Voice Transf 24. Voice Transformation o - habla.dc.uba.arhabla.dc.uba.ar/gravano/ith-2014/presentaciones/Stylianou_2008.pdf · 489 Voice Transf 24. Voice Transformation o Y. Stylianou

489

Voice Transfo24. Voice Transformation

Y. Stylianou

Voice transformation refers to the various modifi-cations one may apply to the sound produced bya person, speaking or singing. In this chapter wegive a description of various ways in which onecan modify a voice and provide details on how toimplement these modifications using a simple, butquite efficient, parametric model based on a har-monic representation of speech. By discussing thequality issues of current voice transformation algo-rithms in conjunction with the properties of speechproduction and perception systems we try to pavethe way for more-natural voice transformationalgorithms in the future.

24.1 Background ......................................... 489

24.2 Source–Filter Theoryand Harmonic Models ........................... 49024.2.1 Harmonic Model .......................... 49024.2.2 Analysis Based

on the Harmonic Model ................ 49124.2.3 Synthesis Based

on the Harmonic Model ................ 491

24.3 Definitions ........................................... 49224.3.1 Source Modifications .................... 49224.3.2 Filter Modifications ...................... 49324.3.3 Combining Source

and Filter Modifications ................ 494

24.4 Source Modifications ............................. 49424.4.1 Time-Scale Modification ............... 49524.4.2 Pitch Modification ........................ 49624.4.3 Joint Pitch

and Time-Scale Modification ......... 49624.4.4Energy Modification...................... 49724.4.5Generating the Source

Modified Speech Signal ................. 497

24.5 Filter Modifications ............................... 49824.5.1 The Gaussian Mixture Model .......... 499

24.6 Conversion Functions ............................ 499

24.7 Voice Conversion................................... 500

24.8 Quality Issues in Voice Transformations .. 501

24.9 Summary ............................................. 502

References .................................................. 502

24.1 Background

Voice transformation refers to the various modificationsone may apply to the sound produced by a person, speak-ing or singing. Voice transformation involves signalprocessing and the physics (or at least the understanding)of the speech production process and natural languageprocessing. Driven mainly by its applications, signalprocessing has evolved faster than the physics of speechprocessing, even giving the impression that signal pro-cessing alone may be required to achieve high-qualityvoice transformation. To an external observer, this issimilar to the problem of how to make an omelette with-out eggs. It is not surprising therefore that, although forsome categories of voice transformation good quality ofspeech is produced, this is not true in general. While itis relatively easy to explain to a non-speech expert thenecessity of speech modeling by providing examplesfrom the history of telecommunications, this is not ob-

vious for voice transformation. About two decades ago,it was easy to explain the applications of voice trans-formation technology to a speech processing engineerby providing examples from a specific area of speechtechnology: concatenating speech synthesis. In the late2000s, providing a reason for voice transformation toboth a speech expert and nonexpert faced the same diffi-culty. One reason for this was that the main application ofvoice transformation, that of concatenating speech syn-thesis, had evolved in a direction where it seemed thatsignal processing was no longer needed for this applica-tion. Such a point of view, however, was also supportedby the quality problems perceived in a modified speechsignal.

Recently, interest in voice transformation has in-creased substantially, and it is again the applicationof speech synthesis that is setting the pace. Voice

PartD

24

490 Part D Text-to-Speech Synthesis

transformation is a flexible, possibly simple, and effi-cient way to produce the variety needed in the currenttext-to-speech (TTS) systems based on the concate-nation of units (both large and small) [24.1]. In thischapter, we give a description of various ways inwhich one can modify a voice and provide details ofhow to implement these modifications using a sim-

ple, but quite efficient, parametric model based ona harmonic representation of speech. Discussing qual-ity issues of current voice transformation algorithmsin conjunction with properties of the speech produc-tion and perception systems we try to pave the wayfor more-natural voice transformation algorithms in thefuture.

24.2 Source–Filter Theory and Harmonic Models

24.2.1 Harmonic Model

When designing voice transformation techniques it isoften convenient to refer to the source–filter model ofspeech production. According to this model, speechis viewed as the result of passing a glottal exci-tation signal (source) through a time-varying linearfilter that models the resonant characteristics of thevocal tract. The most well-known source–filter sys-tem is that based on linear prediction (LP) ofspeech [24.2]. In its simplest form, a time-varyingfilter modeled as an autoregressive (AR) filter is ex-cited by either quasiperiodic pulses (during voicedspeech), or noise (during unvoiced speech). Manyattempts have been made to improve the source (ex-citation) signal in the LP context. This includesmultipulse LP [24.3], and code-excited linear predic-tion (CELP) [24.4]. A more-compact and at the sametime flexible representation of the excitation signalhas been proposed from a family of speech represen-tations referred to as sinusoidal models (SM) [24.5].In SM, the excitation signal for both voiced and un-voiced speech frames is represented by a sum ofsinusoids:

e(t) =K (t)∑

k=0

ak(t)eiφk(t) , (24.1)

where ak(t) and φk(t) are the instantaneous excitationamplitude and phase of the k-th sinusoid, respec-tively, and K (t) is the number of sinusoids, which mayvary in time. Especially for speech signals, a modelwhere the sinusoids are harmonically related is quitevalid (in the mean-squared-error (MSE) sense) whileit allows a simple and convenient way of applyingvarious modifications to the speech signal. In thiscase:

φk(t) = 2πk f0(t) , (24.2)

where f0(t) is the instantaneous fundamental fre-quency, which will also be referred to as the pitchin this chapter. Such a representation is still validfor both voiced and unvoiced speech frames. In thecase of unvoiced speech frames a constant fundamen-tal frequency is considered (i. e., 100 Hz) resultingin a Karhunen–Loeve representation of this speechcategory [24.5]. A further simplification of the excita-tion signal is convenient assuming that the excitationamplitude, ak(t), is constant over time and equal tounity: ak(t) = 1. Based on these simplifications, thetime-varying linear filter that models the resonant char-acteristics of the vocal tract approximates the combinedeffect of:

1. the transmission characteristics of the supraglottalcavities (including radiation at the mouth opening)

2. the glottal pulse shape

Its time-varying transfer function can be written

H( f ; t) = G( f ; t)eiΨ ( f ;t) , (24.3)

where G( f ; t) and Ψ ( f ; t) are, respectively, referred toas the time-varying amplitude and phase of the system.Speech processing is often (if not always) performed ina frame-by-frame basis, where each frame (i. e., about20 ms) is considered to be a stationary process. In thiscase, inside a frame, the filter H( f ; t) is considered aslinear time invariant (LTI). Then, the output speech sig-nal s(t) can be viewed as the convolution of the impulseresponse of the LTI filter, h(t), and the excitation signal,e(t):

s(t) =t∫

0

h(t − τ)e(τ)dτ . (24.4)

Recognizing then that the excitation signal is just thesum of K (t) eigenfunctions of the filter, H( f ), the

PartD

24.2

Voice Transformation 24.2 Source–Filter Theory and Harmonic Models 491

following speech model is obtained:

s(t) =K (t)∑

k=0

G[ fk(t)]ei{φk(t)+Ψ [ fk(t)]}

=K (t)∑

k=0

Ak(t)eiθk(t) , (24.5)

where fk(t) = k f0(t) (the eigenfrequencies). The har-monic amplitude Ak(t) of the k-th harmonic is the systemamplitude G[ fk(t)] (the eigenvalue). The phase θk(t) ofthe k-th harmonic is the sum of the excitation phase φk(t)and the system phase Ψ [ fk(t)]:

θk(t) = φk(t)+Ψ [ fk(t)] ; (24.6)

θk(t) is often referred to as the instantaneous phase ofthe k-th harmonic.

24.2.2 Analysis Basedon the Harmonic Model

Parameters of the harmonic model of speech may be es-timated by minimizing a least-squares criterion [24.6] orby minimizing a mean-squared error that leads to a sim-ple peak-picking approach [24.5]. The peak-pickingapproach results in a sinusoidal rather than a harmonicmodel. A second step is then required to fit a harmonicmodel to this sinusoidal model by selecting the funda-mental frequency that best represents the set of estimatedsinusoids. At each analysis time instant, ti

a, a set of pa-rameters are estimated: the fundamental frequency, f i

0,the harmonic amplitudes, Ai

k, and the harmonic phases,θi

k.Use of the harmonic model for voice transforma-

tions is simplified if the distance between two successiveanalysis time instants is equal to the local pitch period,P(ti

a) = 2π/ f i0:

ti+1a = ti

a + P(tia

). (24.7)

Another important step before synthesis is required:the estimation of the amplitude and phase envelopes,A( f ) and θ( f ) (i. e., a continuous function of frequency)from the discrete set of amplitude and phase values,respectively.

While a number of methods can be used to estimatethe amplitude envelope, for example, the linear predic-tion and homomorphic estimation techniques [24.7], it

is desirable to use a method that yields an envelopethat passes through the measured harmonic amplitudes.Such a technique was developed for the spectral enve-lope estimation vocoder (SEEVOC) [24.8] and was usedin the sinusoidal model in [24.5]. Another approachwas proposed in [24.9]: it provides a continuous fre-quency envelope when values of this envelope specifiedonly at discrete frequencies (i. e., exactly the situationin the previously described harmonic representation).This approach makes use of cepstral coefficients andis based on a frequency-domain least-squares crite-rion combined with regularization to increase estimationrobustness.

For the phase envelope θ( f ), the previous techniquescannot be used since the phase values have been esti-mated modulo 2π (principal values). Therefore, a phaseunwrapping algorithm has to be used. Two main ap-proaches exist:

1. phase continuity by adding appropriate multiples of2π to the principal phase values [24.10]

2. continuity by integration of the phase derivative

These algorithms try to obtain a continuous phase en-velope in the frequency domain. An extension of thesetechniques to preserve the continuity in the time domainas well has been proposed using the information of phasefrom previous voiced frames [24.11].

An alternative to the phase envelope approach is theuse of a minimum phase model for the system phase,while for the excitation phase a representation of the ex-citation in terms of its impulse locations (onset times) isused [24.12]. This approach, however, lacks robustnessbecause estimation of the onset times requires precisionthat is not always easy to obtain.

Next, we will consider the case when a spectralenvelope, A( f ), and phase envelope, θ( f ), are pro-vided.

24.2.3 Synthesis Basedon the Harmonic Model

Without speech modification, synthesis time instants,tis coincide with the analysis time instants ti

a, i.e., tis =

tia, ∀i.

Let (Aik, θ

ik, f i

0) and (Ai+1k , θi+1

k , f i+10 ) denote the

set of parameters at synthesis time instant tis and ti+1

s forthe k-th harmonic, respectively. Amplitudes and phasesare obtained by sampling the phase and amplitude (spec-tral) envelopes at the harmonics of the fundamentalfrequencies f i

0 and f i+10 . The instantaneous amplitude

Ak(t) is then obtained by linear interpolation of the

PartD

24.2


estimated amplitudes at the frame boundaries:

Ak(t) = Aik + Ai+1

k − Ai+1k

ti+1s − ti

s

t for tis ≤ t < ti+1

s .

(24.8)

In contrast to the third-order polynomial used in [24.13,14], the harmonic model allows the use of a simple first-degree polynomial for the phase. First, the phase at ti+1

sis predicted from the estimated phase at ti

s by

θi+1k = θi

k + k2π f0av(ti+1s − ti

s

), (24.9)

where f0av is the average value of the fundamentalfrequencies at ti

s and ti+1s :

f0av = f i0 + f i+1

0

2. (24.10)

Next, the phase θi+1k is augmented by the term 2πMk

(Mk is an integer) in order to approach the predictedvalue. Therefore, the value of Mk is given by

Mk =⟨

1

2π

(θi+1

k − θi+1k

)⟩. (24.11)

Then, the instantaneous phase θk(t) is simply obtainedby linear interpolation

θk(t) = θik + θi+1

k +2πMk − θik

ti+1s − ti

s

t , tis ≤ t < ti+1

s .

(24.12)

Having determined the instantaneous values of the har-monic amplitudes and phases the estimated speechsignal (a harmonic representation of the speech signal)is then obtained by:

s(t) =K∑

k=0

Ak(t) cos [θk(t)] , (24.13)

where Ak(t) is given by (24.8) and θk(t) by (24.12).Based on the source–filter model various speech

modification methods can now be defined. Some ofthese refer only to the source signal, others only to thefilter, while others apply to both the source and filter.Moreover, by developing the source–filter model in thecontext of the harmonic representation of speech signals,a mathematical notation regarding these modificationscan be introduced that will be used throughout the restof the chapter.

24.3 Definitions

24.3.1 Source Modifications

Modifications in the source signal are usually referredto as prosodic modifications and include three maintypes: time-scale modification, pitch modification, andintensity modification.

Time-Scale ModificationThe goal of time-scale modification is to change theapparent rate of articulation without affecting the per-ceptual quality of the original speech. This requires thepitch contour to be stretched or compressed in time,and the formant structure to be changed at a slower orfaster rate than the rate of the input speech, but other-wise not be modified. Figure 24.1 shows an example oftime stretching where the pitch period contour is sloweddown but not modified.

Pitch ModificationThe goal of pitch modification is to alter the funda-mental frequency in order to compress or expand thespacing between the harmonic components in the spec-trum while preserving the short-time spectral envelope

(the locations and bandwidths of the formants) as wellas the time evolution. In contrast to time-scale modifica-

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Fig. 24.1 Pitch-period contour: original and time-stretchedby a factor of 0.6

PartD

24.3

Voice Transformation 24.3 Definitions 493

tions, in this case the pitch contour is modified withoutmodifying, however, the time resolution of the pitchcontour. Figure 24.2 shows an example of pitch mod-ification by constant pitch-scale factor (0.6): the timeevolution is preserved and the pitch-period contour isscaled by 0.6. In this case, the input fundamental fre-quency is increased by a factor of 1/0.6. This could givethe impression that a male voice will sound more likea female voice, while a female voice will more soundlike a child’s voice.

Intensity ModificationIt is widely considered that intensity modification isthe simplest modification among the prosodic modifi-cations. This is because it can be easily performed byassociating an intensity scale factor at each analysis timeinstant of a signal. The signal is then just multiplied bythis scale factor. In the case of a parametric model likethe harmonic model developed previously, the scale fac-tor is applied to the harmonic amplitudes Ak(t) in (24.5).It may seem strange to modify a prosodic feature bychanging a parameter corresponding to the vocal-tractfilter. However, it should be remembered that the filterhas been considered as an LTI filter; therefore, multiply-ing the amplitude of the excitation signal by a constantresults in multiplying the harmonic amplitudes, Ak(t),by the constant.

24.3.2 Filter Modifications

By filter modification we mean the modification of themagnitude spectrum of the frequency response of the vo-cal tract system, |H(ω)|. It is widely accepted that |H(ω)|carries information of speaker individuality. Represen-tations of the magnitude spectrum (i. e., mel frequencycepstral coefficients (MFCC), line spectrum frequencies(LSF), etc.) have been used a lot in the area of speakeridentification and recognition as well as for speaker nor-malization for robust speech recognition. Therefore, bymodifying the magnitude spectrum of the vocal tract,speaker identity may be controlled. We may distinguishtwo types of filter modification, which are describedbelow.

Without a Specific TargetIn this case, the filter characteristics of a speaker aremodified in a general way without having a specifictarget (speaker) in mind. For example, we may wishto modify the overall quality of a speech signal pro-duced by a female speaker so that it sounds as if ithad been produced by an older female speaker. Basedon the source–filter theory for the production of speech

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Fig. 24.2 Pitch-period contour: original and modified byapplying a pitch modification factor of 0.6

we know that the formants for a female voice are dis-tributed in higher frequencies than the formants from anolder female voice. Similar observations are valid forthe harmonic frequencies. Therefore, one can modify ina general way the power spectrum of a speaker so that theresulting spectrum has the characteristics of a family ofspeakers (child’s, old person’s voices, etc.). Figure 24.3shows an example of filter modification to modify thespectrum from a female voice to a spectrum similar toan old female person. For this one should compress the

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Fig. 24.3 Female (solid line) to an old female (dashed line) filtermodification

PartD

24.3


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Fig. 24.4 Source (solid line) to target (dashed line) filter transfor-mation. The transformed filter is shown by a dashed–dot line

frequency information so that formants and harmonicsare moved towards lower frequencies. The result shownin Fig. 24.3 was obtained by combining two operations:lowering the sampling frequency of the source signal(female voice, 44 100 Hz) to 18 000 Hz, and then apply-ing time-scale modification with a factor of 8/9. Theresult signal can be played back at 16 000 Hz withoutany modification in the articulation rhythm. The qualityof the modified signal is similar to that the initial signal.

With a Specific TargetIn this case, the filter of a speaker (the source speaker) ismodified in such a way that the modified filter approx-imates in the mean-squared sense the characteristics ofthe filter of another speaker (the target speaker). Usuallywe refer to this type of modification as a transformationor conversion. An example of a such transformation isdepicted in Fig. 24.4. In this example the original spec-trum is shown by a solid line, the target spectrum bya dashed line, and the transformed original to targetspectrum by a dashed–dot line. To obtain the trans-formed spectrum, there is a learning process using manysimilar examples of the source and the target spec-trum; therefore, the transformed spectrum is equal tothe average spectrum of the target spectra used during

the training process. Details about this type of spectraltransformation will be provided in the next section.

24.3.3 Combining Sourceand Filter Modifications

To transform a female into a male voice, performing fil-ter modification or only pitch modification alone maynot provide convincing results. In most cases, sourceand filter modifications must be combined. For exam-ple, the prosody characteristics of a speaker may bea critical cue used for the identification of the speakerby others (speaking style) while at the same time, vocal-tract characteristics are also important for identification.Therefore, if we want to modify the voice of the speakerso that it sounds like the voice of another speaker,prosody and vocal tract modifications should be com-bined. If a target speaker is provided then this combinedsource and filter modifications is referred to as voiceconversion or transformation. In contrast, when a spe-cific target is not provided, this is usually referred to asvoice modification.

Voice morphing is another type of combined sourceand/or filter modifications. In this case the same twosentences are uttered by two speakers and then a thirdspeaker may be generated having characteristics fromboth speakers. This is mainly achieved by a dynamictime warping (DTW) algorithm between the two sen-tences, aligning the acoustic data and then applyinga linear or other type of interpolation between the aligneddata (source and/or filter characteristics). Sometimes thistype of voice transformation is confused with voice con-version. Note that in voice conversion the sentence to beconverted, uttered by the source speaker, has never beenuttered by the target speaker. However, in voice morph-ing there are two source speakers that generate a newvoice saying the same text as the two source voices.In voice conversion, there is only one source speakerand one target speaker, and the voice characteristics ofthe source speaker should be transformed into the voicecharacteristics of the target speaker (i. e., a new speakeris not generated in this case).

In the next section we will provide details about themain prosodic (time and pitch) modifications and thefilter modifications. Then a system for voice conversionwill be presented.

24.4 Source Modifications

Pitch synchronous analysis is the key to the simplicityof many source (prosodic) modification algorithms and

is defined as follows. Given an analysis time instant, tia,

the next analysis time instant, ti+1a is determined by the

PartD

24.4

Voice Transformation 24.4 Source Modifications 495

local pitch period at tia, P(ti

a), using (24.7). The length ofthe analysis window is proportional to the local pitch pe-riod (usually two local pitch periods are used). We maydistinguish two types of pitch synchronous analysis. Thefirst one may be referred to as strict pitch synchronousanalysis, where the analysis time instants are supposed tocoincide with the glottal closure instants (GCIs, some-times called pitch marks). In the other, referred to asrelaxed pitch synchronous analysis, the analysis timeinstants do not (necessarily) coincide with the GCIs.Since the estimation of pitch marks from the speech sig-nal is not a robust process, resulting sometimes in anincoherent synthesis, relaxed pitch synchronous analy-sis seems to be easier to use than the fixed approach.However, this is not true. Pitch modification requiresthe re-estimation of phases. Coherent synthesis mainlymeans synthesis without linear phase mismatches. Strictpitch synchronous methods explicitly remove any linearphase mismatch between successive frames by usingGCIs. Relaxed pitch synchronous methods, however,need to re-estimate the linear phase component for thenew pitch values, which is not a trivial task. Phase mod-els [24.12] and estimation of phase envelopes [24.11]try to overcome these problems.

For the system presented here, we will considerthat the analysis time instants (Sect. 24.2.2) have beendetermined in a relaxed pitch synchronous way.

Next, we will see how the pitch synchronous schemeallows the use of simple and flexible techniques fortime-scale and pitch-scale modifications. The first stepconsists of finding out the synthesis time instants ti

s (orsynthesis pitch marks) according to the desired time-scale and pitch-scale modification factors. The modifiedsignal is then obtained by using the new synthesis timeinstants.

24.4.1 Time-Scale Modification

We recall that the objective of time-scale modificationis to alter the apparent rate of articulation without af-fecting the spectral content: the pitch contour and timeevolution of the formant structure should be time scaled,but otherwise not modified [24.15].

From the stream of analysis time instants tia and the

desired time-scale modification factor β(t), (β(t) > 0)the synthesis time instants ti

s will be determined. Themapping ti

a → tis = D(t) is referred to as the time-scale

warping function, which is defined as the integral of β(t):

D(t) =t∫

0

β(τ)dτ . (24.14)

Note that for a constant time modification rate β(t) = β,the time-scale warping function is linear: D(t) = βt. Thecase β > 1 corresponds to slowing down the rate of ar-ticulation by means of a time-scale expansion, while thecase β < 1 corresponds to speeding up the rate of ar-ticulation by means of a time-scale compression. Thus,speech events that take place at a time tor in the origi-nal time scale will occur at a time tmo = βtor in the new(modified) time scale.

As an example, let us assume that at each analysis tim-instant ti

a a time-scale modification factor bs has beenspecified. Thus, β(t) is a piecewise constant function,i. e., β(t) = βs, ti

a ≤ t < ti+1a . It follows therefore that the

time-scale warping function D(t) can then be written

D(t) = D(tia)+βs

(t − ti

a

), ti

a ≤ t < ti+1a (24.15)

with D(t1a ) = 0.

Having specified the time-scale warping functionD(t), the next step consists of generating the streamof the synthesis time instants ti

s, while preserving thepitch contour: the pitch in the time-scaled signal attime t should be as close as possible to the pitch inthe original signal at time D−1(t). In other words,t → P′(t) = P[D−1(t)]. We now have to find a stream ofsynthesis pitch marks (synthesis time instants) ti

s, suchthat ti+1

s = tis + P′(ti

s). To solve this problem, the use ofa stream of virtual pitch marks, ti

v, in the original signalrelated to the synthesis pitch-marks by

tis = D

(tiv

),

tiv = D−1(ti

s

), (24.16)

is proposed in [24.15]. Assuming that tis and ti

v are

known, we determine ti+1s (and ti+1

v ), such that ti+1s − ti

sis approximately equal to the pitch in the original signalat time ti

v. This can be expressed as

ti+1s − ti

s = 1

ti+1v − ti

v

ti+1v∫

tiv

P(t)dt (24.17)

with ti+1s = D(ti+1

v ). According to this equation, the syn-thesis pitch period ti+1

s − tis at time ti

s is equal to the meanvalue of the pitch in the original signal calculated overthe time interval ti+1

v − tiv. Note that this time interval

ti+1v − ti

v is mapped to ti+1s − ti

s by the mapping functionD(t).

The integral equation (24.17) is easily solved be-cause D(t) and P(t) are piecewise linear functions.Figure 24.5 illustrates an example of the computation ofsynthesis pitch marks for time-scale modification by 1.5.

PartD

24.4


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Fig. 24.5 Computation of the synthesis pitch marks fortime-scale modification by 1.5

24.4.2 Pitch Modification

The goal of the pitch-scale modification is to alter thefundamental frequency of a speaker while the spectralenvelope of the speaker’s vocal-tract system functionis unchanged. Obviously, pitch modification is only ap-plied on the voiced speech frames. The first step consistsof computing the synthesis time instants ti

s from thestream of the analysis time instants ti

a and the pitch-scalemodification factors a(t), with a(t) > 0. We recall thatthe analysis time instants are set in a pitch synchronousway. We require the same for the synthesis time instants:ti+1s = ti

s + P′(tis), where P′(ti

s) is approximately equalto the pitch period in the original signal around time ti

ascaled by 1/α(ti

a):

P′(tis

) = P(tia

)

α(tia

) . (24.18)

Given the synthesis time instant tis, the next synthesis

time instant ti+1s is obtained by setting the synthesis

pitch period to be equal to the mean value of the scaledpitch period (by 1/α(ti

a)) in the original signal calculatedover the time frame ti+1

s − tis:

ti+1s − ti

s = 1

ti+1s − ti

s

ti+1s∫

tis

P(t)

α(t)dt . (24.19)

This integral equation is easily solved as P(t) is a piece-wise linear function and α(t) is a piecewise constantfunction:

α(t) = a(tia

)for ti

a ≤ t < ti+1a . (24.20)

Figure 24.6 shows an example of a mapping betweenthe analysis and synthesis time instants for pitch modi-fication by 1.5.

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Fig. 24.6 Computation of the synthesis pitch marks forpitch modification by 1.5

24.4.3 Joint Pitchand Time-Scale Modification

Based on the procedures presented above, joint pitch andtime-scale modifications can easily be obtained. Givena pitch and time-scale modification factor at each analy-sis time instant and combining (24.17) and (24.19), thesynthesis time instants can be obtained by solving thefollowing integral equation

ti+1s − ti

s = 1

ti+1v − ti

v

ti+1v∫

tiv

P(t)

α(t)dt . (24.21)

The synthesis time instants determined by theprocedures above are not, in general, univocally asso-ciated with the analysis time instants (see for exampleFigs. 24.5 and 24.6). A solution consists of replacing thevirtual pitch marks by the nearest analysis time instant.In this case, however, another problem arises: two ormore successive frames could be the same and then theharmonic parameters (amplitudes and phases) will notvary within the frame, meaning that a high-quality modi-fied synthetic signal is not produced. It follows thereforethat the repeated analysis time instants should be elimi-

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Fig. 24.7 Elimination of repeated analysis time instantsfrom the example in Fig. 24.6

PartD

24.4

Voice Transformation 24.4 Source Modifications 497

nated. As an example, in Fig. 24.7 the repeated analysistime instants in Fig. 24.6 are eliminated.

24.4.4 Energy Modification

Energy modification is performed by associating an in-tensity scale factor, c(ti

s), at each synthesis time instant.Then, the harmonic amplitudes are multiplied by thesquare root of the current harmonic intensity scale factor

A′k

(tis

) =√

c(tis

)Ak

(tis

)for k = 1, . . . , K ,

(24.22)

where K is the number of harmonics. The modified am-plitudes should then be used in estimating the amplitudeenvelope (Sect. 24.2.2).

24.4.5 Generating the SourceModified Speech Signal

In synthesis, the first step is the computation of theharmonic amplitudes and phases at the shifted har-monic frequencies. Note that in the case of time-scalemodifications, the original amplitudes and phase maybe preserved. In general, therefore, the amplitudesand phases are obtained by sampling the phase andamplitude envelopes at the corresponding harmonic fre-quencies. In the case of pitch modification, the phase andamplitude envelope should be sampled using the modi-fied fundamental frequency: f ′

0(tia) = α(ti

a) f0(tia). Given

a spectrum, this results in a different number of har-monics from those initially included in the spectrum.When α(ti

a) > 1, fewer harmonics are included in thespectrum, and when α(ti

a) < 1, more harmonics are in-cluded. This means that the initial energy of the signalwill be changed. Therefore, the amplitudes of the shiftedharmonics are normalized in such a way that the final en-ergy of the pitch-modified signal is equal to the energyof the unmodified one.

Using the new synthesis time instants and themodified set of parameters (amplitudes and phases) cor-responding to each time instant, the source modifiedspeech signal is obtained in exactly the same way asshown in Sect. 24.2.3. Examples of time-scale modifi-cation and pitch modification, both using a modificationfactor of 1.3, are depicted in Figs. 24.8 and 24.9, respec-tively.

An alternative to the parametric harmonic modelfor source modifications is the time-domain pitchsynchronous overlap add (TD-PSOLA) [24.16].TD-PSOLA relies heavily on the source–filter speechproduction model, although the parameters of this

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Fig. 24.8 (a) Original speech signal. (b) Time-scaled by 1.3. Timeis provided in samples (sampling frequency: 16 kHz)

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Fig. 24.9 (a) Original speech signal. (b) Pitch modified by 1.3. Timeis provided in samples (sampling frequency: 16 kHz)

model are not estimated explicitly. TD-PSOLA ischaracterized by simplicity and low computational com-plexity, allowing good-quality prosodic modificationsof speech. It is widely adopted for text-to-speech syn-thesis based on concatenation of acoustic units likediphones. Other methods similar to TD-PSOLA havealso been proposed, including multiband resynthesis

PartD

24.4


overlap add (MBROLA) [24.1]. The synchronized over-lap add (SOLA) [24.17] and the waveform similarityoverlap add (WSOLA) [24.18] methods have mainlybeen proposed for time-scale modification. In SOLAand WSOLA, successive speech frames to be over-lapped are cross-correlated, providing the time shiftto ensure that the two overlapping frames are syn-chronized and thus add coherently. TD-PSOLA relieson GCIs (pitch marks for voice sounds) to syn-chronize the speech frames. The use of pitch marksallows TD-PSOLA to apply a simple mechanism forpitch modification; this is not possible for the SOLAand WSOLA techniques. Examples of how to applyTD-PSOLA for speech modifications using the map-ping of analysis and synthesis time instants are providedin Chap. 19.

Nonparametric approaches such as TD-PSOLA,SOLA, and WSOLA, do not allow complex modifi-cations of the signal, such as increasing the degreeof friction, or changing the amplitude and phase rela-tionships between the pitch harmonics. Another majordrawback is the manipulation of noise-like sounds

presented in speech. For example, TD-PSOLA elimi-nates/duplicates short-time waveforms extracted fromthe original speech signal by windowing. When this ap-proach is applied to unvoiced fricatives a tonal noiseis produced because the repetition of segments ofa noise-like signal produces an artificial long-time au-tocorrelation in the output signal, perceived as somesort of periodicity [24.15]. A simple solution to thisproblem consists of reversing the time-axis wheneverthe TD-PSOLA algorithm needs to duplicate unvoicedshort-time signals [24.15]. This solution reduces the un-desirable correlation in the output signal but the tonalquality does not completely disappear. This solution can-not be applied when the time-scale factor is greater than2. Moreover, this solution cannot be used when voicedfricative frames are processed.

On the other hand, sinusoidal models have beenfound to be an efficient representation of voicedspeech [24.5]. For a flexible representation of the un-voiced sounds and for high-quality pitch and time-scalemodification of speech, hybrid [i. e., harmonic plus noise(HNM) [24.6]] models are more suitable.

24.5 Filter Modifications

Next, we will consider the case of filter modificationwith a specific target. This provides a more-generalframework for filter modification than without a specifictarget, since it has a higher time resolution; the modi-fication filter should be changed faster than in the casewhere a nonspecific target is provided. In this context,a set of source and target spectral envelopes is assumedgiven that an appropriate representation of the vocal tractspectral envelope is provided (i. e., using cepstral coeffi-cients, line spectrum frequencies, mel frequency cepstralcoefficients). To convert the source spectral envelopeto the target spectral envelope, a training (or learningstep) is necessary. During this step, a conversion func-tion is trained. For this purpose, the source and the targetspeaker utter the same sentences.

One of the earliest approaches to the filter conversionis the mapping codebook method [vector quantization(VQ)] of Abe et al. [24.19], which was originally intro-duced for speaker adaptation by Shikano et al. [24.20].The basic idea of this technique is to make mappingcodebooks that represent the correspondence betweenthe two speakers. A conversion of acoustic featuresfrom one speaker to another is therefore reduced to theproblem of mapping the codebooks of the two speak-

ers [24.19]. The main shortcoming of this method isthe fact that the acoustic space of the converted sig-nal is limited to a discrete set of envelopes. To avoidthe limitations of the discrete space represented by VQ,a fuzzy vector quantization (FVQ) has been proposedby Kuwabara et al. [24.21]. A quite different approach,also based on VQ, has been proposed by Iwahashiet al. [24.22] using speaker interpolation. The use oflinear multivariate regression (LMR) for mapping oneclass from the VQ space of the source speaker to the cor-responding class in the VQ space of the target speakerhas been proposed by Valbret et al. [24.23]. In thesame communication [24.23], Valbret et al. proposeda spectral transformation approach based on dynamicfrequency warping (DFW). In LMR a simple lineartransformation function for each class has been pro-posed, while in DFW a third-order polynomial is used.All these methods have been developed in the contextof VQ. Most authors agree that the mapping codebookapproach, although it provides an impressive percep-tive voice conversion effect, is plagued by poor qualityand lack of robustness [24.24]. Approaches based onLMR and DFW also introduce discontinuities into thespectral information, as the acoustic space of a speaker

PartD

24.5

Voice Transformation 24.6 Conversion Functions 499

is partitioned in discrete regions. DFW succeeds inmoving the formant frequencies but it has little or noeffect on their amplitudes and bandwidths. Mappingfunctions have also been proposed using more-robustmodeling compared to VQ of the acoustic space ofa speaker based on the Gaussian mixture model (GMM).Assuming that the source and target vectors obtainedfrom the speakers acoustic space are jointly Gaussian,a continuous probabilistic mapping function based onGMM has been proposed [24.25, 26]. A similar map-ping function has been proposed by Kain et al. [24.27],jointly modeling the source and target vectors withGMM.

All of these techniques are based on parallel train-ing data, where both the source and target speaker utterthe same sentence. Then, a DTW is used to align thetwo signals in time in order to extract the aligned sourceand target training vectors. Approaches without the re-quirement of parallel data have also been proposed in theliterature [24.28,29]. However, using the same mappingfunctions for parallel and nonparallel data, it has beenshown that training with parallel data provides betterconversion results [24.28].

In the following, we will present a state-of-the-art system for filter modification (spectral conversion)based on GMM making use of parallel data [24.26].

24.5.1 The Gaussian Mixture Model

The Gaussian mixture density is a weighted sum of mcomponent densities and given by the equation

p(x|Θ) =m∑

i=1

αi pi (x|θi ) , (24.23)

where x = [x1 x2 x3 · · · x p]T is a p-by-1-dimensionalrandom vector, pi (x|θi ), for i = 1, · · · , m, are the com-ponent densities and αi are the mixture weights. Eachcomponent density, pi (x|θi ), is a p-dimensional normaldistribution

pi (x|θi ) = N(x; μi ,Σi ) (24.24)

with μi the p-by-1 mean vector and Σi the p-by-p co-variance matrix. The mixture weights, αi , are normalizedpositive scalar weights (

∑mi=1 αi = 1 and αi ≥ 0). This

ensures that the mixture is a true probability densityfunction (PDF). The complete Gaussian mixture den-sity is parameterized by the mixture weights, the meanvectors and the covariance matrices from all componentdensities, which is represented by the notation,

Θ = (αi ,μi ,Σi ) , i = 1, · · · , m . (24.25)

The Gaussian mixture model (GMM) is a classicparametric model used in many pattern-recognition tech-niques [24.30] and speech applications such as speakerrecognition [24.31]. In the GMM context, a speaker’svoice is characterized by m acoustic classes represent-ing some broad phonetic events, such as vowels, nasalor fricatives. The probabilistic modeling of an acousticclass is important since there is variability in featurescoming from the same class due to variations in pro-nunciation and co-articulation. Thus, the mean vectorμi represents the average features for the acoustic classωi , and the covariance matrix Σi models the variabilityof features within the acoustic class.

GMM parameters are usually estimated by a stan-dard iterative parameter estimation procedure, which isa special case of the expectation-maximization (EM) al-gorithm [24.32, 33]. Initialization of the algorithm maybe provided by VQ.

24.6 Conversion Functions

Let xt and yt be a set of p-dimensional vectors cor-responding to the spectral envelopes of the source andthe target speaker, respectively, where t = 1, . . . , n. It istherefore assumed that these vectors have been obtainedby speech samples from both speakers that have beenaligned in time using a classic dynamic time-alignmentalgorithm [24.34]. We also assume that a Gaussian mix-ture model (αi ,μi ,Σi , for i = 1, . . . , m) has been fittedto the source vectors (xt, t = 1, . . . , n).

It is worth noting that, if we take the limit case wherethe GMM is reduced to a single class and if the source

vectors xt follow a Gaussian distribution N(x; μ,Σ) andthat the source and target vectors are jointly Gaussian,the minimum mean-square error estimate of the targetvector is given by [24.35]

E[y|x = xt] = ν +ΓΣ−1(xt −μ) , (24.26)

where E[] denotes expectation, and ν and Γ are, respec-tively, the mean target vector

ν = E[y] ,

PartD

24.6


and the cross-covariance matrix of the source and targetvectors

Γ = E[(y −ν)(x−μ)T] ,

where the superscript T denotes transposition [24.36].In [24.27], a direct extension of (24.26) to the GMM

case was proposed. However, such an extension is notsupported by the theory of statistics. Moreover, such anextension makes the assumption of a one-to-one corres-pondence between the source and target space, whichis not valid in practice. To overcome these difficulties,and motivated by (24.26) the following conversion func-tion between the source and the target data has beenproposed [24.25]:

F (xt) =m∑

i=1

P(ωi |xt)[νi +ΓiΣ

−1i (xt −μi )

].

(24.27)

The conversion function F is entirely defined by thep-dimensional vectors νi and the p-by-p matrices Γi ,for i = 1, . . . , m (where m is the number of mixturecomponents). This means that νi and Γi are the param-eters to be estimated. The parameters of the conversionfunction are computed by least squares optimization onthe learning data so as to minimize the total squared

conversion error

ε =n∑

t=1

||yt −F (xt)||2 . (24.28)

Since the conversion function given by (24.27) is linear,the optimization of its parameters is equivalent to theresolution of a set of linear equations in the least-squaressense. Details of the minimization of (24.28) may befound in [24.37]. The mapping function (24.27) can beused with full or diagonal covariance matrices. Note thatthe conversion function is reduced to

F (xt) =m∑

i=1

P(ωi |xt)νi (24.29)

if the correction term that depends on the difference be-tween the source vector xt and the mean of the GMMcomponent μi in (24.27) is omitted. This reduced con-version function is similar to the formula proposedby Abe et al. [24.19] in the mapping codebook ap-proach. Comparing (24.29) and (24.27) it follows thatin VQ-type mapping functions the variability of thetransformed spectral envelope is strongly restricted.

An example of filter conversion based on the ap-proach described in this section has already beenpresented in Fig. 24.4.

24.7 Voice Conversion

Combining source and filter modifications a systemthat controls speaker’s quality and individuality canbe obtained. Continuing with the harmonic model asan example of representing speech, a speech signalproduced by the source speaker is analyzed in a pitch-synchronous way (Sect. 24.2.1) to extract a set ofsource spectral envelopes. Given the spectral conver-sion function in (24.27), the target spectral envelopesin each frame are estimated by applying (24.27) to

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Fig. 24.10 Block diagram of a voiceconversion system; ti

a and tis repre-

sent the analysis and synthesis timeinstants, respectively

the source spectral envelopes. The next step is to ap-ply the appropriate prosodic or source modificationsin order to capture the prosodic patterns of the targetspeaker (Sect. 24.4). For this, prosodic profile anal-ysis (i. e., characteristic articulation rate, stress, andemotions, pitch fluctuations) is required for both speak-ers. Determining such a profile is not a trivial taskand has not yet been achieved in a convincing way.Thus, most voice conversion systems today make use

PartD

24.7

Voice Transformation 24.8 Quality Issues in Voice Transformations 501

of average prosodic modification factors. A block dia-gram for the conversion system based on the harmonic

model and the voice conversion function is presented inFig. 24.10.

24.8 Quality Issues in Voice Transformations

Voice transformations are usually evaluated in sub-jective tests. The overall impression from the resultsobtained from these tests is that time-scale modifica-tion is quite successful for moderate scale factors, whilepitch-modified signals by pitch scale factors over 1.5 andbelow 0.7, suffer from various artifacts, making listenersclassify the modifications as not natural. Voice conver-sion reaches a high score for transforming the identity ofthe source speaker to that of the target speaker. However,there are serious quality problems, which are mostly re-ferred to as muffling effects. To improve the quality ofthe speech produced by various proposed voice trans-formation algorithms a better understanding of speechproduction and perception mechanisms is necessary. Forexample, when we want to increase the loudness of ourvoice while sitting in a cafeteria, we add stress to a partof our speech signal, like consonants, and not to all thespeech events we produce. One hypothesis for this is thatconsonants carry more of the information load, whichis connected with the intelligibility of the message wewould like to transmit. According to this hypothesis weonly increase the stress to these sounds by an amountthat is sufficient to mask the cafeteria noise. Increasingthe stress does not mean that the amplitudes of all thefrequencies for this sound are increased. Stress means anincrease of the subglottal pressure, which will result inan abrupt glottal closure by accentuating the Bernoullieffect on airflow through the glottis [24.38]. This corre-sponds to more energy mostly at high frequencies. Fromthis example, it is obvious that even a simple intensitymodification is not as simple as we thought. Continuingthe above example, the increase of the subglottal pres-sure will increase the tension in the vocal folds, resultingin an increase of the pitch. This shows that modifyingone parameter may require the modification of anotheras well.

In most Western languages consonants (we recallthat consonants carry important information load) areshorter in duration than vowels (which carry more-prosodic information). Our perceptual system requiressome time to process the perceived sounds. When wewant to speak faster, we somehow protect the conso-

nants. Pickett [24.39] has done extensive studies on thedegree of change in vowels and consonants in speak-ing at a faster or slower rate. In [24.39], it was reportedthat, when going from normal to the faster rate, the vow-els were compressed by 50% while the consonants werecompressed by 26%. However, going from the slow-est to the fastest rate, both vowels and consonants werecompressed by about 33% [24.38]. This shows that time-scale modifications should take into account phoneticinformation. Speaking at faster or slower rate again in-troduces modifications in pitch values since there arefluctuations in the subglottal pressure. This means thattime-scale modifications should be performed jointlywith pitch modifications.

In the source–filter theory presented at the begin-ning of the chapter, it was assumed that glottal airflowsource is not influenced by the vocal tract. In reality,there is a nonlinear coupling between the source andthe filter. Results from studies on the fine structure ofthe glottal airflow derivative waveform show that an in-crease in the first-formant bandwidth and modulationof the first-formant frequency occurs during the glottalopen phase [24.40]. Obviously, when pitch modificationis applied, these interactions should be respected.

Attempts have been made to incorporate some ofthese observations into the modification algorithms.In [24.41], a higher intelligibility score was achieved fortime-scale-modified speech signals when nonstationar-ity measurements in the signal were taken into account.In [24.42], the interaction between pitch and spectralenvelopes was modeled in a statistical way. This wasused to postprocess pitch-modified signals. Perceptualtests have shown that this postprocessing improved thenaturalness of the pitch-modified signal.

To improve further the quality of voice transforma-tions more effort should be made taking into accountnonlinear phenomena during the production process andresults from the natural language processing area. Inother words, voice transformation requires more thanjust modeling of the speech signal; it requires under-standing of the speech process (production, perception,and language).

PartD

24.8


24.9 Summary

In this chapter, we have described voice transformationsthrough a simple harmonic representation of speech.We began with the description of the basic source–filter theory for the production of speech and providinga mathematical description of speech production usingthis theory in the context of a harmonic model. Weused this description to define voice transformation byspecifying modifications for the source, for the filter,and their combination. We then provided formal defi-nitions of these modifications and their application inthe context of the harmonic model was also derived anda set of conditions for the pitch synchronous analysisof speech was described. Techniques for filter modi-fications were discussed and a state-of-the-art methodbased on a GMM description of the acoustic space

of a speaker was developed. A mapping function thatmade use of the complete description of each compo-nent of the GMM was provided. Finally, we discussedspeech quality issues related to voice transformationsand noted that, for improving speech quality in the fu-ture, we need to give more realism to the source–filtermodel by taking into account the nonlinear couplingbetween the source and filter and to processes relatedto our perception system. In other words, just model-ing the speech signal may be enough for transmissionthrough the networks, but it is not sufficient for modi-fying the signal in a way that is perceived by humansto be natural. For this, we need to understand speechand then develop algorithms able to incorporate thisunderstanding.

References

24.1 T. Dutoit: An Introduction to Text-to-Speech Syn-thesis (Kluwer Academic, Dordrecht 1997)

24.2 J.D. Markel, A.M. Gray: Linear Prediction of Speech(Springer, Berlin, Heidelberg 1976)

24.3 B. Atal, J. Remde: A new model of LPC excitationfor producing natural-sounding speech at low bitrates, Proc. IEEE ICASSP, Vol. 7 (1982) pp. 614–617

24.4 M.R. Schroeder, B.S. Atal: Code-excited linear pre-diction (CELP): High-quality speech at very low bitrates, Proc. IEEE ICASSP, Vol. 10 (1985) pp. 937–940

24.5 R.J. McAulay, T.F. Quatieri: Speech analy-sis/synthesis based on a sinusoidal representation,IEEE ICASSP 34, 744–754 (1986)

24.6 Y. Stylianou: Modeling speech based on harmonicplus noise models. In: Nonlinear Speech Modelingand Applications, ed. by G. Chellot, A. Espos-ito, M. Faundez (Springer, Berlin, Heidelberg 2005)pp. 375–383

24.7 A.V. Oppenheim, R.W. Schafer: Homomorphicanalysis of speech, IEEE Trans. Audio Electroacoust.16, 221–228 (1968)

24.8 D.B. Paul: The spectral envelope estimationvocoder, IEEE ICASSP 29, 786–794 (1981)

24.9 O. Cappé, E. Moulines: Regularization techniquesfor discrete cepstrum estimation, IEEE Signal Pro-cess. Lett. 3(4), 100–102 (1996)

24.10 A.V. Oppenheim, R.W. Schafer: Discrete-Time Sig-nal Processing (Prentice Hall, Englewood Cliffs1989)

24.11 Y. Stylianou, J. Laroche, E. Moulines: High-qualityspeech modification based on a harmonic + noisemodel, Proc. Eurospeech, Vol. 95 (1995) pp. 451–454

24.12 T.F. Quatieri, R.J. McAulay: Shape invariant time-scale and pitch modification of speech, IEEE ICASSP40, 497–510 (1992)

24.13 R.J. McAulay, T.F. Quatieri: Low-rate speech codingbased on the sinusoidal model. In: Advances inSpeech Signal Processing, ed. by S. Furui, M. Sondhi(Marcel Dekker, New York 1991) pp. 165–208, Chap.6

24.14 L. Almeida, F. Silva: Variable-frequency synthesis:An improved harmonic coding scheme., Proc. IEEEICASSP, Vol. 9 (1984) pp. 437–440

24.15 E. Moulines, J. Laroche: Techniques for pitch-scaleand time-scale transformation of speech. Part I.Non parametric methods, Speech Commun. 16,175–205 (1995)

24.16 E. Moulines, F. Charpentier: Pitch-synchronouswaveform processing techniques for text-to-speech synthesis using diphones, Speech Commun.9, 453–467 (1990)

24.17 S. Roucos, A. Wilgus: High-quality time-scalemodification of speech, Proc. IEEE ICASSP (1985)pp. 493–496

24.18 W. Verhelst, M. Roelands: An overlap-add tech-nique based on waveform similarity (wsola)for high quality time-scale modification ofspeech, Proc. IEEE ICASSP, Vol. 2 (1993) pp. 554–557

24.19 M. Abe, S. Nakamura, K. Shikano, H. Kuwabara:Voice conversion through vector quantization,Proc. IEEE ICASSP, Vol. 1 (1988) pp. 655–658

24.20 K. Shikano, K. Lee, R. Reddy: Speaker adapta-tion through vector quantization, Proc. IEEE ICASSP,Vol. 11 (1986) pp. 2643–2646

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Voice Transformation References 503

24.21 H. Kuwabara, Y. Sagisaka: Acoustic characteristicsof speaker individuality: Control and conversion,Speech Commun. 16(2), 165–173 (1995)

24.22 N. Iwahashi, Y. Sagisaka: Speech spectrum trans-formation based on speaker interpolation, Proc.IEEE ICASSP, Vol. 1 (1994) pp. 461–464

24.23 H. Valbret, E. Moulines, J. Tubach: Voice transfor-mation using PSOLA techinques, Speech Commun.11(2-3), 175–187 (1992)

24.24 H. Mizuno, M. Abe: Voice conversion algorithmbased on piecewise linear conversion rule offormant frequency and spectrum tilt, Speech Com-mun. 16, 153–164 (1995)

24.25 Y. Stylianou, O. Cappé, E. Moulines: Statisticalmethods for voice quality transformation, Proc.Eurospeech, Vol. 95 (1995) pp. 447–450

24.26 Y. Stylianou, O. Cappé, E. Moulines: Continuousprobabilistic transform for voice conversion, IEEETrans. Speech Audio Process. 6(2), 131–142 (1998)

24.27 A. Kain, M. Macon: Spectral voice conversion fortext-to-speech synthesis, Proc. IEEE ICASSP, Vol. 5(1998) pp. 285–288

24.28 A. Mouchtaris, J.V. derSpiegel, P. Mueller: Nonparallel training for voice conversion based on aparameter adaptation, IEEE Trans. Audio SpeechLanguage Process. 14(3), 952–963 (2006)

24.29 D. Suendermann, H. Hoege, A. Bonafonte, H. Ney,A. Black, S. Narayanan: Text-independent voiceconversion based on unit selection, Proc. IEEEICASSP, Vol. 1 (2006) pp. 81–84

24.30 R.O. Duda, P.E. Hart: Pattern Classification andScene Analysis (Wiley, New York 1973)

24.31 R.C. Rose, D.A. Reynolds: Text independent speakeridentification using automatic acoustic segmenta-tion, Proc. IEEE ICASSP, Vol. 1 (1990) pp. 293–296

24.32 A.P. Dempster, N.M. Laird, D.B. Rubin: Maximumlikelihood from incomplete data via the EM algo-rithm (methodological), J. R. Stat. Soc. B 39(1), 1–22(1977)

24.33 A.P. Dempster, N.M. Laird, D.B. Rubin: Maximumlikelihood from incomplete data via the EM algo-rithm (discussion), J. R. Stat. Soc. B 39(1), 22–38(1977)

24.34 L.R. Rabiner, B.-H. Juang: Fundamentals of SpeechRecognition (Prentice Hall, Upper Saddle River1993)

24.35 S.M. Kay: Fundamentals of Statistical Signal Pro-cessing: Estimation Theory, PH Signal Process. Ser.(Prentice Hall, Upper Saddle River 1993)

24.36 C. Chatfield, A.J. Collins: Introduction to Multivari-ate Analysis (Chapman Hall, Boca Raton 1980)

24.37 Y. Stylianou: Harmonic plus Noise Models forSpeech, Combined with Statistical Methods, forSpeech and Speaker Modification, Ph.D. Thesis(Ecole Nationale Supèrieure des Télécommunica-tions, Paris 1996)

24.38 T.F. Quatieri: Discrete-Time Speech Signal Process-ing (Prentice Hall, Englewood Cliffs 2002)

24.39 J.M. Pickett: The Sounds of Speech Communication(Pro-Ed, Austin 1980)

24.40 C. Jankowski: Fine Structure Features for SpeakerIdentification, Ph.D. Thesis (Massachusetts Insti-tute of Technology, Cambridge 1996)

24.41 D. Kapilow, Y. Stylianou, J. Schroeter: Detection ofnon-stationarity in speech signals and its appli-cation to time-scaling, Proc. Eurospeech, Vol. 99(1999) pp. 2307–2310

24.42 A. Kain, Y. Stylianou: Stochastic modeling of spec-tral adjustment for high quality pitch modification,Proc. IEEE ICASSP, Vol. 2 (2000) pp. 949–952

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Voice Transf 24. Voice Transformation o - habla.dc.uba.arhabla.dc.uba.ar/gravano/ith-2014/presentaciones/Stylianou_2008.pdf · 489 Voice Transf 24. Voice Transformation o Y. Stylianou

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