DISPERSION PHASE VECTOR QUANTIZATION FOR
`ENHANCEMENT OF WAVEFORM INTERPOLATIVE CODER
`Oded Gottesman
`
`Signal Compression Laboratory
`Department of Electrical and Computer Engineering
`University of California
`Santa Barbara, California 93106, USA
`E-mail: oded@kane.ece.ucsb.edu
`
`ABSTRACT
`This paper presents an efficient analysis-by-synthesis
`vector quantizer for the dispersion phase of the excitation
`signal which was used
`to enhance a waveform-
`interpolative coder. The scheme can be used to enhance
`other harmonic coders, such as the sinusoidal-transform
`coder and the multiband-excitation coder. The scheme
`incorporates perceptual weighting, and does not require
`any phase unwarping. The proposed quantizer achieves a
`segmental signal-to-noise ratio of up to 14dB for as low as
`6-bit quantization. Subjective testing shows improvement
`in synthesized speech quality using the quantized phase
`over a male speaker extracted phase. The improvement
`was larger for female speakers.
`
`1.
`
`INTRODUCTION
`
`Recently, there has been growing interest in developing
`toll-quality speech coders at rates of 4kbps and below. The
`speech quality produced by waveform coders such as
`linear predictive
`(CELP) coder
`[[1]]
`code-excited
`degrades rapidly at rates below 5kbps. On the other hand,
`parametric coders such as the Waveform-interpolative
`(WI) coder [[5]-[15]], the sinusoidal-transform coder
`(STC) [[2],[3]], and the multiband-excitation (MBE)
`coder [[4]] produce good quality at low rates, but they do
`not achieve toll quality. In parametric coders the phase
`information is commonly not transmitted, and this is for
`two reasons: first, the phase is of secondary perceptual
`significance; and second, no efficient phase quantization
`scheme is known. WI coders [5-[15]] typically use a fixed
`phase vector for the slowly evolving waveform (SEW), for
`example, in [[10],[15]] fixed male speaker extracted phase
`was used. On the other hand, Waveform coders such as
`CELP [[1]], by directly quantizing
`the waveform,
`
`This work was supported in part by the University of California MICRO
`program, ACT Networks, Inc, Advanced Computer Communications,
`Cisco Systems, Inc., DSP Group, Inc., Fujitsu Laboratories of America,
`Inc., Hughes Electronics Corp., Intel Corp., Lucent Technologies, Inc.,
`Nokia Mobile Phones, Qualcomm, Inc., Rockwell International Corp., Sun
`Microsystems, Inc., and Texas Instruments, Inc.
`
`implicitly allocate an excessive number of bits to the phase
`information - more than is perceptually required.
`
`the past, phase modeling and quantization was
`In
`investigated. In [[16]] a random phase codebook was used
`at a relatively high number of phase quantization bits. In
`[[17],[18]] a non-causal all-pole filter’s phase model was
`discussed, but quantization was not optimized. Such a
`model
`is occasionally
`limited
`in matching
`the
`physiological excitation’s phase. In addition, none of the
`above methods have incorporated perceptual weighting.
`
`In this work, we propose a novel, efficient analysis-by-
`synthesis (AbS) quantization scheme for the phase at a
`very low bitrate, which can be used for parametric coders
`as well as for waveform coders. The proposed quantizer
`has been implemented as part of a WI system to quantize
`the SEW phase, and
`its performance has been
`investigated.
`
`This paper is organized as follows. In Section 2 we discuss
`the dispersion phase quantizer, with emphasis on the
`distortion measure, and the respective optimal codebook
`design. In Section 3 we then describe the objective results
`obtained by the designed codebook, as well as results of a
`subjective test which compares the proposed quantizer,
`using only 4 bits, with a fixed phase vector extracted from
`a male speaker. Finally, we summarize our work.
`
`PHASE QUANTIZATION
`2.
`The dispersion-phase quantization scheme is illustrated in
`Figure 1. Consider a pitch cycle which is extracted from
`the residual signal, and is cyclically shifted such that its
`pulse is located at position zero. Let its DFT be denoted
`by R; the resulting DFT phase is the dispersion phase, j
`,
`which determines, along with the magnitude R , the
`waveform’s pulse
`shape. After quantization,
`the
`$R , are
`components of the quantized magnitude vector,
`multiplied by the exponential of the quantized phases,
`j k , to yield the quantized waveform DFT, $R , which is
`$( )
`subtracted from the input DFT to produce the error DFT.
`The error DFT is then transformed to the perceptual
`
`Saint Lawrence Communications, LLC
`IPR2016-00704
`Exhibit 2013
`
`

`
`domain by weighting it by the combined synthesis and
`weighting filter W(z). The encoder searches for the phase
`that minimizes the energy of the perceptual domain error,
`allowing a refining cyclic shift of the input waveform
`during the search, to eliminate any residual phase shift
`between the input waveform to the quantized waveform.
`
`Pitch-Cycle
`Waveform’s DFT
`
`Crude
`Linear-Phase
`Alignment
`
`Refined
`Linear-Phase
`Alignment
`
`R^
`
`-
`
`R
`
`+
`
`Magnitude
`Codebook
`
`Phase
`Codebook
`
`x
`
`^
`|R|
`
`e jj^
`
`Pitch
`
`min||*||2
`
` (2)
`
`=
`
`W
`kk
`
`2
`
`g
`(
`/
`A z
`( )
`(
`A z A z
`
`1
`/
`
`)
`g
`
`)
`
`2
`
`p
`
`2
`
`P
`
`j
`
`(
`
`)
`
`k
`
`=
`
`e
`
`z
`
`where A(z) is the LPC polynomial, and the spectral
`weighting parameters satisfy:
`<
`g
`g
`
`0
`
`2
`
`1
`
`1
`
` (3)
`
`We can rewrite equation (1) in vector notation:
`=
`- -
`
`
`
`
`($ )R R W R R$ ) /
`H
`
`, $ )R R
`
`(
`
`D
`w
`
`(
`
`K
`
`W(z)
`
`where,
`
`[
`R = R
`
`
`
`( ),...,1
`
`]
`
`
`
`
`R K T( )
`
`is the input DFT vector,
`[
`
`$
`$( ),..., $(R = R R K
`1
`
`
`
`]
`
`)
`
`T
`
`Figure 1. Block diagram of the AbS dispersion phase’s
`vector quantization.
`
`2.1. Waveform Matching Distortion
`
`Phase dispersion quantization aims to improve waveform
`matching. Efficient AbS quantization can be obtained by
`using the perceptually weighted distortion measure:
`p
`
`(4)
`
`(5)
`
`(6)
`
`(7)
`
`is the quantized DFT vector, and
`{
`}
`W = diagonal Wkk
`The magnitude is perceptually more significant than the
`phase; and should, therefore, be quantized first. Since
`phase is quantized to fewer bits, unless magnitude is
`quantized first,
`the magnitude spectral matching
`is
`unnecessarily sacrificed for excessive waveform matching.
`Additional justification for the above is provided from
`computational complexity considerations. For the above
`distortion measure, the quantized phase vector is given by:
`{
`}
`j j j=
`
`$ )
`jR e R
`,
`(
`Dw
`arg min
`}
`{
`=
`- -
`$ )
`$ )
`j j j
`j
`H
`j
`argmin R e R W R e R
`(
`(
`(cid:236)(cid:237)(cid:238) (cid:252)(cid:253)(cid:254)(cid:242)
`
`f f
`j jf
`( ) $ ( $ , )
`r
`arg max
`w
`
`$
`
`i
`
`$
`
`i
`
`$
`
`i
`
`d
`
`i
`
`(8)
`
`$
`
`=
`
`$
`
`i
`
`$
`
`i
`
`$
`
`i
`
`p
`
`2
`
`0
`
`r
`w
`
`where i is the running phase codebook index, and the
`respective phase exponent matrix is given by:
`j =
`e j
`
`{
`diagonal e
`
`j
`$ (
`j
`i
`
`k
`
`)
`
`}
`
`$
`
`i
`
`(9)
`
`-(cid:242)1
`f
`( )
`r
`p
`w
`2
`-(cid:229) (cid:229)
`1
`$
`=
`W R
`R
`kk
`P
`K
`
`2
`
`0
`
`f
`
`r$ ( )
`w
`
`2
`
`f
`
`d
`
`2
`
`k
`
`k
`
`P
`
`=
`k
`
`( )
`W R k
`kk
`
`2
`
`$( )
`R k
`
`(1)
`
`1
`
`0
`
`=
`
`w
`
`K
`
`D
`
`=
`
`=-
`
`k
`
`where
`rw( )f - weighted (synthesized) band-limited pulse
`prototype,
`f - weighted (synthesized) quantized pulse prototype,
`$ ( )
`rw
`Rk , $Rk - Fourier series coefficients of the non-weighted
`r f , respectively,
`pulse prototypes r( )f , and $( )
`$( )R k - DFT coefficients of r( )f , and
`R(k),
`respectively,
`
`
`
`$( )r f ,
`
`ŒºŒ œßœ
`
`P 2
`
`P - pitch period in samples,
`
`K - number of harmonics, K=
`
`Wkk - combined spectral-weighting and synthesis of the k-
`th harmonic given by:
`
`Equivalently, the quantized phase vector can be simplified
`to:
`
`-
`-
`£
`£
`

`
`$
`
`
`
`$
`
`i
`
`K
`
`k
`
`-(cid:236)(cid:237)(cid:238) (cid:252)(cid:253)(cid:254)
`j
`j j=
`( ) $( ) cos(
`arg max
`W R k R k
`kk
`=
`1
`where j (k) is the phase of, R(k), the k-th input DFT
`coefficient.
`
`j
`
`( )
`k
`
`$( ) )
`k
`
`i
`
`(10)
`
`The average global distortion measure for M vector set is:
`
`(cid:229)(cid:229) (cid:229)
`
`D
`
`
`w Global,
`
`=
`
`1
`M
`
`D
`w
`=
`{
`m Data
`}
`Vectors
`
`$
`j
`
`,R e R
`m
`
`m
`
`$
`
`(
`
`)
`
`m
`
`(11)
`
`=
`
`1
`M
`
`=
`{
`m Data
`}
`Vectors
`
`1
`K
`
`m
`
`K
`m
`
`=
`1
`
`k
`
`W
`,
`kk m
`
`
`
`R k( )
`
`m
`
`j
`$ (
`
`j
`
`k
`
`)
`
`m
`
`e
`
`
`
`R k$( )
`
`2
`
`m
`
`2.2.
`
`Centroid Equations
`
`The centroid equation [[19]] of the k-th harmonic’s phase,
`for the j-th cluster, which minimizes the global distortion
`in equation (11), is given by:
`j
`$( )
`k
`
`th
`
`•
`
`[[20]]
`
`filtered
`
`speech
`
`• Phase Bits: 0-6 every 20ms, a bitrate of 0-300
`bit/second.
`8 pitch ranges were selected, and training has been
`performed for each range.
`• Modified
`IRS
`(MIRS)
`(Female+Male)
`• Training Set: 99,323 vectors.
`• Test Set: 83,099 vectors.
`• Non-MIRS filtered speech (Female+Male)
`• Training Set: 101,359 vectors.
`• Test Set: 95,446 vectors.
`• The magnitude was not quantized.
`The segmental weighted signal-to-noise ratio (SNR) of the
`quantizer is illustrated in Figure 2. The proposed system
`achieves approximately 14dB SNR for as low as 6 bits for
`non-MIRS filtered speech, and nearly 10dB for MIRS
`[[20]] filtered speech.
`
`14
`
`12
`
`Non-MIRS (Flat)
`
`MIRS
`
`0
`
`1
`
`2
`
`3
`Phase Bits
`
`4
`
`5
`
`6
`
`10
`
`468
`
`Seg. Weighted SNR: dB
`
` Figure 2. Segmental weighted SNR of the phase VQ
`versus the number of bits, for MIRS and for Non-MIRS
`(Flat) speech.
`
`3.2.
`
`Subjective Results
`
`Recent WI coders have used a male speaker extracted
`dispersion phase [[10],[15]]. We have conducted a
`subjective A/B test to compare our dispersion phase VQ,
`using only 4 bits, to a male extracted dispersion phase.
`The test data included 16 MIRS speech sentences, 8 of
`which are of female speakers, and 8 of male speakers.
`During the test, all pairs of file were played twice in
`alternating order, and the listeners could vote for either of
`the systems, or for no preference. The speech material was
`synthesized using WI system in which only the dispersion
`phase was quantized every 20ms. Twenty one listeners
`participated in the test. The test results, illustrated in
`Figure 3, show improvement in speech quality by using
`the 4-bit phase VQ. The improvement is larger for female
`speakers than for male. This may be explained by a higher
`number of bits per vector sample for female, by less
`spectral masking for female’s speech, and by a larger
`amount of phase-dispersion variation for female.
`
`1 1
`
`K
`
`m
`
`j
`
`cluster
`
`=
`
`atan
`
`=
`{
`m j
`
`th
`
`cluster
`
`}
`
`=
`{
`m j
`
`th
`
`cluster
`
`}
`
`K
`
`m
`
`غŒŒŒŒ øßœœœœ(cid:229)(cid:229)
`
`(12)
`
`( ) )
`k
`m
`
`( )
`k
`
`)
`
`m
`
`j j
`
`sin(
`
`cos(
`
`$( )
`W R k
`,
`kk m
`
`m
`
`( )
`R k
`
`m
`
`$( )
`W R k
`,
`kk m
`
`m
`
`( )
`R k
`
`m
`
`These centroid equations use trigonometric functions of
`the phase, and therefore do not require any phase
`unwarping.
`
`2.3.
`
`Variable Dimension VQ
`
`The phase vector’s dimension depends on the pitch period
`and, therefore, a variable dimension VQ has been
`implemented. In our WI system the possible pitch period
`value was divided into eight ranges, and for each range of
`pitch period an optimal codebook was designed such that
`vectors of dimension smaller than the largest pitch period
`in each range are zero padded.
`
`Pitch changes over time cause the quantizer to switch
`among the pitch-range codebooks. In order to achieve
`smooth phase variations whenever such switch occurs,
`overlapped training clusters were used.
`
`3.
`
`EXPERIMENTAL RESULTS
`Objective Results
`
`3.1.
`
`Our phase-quantization scheme has been implemented as a
`part of WI coder, and used to quantize the SEW phase.
`The objective performance of the suggested phase VQ has
`been tested under the following conditions:
`
`(cid:229)
`-
`j
`-
`-
`-
`

`
`[5] Y. Shoham, "High Quality Speech Coding at 2.4 to
`4.0 kbps Based on Time-Frequency-Interpolation",
`IEEE ICASSP’93, Vol. II, pp. 167-170, 1993.
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`IEEE
`ICASSP’93, Vol. II, pp. 175-178, 1993
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`to 2.4 KBPS”,
`IEEE
`ICASSP’97, pp. 1599-1602, 1997.
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`IEEE
`Workshop on Speech Coding for Telecommunications,
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`P.830,
`“Recommendation
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`
`4bit VQ
`Male Extracted
`
`No Preference
`
`50.00%
`
`45.00%
`
`40.00%
`
`35.00%
`
`30.00%
`
`25.00%
`
`20.00%
`
`15.00%
`
`10.00%
`
`5.00%
`
`0.00%
`
`Subjective Score
`
`Female
`1
`
`2
`Male
`Figure 3. Results of subjective A/B test for comparison
`between the 4-bit phase VQ, and male extracted fixed
`phase.
`
`dispersion-phase
`the
`for
`design
`codebook
`The
`quantization involves a tradeoff between robustness in
`terms of smooth phase variations and waveform matching.
`Locally optimized codebook for each pitch value may
`improve the waveform matching on the average, but may
`occasionally yield abrupt and excessive changes which
`may cause temporal artifacts.
`
`4.
`
`SUMMARY
`
`This paper presented an efficient Analysis-by-Synthesis
`vector quantizer for the dispersion phase of the excitation
`signal which was used to enhance a WI coder. The scheme
`incorporates perceptual weighting, and does not require
`any phase unwarping. The proposed quantizer achieves a
`segmental SNR of up to 14dB for as low as 6-bit
`quantization. Subjective testing shows improvement in
`synthesized speech quality using the quantized phase over
`a male speaker extracted phase. The improvement was
`larger for female speakers.
`
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