstrum using Discrete Cosine Transform (DCT). We call this as the Discrete Cosine Transformed Cepstrum (DCTC). In the first algorithm, we apply the relation between Discrete Fourier Transform (DFT) and DCT. Computing the complex cepstrum using Fourier transform needs the unwrapped phase. The calculation of the unwrapped phase is difficult whenever multiple zeros and poles occur near or on the unit circle. Since DCT is a real function, its phase can only be 0 or π and the phase is unwrapped by representing the negative sign by exp (−jπ) and the positive sign by exp (j0) . The second algorithm obviates the need for DFT and obtains DCTC by representing the DCT sequence itself by magnitude and phase components. Phase is unwrapped in the same way as the first algorithm. We have tested DCTC on a simulated system that has multiple poles and zeros near or on the unit circle. The results show that DCTC matches the theoretical complex cepstrum more closely than the DFT based complex cepstrum. We have explored possible uses for DCTC in obtaining the pitch contour of syllables, words and sentences. It is shown that the spectral envelope obtained from the first few coefficients matches reasonably with the envelope of the signal spectrum under consideration, and thus can be used in applications, where faithful reproduction of the spectral envelope is not critical. We also examine the utility of DCTC as feature set for speaker identification. The identification rate with DCTC as feature vector was higher than that with linear prediction-derived cepstral coefficients.
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References
Bernar, J.B. and Watt, T.L. (1985). Calculating the complex cepstrum without phase unwrapping or integration. IEEE Transactions on Acoustic Speech Signal Processing, 33:1014–1017.
Boersma, P. and Weenink, D. (2003). Praat: doing phonetics by computer. http://www.fon.hum.uva.nl/praat/.
Childers, D.G., Skinner, D.P., and Kemerait, R.C. (1977). The cepstrum: A guide to processing. In Proceedings of the IEEE, vol. 65, pp. 1428–1443.
Dhanya, D. and Ramakrishnan, A.G. (2002). Optimal feature extraction for bilingual OCR. In Document Analysis Systems V Daniel Lopresti, Jianying Hu and Ramanujan Kashi (eds.), Berlin Heidelberg; Springer-Verlag, pp. 25–36.
Duda, R., Hart, P., and Stork, D.G. (2002). Pattern Classification. New York: J. Wiley.
Hessanein, H. and Rudko, M. (1984). On the use of discrete cosine transform in cepstral analysis. IEEE Transactions on Acoustic Speech Signal Processing, 32:922–925.
Martucci, S.A. (1994). Symmetric convolution and the discrete sine and cosine transforms. IEEE Transactions on Signal Processing, 42:1038–1051.
Muralishankar, R. and Ramakrishnan, A.G. (2000). Robust pitch detection using dct based spectral autocorrelation. In Proceedings of International Conference on Multimedia Processing, Chennai, pp. 129–132.
Muralishankar, R. and Ramakrishnan, A.G. (2002). DCT based pseudo complex cepstrum. In Proceedings of the IEEE, ICASSP, pp. I:521–524.
Muralishankar, R., Ramakrishnan, A.G., and Prathibha, P. (2004). Modification of pitch using DCT in the source domain. Speech Communication, 42:143–154.
Oppenheim, A.V. (1969). A speech analysis-synthesis system based on homomorphic filtering. Journal of the Acoustical Society of America, 45:458–465.
Oppenheim, A.V. and Schafer, R.W. (1968). Homomorphic analysis of speech. IEEE Transactions on Audio and Electroacoustics, AU-16:221–226.
Oppenheim, A.V. and Schafer, R.W. (1989). Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall.
O'Shaugnessy, D. (2000). Speech Communications-Human and Machine. 2nd ed. Piscataway, NJ: IEEE Press.
Provenzale, A., Smith, L.A., Vio, R., and Murante, G. (1992). Distinguishing between low-dimensional dynamics and randomness in measured time series. Physica D, 58:31–49.
Quatieri, T.F. (1979). Phase estimation with application to speech analysis-synthesis. PhD thesis, Department of Electrical Engineering, Massachussets Institute of Technology, Cambridge, MA, USA.
Ramakrishnan, A.G. and Saha, S. (1997). ECG coding by wavelet-based linear prediction. IEEE Transactions on Biomedical Engineering, 44(12):1253–1261.
Rao, K.R. and Yip, P. (1990). Discrete Cosine Transform, Algorithms, Advantages, Applications. Academic Press.
Reynolds, D.A. and Rose, R.C. (1995). Robust text-independent speaker identification using gaussian mixture speaker models. IEEE Transactions on Speech and Audio Processing, 3:72–83.
Salahuddin, S., Al Islam, S.Z., Hasan, M.K., and Khan, M.R. (2002). Soft thresholding for DCT speech enhancement. Electronic Letters, 38:1605–1607.
Sokolov, R.T. (1989). Time-domain cepstral transformations. PhD thesis, Michigan Technological University.
Vijay Kumar, B. and Ramakrishnan, A.G. (2002). Machine recognition of printed Kannada text. In Document Analysis Systems V, editor, Daniel Lopresti, Jianying Hu and Ramanujan Kashi. Berlin Heidelberg: Springer-Verlag, pp. 37–48.
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Muralishankar, R., Ramakrishnan, A.G. Pseudo Complex Cepstrum Using Discrete Cosine Transform. Int J Speech Technol 8, 181–191 (2005). https://doi.org/10.1007/s10772-005-2169-3
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DOI: https://doi.org/10.1007/s10772-005-2169-3