SPEECHCODING

Keiichi

Tokuda’BASED
Hidetoshi

ON ADAPTIVE
Matsumura’

MEL-CEPSTFtAL
Takao Kobayashi’

ANALYSIS
SatoshiIma?

‘Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, Tokyo, 152 JAPAN2Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama, 227 JAPANABSTRACTIn this paper, we propose an ADPCM
coder whichuses a backward adaptive predictor based on the adap
tive mel-cepstral analysis. The spectrum represented by
the mel-cepstral coefficients has frequency resolution similar to that of the human ear which has high resolution atlow frequencies. In the coder, since the transfer functionsof noise shaping and postflltering are also defined throughthe mel-cepstral coeflicients, the effects of nose shaping andpost6ltering should fit with characteristics of the human
auditory sensation. We incorporate a pitch predictor into
the ADPCM coder, and evaluate the speech quality basedon objective and subjective performance tests. It is shownthat the coder at 16 kb/s can produce a high quality speechcomparable with that of the CCITT G.721 ADPCM coder
at 32kb/s with no algorithmic delay.

1.

INTRODUCTION

Many speech coding systems have used the AR spectral
representation for short-term prediction. However, in somecases, spectral zeros are important and a more generalmodel is required. Although many techniques have been
proposed for simultaneous determination of both poles andzeros, they are not always successful for a variety of reasons(e.g., stability or convergence). On the other hand, thecepstral coefficients [l] can represent spectral poles and zeros with equal weights. Furthermore, the mel-cepstrum [2]is defined as frequency-transformed cepstrum so that thespectrum represented by the mel-cepstral coefficients has
frequency resolution similar to that of the human ear which
has high resolution at low frequencies. Therefore, it is expected that the mel-cepstral representation can be used for
efficient spectral modeling in speech coders instead of theAR modeling. Although the cepstrum has been utilized forshort-term adaptive predictor in the homomorphic vocoder[3], and the frequency-transformed AR model was also applied to an ADPCM system [4], the mel-cepstrum has notbeen applied to speech coding.
To demonstrate the effectiveness of the mel-cepstral representation in speech coding, we propose an ADPCM coder
which uses a short-term adaptive predictor based on melcepstral representation of speech spectrum. In the coder,
the mel-cepstral co&dents are updated by the algorithm
for adaptive mel-cepstral analysis (51. Since the transfer
functions of noise shaping and postfiltering are also definedFig. 1. Adaptive mel-cepstral analysis
through the mel-cepstral coefficients, the effects of noise
shaping and postfiltering should fit with characteristics ofthe human auditory sensation.
The speech quality of the coder is evaluated by both objective and subjective performance tests. It is shown thata high quality speech corresponding to that of the CCITT
G.721 ADPCM coder at 32kb/s can be produced by theproposed coder at 16 kb/s with no algorithmic delay.
2.

ADAPTIVE

MEL-CEPSTRALANALYSIS

We model the speech spectrum D(eiU) by using the M-thorder mel-cepstral coefficients 2;(m) as follows:M

D(z) = exp CC(m) Z-”(1)

m=O

wherei-l =z--I- Qlal<l.
1 - ox-’ ’For example, when the sampling frequency is 8kHz, thephase characteristics (;, of the all-pass transfer function
z--I =e -jO for o = 0.31 is a good approximation to theme1 frequency scale [6] based on subjective pitch evaluations.
In the mel-cepstral analysis [5], the gain factor of D(z) is
assumed to be unity so that the impulse response at time
0 equals unity. Then: under this condition, the coefficients2(m) are determined to minimize
E = E [e’(n)],(3)

where e(u) is the output of the inverse filter l/D(r), asshown in Fig. 1. The adaptive mel-cepstral analysis [5]solves the minimization problem by an adaptive 6lter approach; the coefficients Z(m) are updated sample by sample
based on an instantaneous estimate for the gradient of E.
It has been shown [5] that the adaptive algorithm has s&iciently fast convergence characteristics for speech analysis.
Since the transfer function D(z) is theoretically minimum
phase and the gain factor of D(z) is normalized to unity,

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EncoderDecoderFig. 2. Basic structure of the coder based on adaptive mel-cepstral analysis
Encoder

Decodera4&IFig. 3. Structure of the coder based on adaptive mel-cepstral analysis
the impulse response of l/D(r) at time 0 equals unity. As aresult, the signal e(n) can be viewed as the linear prediction
error. Therefore, instead of the linear prediction method,
the adaptive mel-cepstral analysis can be used for the shortterm adaptive prediction.
Although the transfer functions D(t) and l/D(z) are
not rational functions, MLSA filters [2], [5] can approximate D(z) and l/D(z) with sufficient accuracy and become
minimum-phase IIR systems.
3.
3.1.

STRUCTURE

OF THE CODER

Basic Structure

Fig. 2 shows the basic structure of the proposed coder.
The coefficients E(m) are updated in a backward adaptive
fashion, that is, they are updated based on i(n) rather thane(n). We choose a scalar adaptive quantizer proposed in [7]for Q. The z-transform of the decoded speech i(n) isR(r)= X(r)+ Q(z)(4)

where X(z) and Q(r) are the z-transforms of z(n) and q(n),respectively, and q(n) is the quantization noise generated by
the quantizer Q. The transfer function D(z) is realized using
the MLSA filter. It is noted that D(z) - 1 has no delay-freepaths. The specific structures of D(r) and D(r) - 1 used inthis paper can be seen in [S].
3.2.

Noise Shaping and Postfiltering

Fig. 3 shows the structure of the proposed coder withnoise shaping and postfiltering based on the mel-cepstral
analysis. The r-transform of the decoded speech s(n) is2(z)= {X(z)y and p control the amount of noise shaping and postfiltering, respectively. The case where 7 = 0 and p = 0 corresponds to the basic structure shown in Fig. 2. Fig. 4(a)shows an example of noise shaping and postflltering for
y = 0.3 and ,0 = 0.2. For comparison, characteristics of conventional noise shaping and postCkring 191,[lo] are shownin Fig. 4(b). They are de&red by+ D’(*)Q(*)}D*(r).

(5)

The transfer function D7 (2) shapes the noise spectrum, andwhere B(r) is the prediction polynomial of z-l obtainedby the linear prediction method. It is seen that the estimated speech spectrum D(gw) has high resolution at low
frequencies; accordingly, spectra of noise shaping D7(&w)
and postfiltering B’(gy)alSo have high resolution at low
frequencies. Thus, the efkts of noise shaping and postfilking should fit to characteristics of the human auditory
sensation and can improve the perceptual performance ofthe coder. Informal listening tests indicate that the subjective performance when Q = 0, i.e., the cepstrum is used, isinferior to that with Q = 0.31. The result is expected sincenoise shaping and postfiltering are performed on linear fre
quency scale when Q = 0.
The transfer functions D(z) and B(z) are realized using
the MLSA filters. We can also realize Dy(r) and D’(z) in
the same manner as D(r) and D(z), by multiplying Z(m) by
7 and /3,respectively. To avoid large gain excursions at thepostfilter output, we add the output gain control [lo] whichscales the postfilter output signal so that it has roughly thesame power as the unfiltered speech.
3.3.

Structure with Pitch

Predictor

Fig. 3 shows the structure of the coder with pitch predictor. The z-transform of the decoded speech i(n) isB@(Z) is the postfilter. The transfer function B(z) is thesame as D(r) except that c,(l) is forced to be zero to compensate for the global spectral tilt. The tunable parameters

x(z)

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+ sQ(z,(7)EncoderDecoderFig. 5. Structure of the coder with pitch predictor.

iz
P 80+j 60-5
6 40Ig 20ilIOO

Spectralestimt~~~~ 001234-200

2020
Postfilter

123
FrequencyW3z); -20
0l/A,(e’93412123
FrequencyW-h)

Postfilter

4= -40-4-201
0123Frequencyodlz)

0123
FrequencyOcHz14(a) mel-cepstral
analysisFig. 6. Effect of noise shaping and postfiltering basedon pitch predictor.

-::m00Ap(z)123

are defined by
P+l4An(z)20= 1+ l,Postfilterca(k) z-’
kc,+1(jP+l00123401234
FrequencyMHz)

-20

Ap(z)

Fig. 4. Noise shaping and postfiltering.
The transfer function of the pitch prediction filter is givenA(z)= 1+1 - cp

P+lca(k)*-‘.
k=p-1

The pitch period p and the pitch predictor coefficients a(k)are calculated from the correlation of i(n), which is obtained by using an exponential window and updated every
sample. A stabilization technique [11] is applied to the coefficients a(k) and they are forced to be zero at unvoiced
samples detected by a simple voiced/unvoiced decision algorithm. The noise shaping and postfiltering are based on
those proposed in [12]: (131: the transfer functions A,(z),cP+la(k)z-'

k=p-1

FrequencyOcHz1(b) Linearpredictionmethodby=l-ep

ca(k) ,
k=p-1

respectively. The tunable parameters e, and lp control‘theamount of noise shaping and postfiltering, respectively. In
the decoder, p, a(k) are also calculated from the quantized
residual samples g(n), i.e., the pitch predictor uses backward adaptation.
Fig. 6 illustrates effects of the noise shaping and postfltering based on pitch prediction. Fig. 4 and Fig. 6 correspond to the same portion of the speech signal. Thus, theeffects of noise shaping and postfiltering can be seen as thecombination of Fig. 4(a) and Fig. 6.
4.
4.1.

PERFORMANCE

Objective

ASSESSMENT

PerformanceThe objective speech quality was evaluated by the segmental SNR. The proposed coder at 16kb/s was tested on
10 sentences uttered by five female and five male speakers,

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cl 16kb/s

cl 16kbls
24kb/scl24kWscl

32kb/s32kbl.s1

rroposed CCI'IT
G.721

-L

1

Proposed II
IIFig. 7. Objective performance assessment basedon segmental Sh’R.
about 40 seconds of total speech. In the test, we let (7. p,
en, Q,) = (0, 0, 0, 0). Fig. 7 shows the result. For comparison, the results of CCITT G.721 ADPCM coder at 16, 24,32kb/s are also shown. From the figure, it is seen that theimprovement of 3dB is achieved by the proposed coder at
16kb/s over the 16kb/s CCITT G.721 ADPCM coder.
4.2.

Subjective

PerformanceFig. 8 shows the result of a speech quality assessment
based on the opinion equivalent Q. The reference signal isthe original speech.
Test signals are decoded
speech signals by the proposed coder at 16kb/s and by the CCITT
G.721 ADPCM coder at 16, 24, 32kb/s, and MNR signals(Q = 6,12,18,24,30,36,42dB).
We chose a parameter set(7, P, e,, cr) = (0.3, 0.2, 0.3, 0.1) for noise shaping andpostfiltering of the proposed coder by informal listening.
From Fig. 8, it is seen that the noise shaping and postfiltering improve the equivalent Q by nearly 12dB in the proposed coder at lbkb/s. Particularly, the postfilter achieves
sign&antnoisereduction.

Thecoderat lbkb/s

without

noise shaping and postfiltering achieves improvement of
5dB over the CCITT G.721 ADPCM coder at 16kb/s. Further, the improvement of more than 17dB is achieved by theproposed lbkb/s coder with noise shaping and postfiltering over the lbkb/s CCITT G.721 ADPCM coder, and thequality corresponds to that of the CCITT G.721 at 32kb/s.
5.

CONCLUSIONS

We have proposed an ADPCM coder in which adaptive
prediction, noise shaping, and postfiltering are carried out
throughthe mel-cepstralcoefficients.

Althoughthe coderrather than a vector quantizer andhas no algorithmic delay, the subjective performance testshows that the coder at lbkb/s produces a high quality
speech corresponding to that of the CCITT G.721 ADPCM
coder at 32kb/s. In this paper, we have not consideredchannel errors. Coder design for noisy channels is a future
problem.
To show effectiveness of mel-cepstral representation of
speech spectrum in speech coding, we chose an ADPCM
coder as an example.
Fkom the result, it is surmised thatthe mel-cepstral representation can also be effective in othertypes of coder, e.g., CELP coders.
uses a scalarquantizerr1 cc1! G.721: withcut noise shaping and postfiltering: with noise shaping and postfiltering

Fig. 8. Subjective performance assessment basedon opinion equivalent Q.
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