CEPSTRAL ANALYSIS Cepstral analysis synthesis on the mel frequency scale, and an adaptative algorithm for it. Cecilia Caruncho Llaguno

Sources Cepstral analysis on the mel frequency scale – Satoshi Imai - Tokio Institute of Technology, 1983 An adaptative algorithm for mel-cepstral analysis of speech – Toshiako Fukada - Canon Inc. Kawasaki, 1992 – Keeichi Tokuda, Takao Kobayasi, and Satoshi Imai - Tokio Institute of Technology, 1992

Basic Concepts Cepstral Analysis – Definition Definition – Features Features Mel frequency scale

Cepstral analysis Main features – Good characteristics for representation – Log spectral envelope → accurate & efficient – Small sensitivity & quantization noise – Small spectral distortion – LMA filter → high quality speech synthesis

Cepstral analysis Complex logarithm Inverse Z transform In unit circle |z|<1

Mel frequency scale Human hearing sense → non-linear frequency scale Linear up to 1000 Hz, logarithmic above.

Mel cepstral analysis system

Spectral envelope extraction by the improved cepstral method Approximation of the mel scale

Spectral envelope extraction by the improved cepstral method Former method: – Fine structure → The spectral envelope is not suficiently separated from the pitch parameter Present method: – Can extract the envelope without being affected by the fine structure.

Mel Log Spectrum Approximation filter Why do we use it? – High quality – Simple – Coefficient sensitivities – Quantization characteristics Transfer function Quantization of the filter parameterfilter parameter

MLSA transfer function Ideal Basic filter:

MLSA transfer function Ideal MLSA filterNot realizablePadé approximation:

Filter parameters

Data rate Filter coefficients → bounded Digitalization → quantizer q → data amount b s (bits/frame)

Data rate Spectral envelope: b s bits/frame Pitch parameter: b p bits/frame Period of transmission: T seconds Averall bit rate of this system: B (bits/second)

Data rate Speech quality T (ms)MqBp (bit)B (kbits/s)Speech quality Very high Fairly good Still good

Spectral distortion Distortion caused by the interpolation Distortion caused by the quantization

Spectral estimation based on mel-cepstral representation Model spectrum

Spectral estimation based on mel-cepstral representation Unbiased Estimator of Log Spectrum by S. Imai and C. Furuichi → minimization of ε

Spectral estimation based on mel-cepstral representation Newton-Raphson method:

Adaptative mel-cepstral analysis algorithm H → Unit matrix → μ... adaptation step size ε (n)... estimate of ε at time n e(n) → output of the inverse filter 1/D(z) at time n →

Adaptative mel-cepstral analysis algorithm

Conclusions MLSA – Simple – Good stathistical features – Small spectral distortions Adaptative algorithm – Computationally efficient – Fast convergence properties

Questions? Thank you for your attention Muchas gracias por su atención