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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
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
Mel frequency scale
Human hearing sense → non-linear frequency scale
Linear up to 1000 Hz, logarithmic above.
Spectral envelope extraction by the improved cepstral method
Approximation of the mel scale
ta n 1 1 2 s in
1 2 co s 2
Gm 0
M
c m co s m
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 parameter
MLSA transfer function
F z b 0 z 1 ·m 1
M 1
b m · z m 1
Ideal MLSA filter Not realizable Padé approximation:
b ... recu rsiv e f ilt er param eter
Data rate
Filter coefficients → bounded
Digitalization → quantizer q → data amount bs
(bits/frame)
b sM 2 2 lo g 2 q 3 if M 9M 2 2 lo g 2 q 14 if M 9
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)
Bb s b p
T
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
Spectral distortion
D T 6 5 TDistortion caused by the interpolation
Distortion caused by the quantization
D Qq M 1
5
Spectral estimation based on mel-cepstral representation
Model spectrum
H z e xpm 0
M
c m z m e xpm 0
M
b m · m z K · D z
D z e xpm 1
M
b m · m z
K e xp b 0
c m b m if m M b m b m 1 if 0 m M
12
I N
D e j 2 d
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:
H · b ib b i
b i b i 1 , b i 2 , ... , b i M T
b i 1 b i b i
Adaptative mel-cepstral analysis algorithm
b i 1 b ib b i
E e 2 n
n a
M n, 0 a 1
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 →
n n 1 1 e 2 n , 0 1
Conclusions
MLSA– Simple– Good stathistical features– Small spectral distortions
Adaptative algorithm– Computationally efficient– Fast convergence properties
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