CEPSTRAL ANALYSIS

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CEPSTRAL ANALYSIS

• Cepstral analysis synthesis on the mel frequency
  scale, and an adaptative algorithm for it.

Cecilia Caruncho Llaguno
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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

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Basic Concepts

• Cepstral Analysis
• Definition
• Features
• Mel frequency scale

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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

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Cepstral analysis
Complex logarithm
Inverse Z transform
In unit circle zlt1
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Mel frequency scale

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

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Mel cepstral analysis system
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Spectral envelope extraction by the improved
cepstral method

• Approximation of the mel scale

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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.

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Mel Log Spectrum Approximation filter

• Why do we use it?
• High quality
• Simple
• Coefficient sensitivities
• Quantization characteristics
• Transfer function
• Quantization of the filter parameter

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MLSA transfer function
Ideal
Basic filter
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MLSA transfer function
Ideal MLSA filter
Not realizable
Padé approximation
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Filter parameters
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Data rate

• Filter coefficients ? bounded
• Digitalization ? quantizer q ? data amount bs
• (bits/frame)

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Data rate

• Spectral envelope bs bits/frame
• Pitch parameter bp bits/frame
• Period of transmission T seconds
• Averall bit rate of this system B (bits/second)

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Data rate

• Speech quality

T (ms) M q Bp (bit) B (kbits/s) Speech quality
15 11 0.25 7 4 Very high
20 8 0.5 7 2 Fairly good
25 5 0.5 6 1.2 Still good

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Spectral distortion
Distortion caused by the interpolation
Distortion caused by the quantization
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Spectral estimation based on
mel-cepstral representation

• Model spectrum

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Spectral estimation based on
mel-cepstral representation

• Unbiased Estimator of Log Spectrum by S. Imai and
  C. Furuichi ? minimization of e

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Spectral estimation based on
mel-cepstral representation

• Newton-Raphson method

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

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

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Questions?

• Thank you for your attention
• Muchas gracias por su atención