A Snack Implementation and Tcl/Tk Interface to theFundamental Frequency Variation Spectrum Algorithm

Kornel Laskowski 1, Jens Edlund2

1 Language Technologies Institute, Carnegie Mellon University, Pittsburgh PA, USA2 KTH Speech, Music and Hearing, Stockholm, Swedenkornel@cs.cmu.edu, edlund@speech.kth.se

AbstractIntonation is an important aspect of vocal production, used for a variety of communicative needs. Its modeling is therefore crucial inmany speech understanding systems, particularly those requiring inference of speaker intent in real-time. However, the estimation ofpitch, traditionally the first step in intonation modeling, is computationally inconvenient in such scenarios. This is because it is often, andmost optimally, achieved only after speech segmentation and recognition.A consequence is that earlier speech processing components,in today’s state-of-the-art systems, lack intonation awareness by fiat; itis not known to what extent this circumscribes their performance.In the current work, we present a freely available implementation of an alternative to pitch estimation, namely the computation of thefundamental frequency variation (FFV) spectrum, which can be easilyemployed at any level within a speech processing system. It is ourhope that the implementation we describe aid in the understanding of this novel acoustic feature space, and that it facilitate its inclusion,as desired, in the front-end routines of speech recognition, dialog act recognition, and speaker recognition systems.

1. IntroductionIntonation is an important aspect of vocal production, usedfor a variety of communicative needs. Its estimationand modeling is therefore crucial to speech classificationand understanding systems. This is particularly true ofthose systems operating in real-time, in which inference ofspeaker intent should be achieved with low latency. At thepresent time, the overwhelming majority of such systemsreconstruct intonation contours from frame-level estimatesof pitch (F0), computed by a pitch-tracking component;these estimates are then normalized to eliminate absolute,speaker-dependent values.Due to its sensitivity to noise and voicing occlusions, pitchis computed and modeled onlyafter speech is segmentedand, often, also recognized. The resulting system flowmakes intonation contours unavailable to early processingcomponents, where they are likely to be at least as usefulas in downstream processing. It is therefore of some im-port that an instantaneous, frame-level characterizationofintonation in speech, available as early as speech detectionitself, be developed. Although pitch is visually appealing,the long-observation-time requirements for accurate pitchestimation do not recommend it as a basis for frame-levelmodeling.The fundamental frequency variation (FFV) spectrum, de-signed to address these concerns (Laskowski et al., 2008a),offers a computationally tractable alternative to character-izing intonation which obviates the need to first estimateabsolute pitch, and then to normalize it out its average.It is based on a simple observation, namely that the rateof change inF0, across two temporally adjacent framesof speech produced by the same speaker, can be inferredby finding the dilation factor required to optimally alignthe harmonic spacing in their magnitude frequency spectra.This can be achieved without knowledge of the frequencyscale (provided it is the same in both frames). Unfortu-nately, FFV processing entails a significant deviation fromtraditional, pitch-centered conceptualizations of intonation,

presenting a steep learning curve for researchers who maywish to use it in their work.This paper addresses the latter problem by presenting ourcurrent implementation of the FFV algorithm (briefly de-scribed in Section 3.) within a free, publicly available andcommonly used speech processing toolkit. The implemen-tation exposes, via a Tcl/Tk interface, the critical parame-ters driving the FFV spectrum computation. We describethese parameters, some of their effects, and their defaultsin Section 4.; Section 5. discusses several possibilities formodeling the spectrum. In Section 6., we present a graph-ical comparison between the spectrum and the output ofa popular pitch tracker (Talkin, 1995), for singing voice.Before concluding, we enumerate in Section 7. several ap-plications in which FFV processing has been shown to beuseful. We expect that this evidence, collectively, may fa-cilitate the inclusion of FFV feature computation in generalspeech analysis software, such as WaveSurfer (Sjolanderand Beskow, 2000) and Praat (van Heuven, 2001), as wellas in the front-ends of dedicated speech understanding sys-tems.

2. The Snack Sound ToolkitThe Snack Sound Toolkit (Sjolander, 2001) is developedand maintained by Kare Sjolander. It is designed to beused with a scripting language, and currently has bindingsfor Tcl/Tk (Ousterhout, 2008), Python (van Rossum, 2008)and Ruby (Matsumoto, 2008). It ships with the standardActiveStatec© distributions of Tcl and Python. Snack al-lows users to create multi-platform audio applications withjust a few lines of code, with commands for basic soundhandling and primitives for waveform and spectrogram vi-sualization. Snack supports WAV, AU, AIFF, MP3, CSL,SD, SMP, and NIST/Sphere file formats. The toolkit is de-signed to be extensible, and new commands, filters, andsound file formats can be added using the Snack C li-brary. The freely available Open Source tool WaveSurfer(Sjolander and Beskow, 2000) provides a graphical user in-

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terface and visualizations for the functionality in Snack;italso can be extended with new custom plug-ins, and be em-bedded in other applications.

3. The FFV Spectrum

The fundamental frequency variation spectrum is a recentlyintroduced representation (Laskowski et al., 2008a) whichcaptures instantaneous, per-frame variation in fundamen-tal frequency. The algorithm relies on the comparison ofthe frequency magnitude spectraFL andFR of the left andright halves of an analysis frame, respectively. The compar-ison is implemented as a dot product following frequencydilation by a factorρ of one ofFL or FR. The dot prod-uct, expressed asg (ρ), yields a continuous spectrum whencomputed over a range ofρ; an example is shown in Fig-ure 1.

−2 −1 0 +1 +20

0.5

1

Figure 1: The FFV spectrum for a randomly chosen voicedspeech frame; the magnitude ofg (ρ), shown along they-axis, is a function of the dilation factorρ shown along thex-axis in octaves per 0.008 s (the temporal separation betweenthe maxima of the two window functions used in computingFL andFR).

FFV processing offers several advantages over other repre-sentations of variation in fundamental frequency; most no-tably, it is alocal estimate,independentof the absolute fun-damental frequency, and it does not require dynamic pro-gramming as employed in most pitch tracking applications.This makes the representation directly amenable to hiddenMarkov modeling (HMMing). Examples of successful us-age in this way (cf. Section 7.) include speaker change pre-diction in dialogue systems, speaker recognition, and dialogact classification in meeting data.

4. The Snack FFV Interface

4.1. Synopsis

Given the path name$file of a file containing a snippetof audio, the following Tcl code frames and prints out theFFV spectrum for each frame:

snack::sound ss read $fileforeach line [s ffv

-tFra tfra -tSep tsep

-tInt tint -tExt text

-winShapeInt < string-literal >-winShapeExt < string-literal >-Ng Ng -tSepRef t

refsep

-filterbank < string-literal >] {

puts $line}

The positive real-valued parameterstFra, tSep, tInt,tExt, tSepRef, the positive integer-valued parameterNg, and the string-valued parameterswinShapeInt,winShapeExt, and filterbank in the above com-mand are described individually in the following subsec-tions.

4.2. Framing Parameters

As mentioned in Section 3., the FFV algorithm relies on anestimate of the frequency magnitude spectra of the left andright halves of each analysis frame. These spectra are com-puted using two asymmetrical analysis windows, placedsymmetrically about the frame’s center, as shown in Fig-ure 2. Parameters governing window shape can be modi-fied from their default values using arguments to the Snackffv function:

t0

tint

texttext

tsep

Figure 2: Relative placement of the left and right windowfunctions,hL andhR, in a single analysis frame of dura-tion 2text + tsep centered on instantt0. The parameterstint, text, andtsep, all in seconds, are as described in thetext. Successive frames are placed such that their respec-tive instantst0 aretfra seconds apart, not shown.

-tFra The frame step between successive analysisframes, in seconds; the default value is 0.008.

-tSep The temporal separation between the maxima ofthe left and right window functions in seconds; the de-fault value is 0.014.

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-tInt The temporal extent of the left and right windowfunctions towards the center of the analysis frame, inseconds; the default value is 0.011.

-tExt The temporal extent of the left and right windowfunctions away from the center of the analysis frame,in seconds; the default value is 0.009.

-winShapeInt The shape of the left and right windowfunctions from their maximum towards the center ofthe analysis frame; currently implemented alternativesincludeHamming and Hann. The default value isHann.

-winShapeExt The shape of the left and right windowfunctions from their maximum away from the centerof the analysis frame; currently implemented alterna-tives includeHamming andHann. The default valueis Hamming.

4.3. Discretization Parameters

FFV spectra such as that shown in Figure 1 are continuous;their discretization requires a specification of a samplingfrequency and range of interest. This is achieved by modi-fying the parametersNg andtSepRef:

-Ng An even integer-valued parameter governing thenumber of values ofg (ρ) which are to be computed,at equi-spaced intervals∆ρ (described below).Ng/2 isthe number ofg (ρ) values computed forρ < 0 and thenumber ofg (ρ) values computed forρ > 0; g (0) isalways computed, for a total number ofNg + 1 valuesof g (ρ). The default value ofNg is 512.

-tSepRef A positive real-valued parameter, expressed inseconds, governing the separation∆ρ between succes-sive values ofρ at whichg (ρ) is sampled,

∆ρ =4

Ng

tsep

trefsep

. (1)

The default value is 0.008.

4.4. Filterbank Specification

As with other signal representations in speech processing,estimates of the FFV spectrum can be passed through asmoothing filterbank to improve the robustness of down-stream modeling. Snack’s defaultffv filterbank can bereplaced by user-specified variants as desired, using thefilterbank parameter.

-filterBank Allows specification of a filterbank. Thecurrently implemented alternatives includeNONE,DEFAULT, andfileName, wherefileNamespecifies thepath name of a file containing a filterbank structuredescription. The default value isDEFAULT, corre-sponding to a filterbank ofNf = 7 filters defined asfollows (the default filters are indexed by the integers{−3,−2,−1, 0,+1,+2,+3} rather than{1, . . . ,Nf}

for convenience):

f−3 [i] =

{

1, if 117 ≤ i ≤ 1390, otherwise

(2)

f−2 [i] =

1, if 246 ≤ i ≤ 2501/2 if i = 245 or i = 2510, otherwise

(3)

f−1 [i] =

1, if 250 ≤ i ≤ 2541/2 if i = 249 or i = 2550, otherwise

(4)

f0 [i] =

1, if 255 ≤ i ≤ 2571/2 if i = 254 or i = 2580, otherwise

(5)

f+1 [i] =

1, if 258 ≤ i ≤ 2621/2 if i = 257 or i = 2630, otherwise

(6)

f+2 [i] =

1, if 262 ≤ i ≤ 2661/2 if i = 261 or i = 2670, otherwise

(7)

f+3 [i] =

{

1, if 373 ≤ i ≤ 3950, otherwise

(8)

Source domain filter limits must lie in[0, Ng]. Afilterbank value ofNONE will output all Ng + 1values ofg (ρ).

4.5. Error Handling

Invalid parameter values, as well as errors due to a miss-ing or a mis-formatted filterbank specification file (whensuch is specified), are posted as exceptions by returning theTCL ERROR error code to the Tcl interpreter.

5. Modeling Alternatives

We list several possible ways in which the informationavailable in the FFV representation may be modeled.

5.1. Peak Localization and Tracking

The value ofg(ρ) at ρ is the cosine distance between themagnitude frequency spectraFL andFR in each analysisframe, following frequency dilation byρ. Whenρ < 0,it is the left-half spectrumFL which is frequency-dilatedby 2+ρ; whenρ > 0 is positive, the right spectrumFR isfrequency-dilated by2−ρ. The cosine distance is computedover a sub-range of the frequencies spanned by the originalFL andFR because, after dilation,FL andFR differ indomain extent.This interpretation ofg(ρ) recommends an obvious appli-cation. For voiced frames in which only one person is vo-calizing, we can localize the peak in the spectrum,

ρ∗ = arg maxρ

g (ρ) . (9)

If desired, the peak can be tracked from frame to frame,using a dynamic programming approach such as that foundin most pitch detection algorithms.

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5.2. Density Modeling and Estimation

In contrast to localizing and optionally tracking the supre-mum ofg(ρ), we can model the entire FFV spectrum, withor without a filterbank. Mathematically, this is similar tomodeling the magnitude frequency spectrum or Mel filter-bank filter responses, instead of formant center frequen-cies (which correspond toρ∗ in this analogy). The filter-bank described in Section 4.4. reduces the dimensionalityof the feature space, and improves robustness by averag-ing g (ρ) over perceptually similar rates of change in fun-damental frequency. However, the outputs of the defaultfilterbank are correlated, and mixture modeling may bene-fit from decorrelation prior to model estimation. This hasbeen shown to be the case in all applications in which FFVspectra have been employed (cf. Section 7.). Decorrelation,if desired, needs to be performed externally to Snack’sffvfunction.

5.3. FFV Modulation Spectrum

Finally, a method that is promising but has not been previ-ously explored is the computation of the modulation spec-trum over the FFV representation. The magnitude mod-ulation spectrum characterizes the frequencies with whichspecific rates of change in fundamental frequency appear.For example, it may reveal that increases in pitch of 1 oc-tave per second (computed for a particular analysis framesize) are observed once per second (see Section 6.2.).

6. An Example: Singing VoiceWe now present several graphical examples of the Snackffv output, and a comparison with the output of the SnackESPS pitch tracker (Talkin, 1995). We do so for singingvoice (Lindblom and Sundberg, 2005), for three reasons.First, the application of FFV processing to singing voicehas not been previously explored, and the current work pro-vides a convenient opportunity to do so. Second, moreimportantly, singing involves long stretches uninterruptedby an absence of voicing, allowing us to ignore what hap-pens at the onset and offset of voicing. This is importantwhen comparing pitch tracker toffv output because thetwo methods behave differently in these environments; inparticular, the output of a pitch tracker is numerically unde-fined in unvoiced regions. Finally, demonstration of singingvoice is easy to grasp, especially visually, and transcendspotentially language- and culture-dependent definitions ofcontours which are considered prosodically meaningful.

6.1. Glissando

We begin with an example of glissando (or portamento), inwhich the voice “slides” across a range of pitches. Our glis-sando recording was made by a professional female vocal-ist in a home environment on a laptop; it was downsampledfrom 44.1 kHz to 16 kHz prior to processing. The output ofthe SnackESPS pitch tracker, invoked using the Tcl com-mand

s pitch -method ESPS-minpitch 60-maxpitch 1000-framelength 0.008-windowlength 0.0075

is shown in Figure 3(a). To the right of panel 3(a), inpanel 3(b), we show the slopep [t] of the pitch curvep [t],in octaves per second,

p [t] =1

tsep

log2

p [t + tsep/2tfra]

p [t − tsep/2tfra]. (10)

As can be seen in the Snackpitch syntax above,tfra, theframe step, is 0.008 s; we have chosen to estimatep [t] inEquation 10 over intervals oftsep = 0.112 s. (Division bytsep in Equation 10 yields rates in octaves per second ratherthan in octaves pertsep seconds).The graphical result in Figure 3(b) can be directly com-pared toffv output. In Snack, we invoke

s ffv -tFra 0.008 -tSep 0.112-tInt 0.088 -tExt 0.072-filterbank NONE

using the same parameter values fortFra (tfra) andtSep(tsep) as are used in Equation 10 (namely,tfra = 0.008 sandtsep = 0.112 s; the values fortInt andtExt are theirdefault values scaled by a factor of 8, which is the ratio oftsep = 0.112 s to its default value oftsep = 0.014 s). Thisleads toNg +1 = 513 values ofg (ρ) per frame; we displaya contour plot of only the 23 values for each frame, centeredon ρ = 0, in Figure 3(c). As can be seen, the agreementwith Figure 3(b) is very high; differences iny-value are dueto the fact that the FFV algorithm computes variation inF0

using windows oftint + text = 0.160 s without dynamicprogramming, rather than over windows of 0.0075 ms withdynamic programming.

6.2. A Scale

Our second example is an 8-note scale, from the same vo-calist. We show the corresponding diagrams in Figure 4.All Snack commands used the same syntax as describedearlier. As can be seen in panel (b) of the figure, the slopep [t] of the ESPS pitch trajectory indicates seven instantsof fast change, corresponding to inter-note transition. Themaxima in Figure 4(c) follow an almost identical trajectory,as in our example of glissando in the previous section.We also show, in Figure 4(d), the modulation spectrum ofthe FFV spectrum, computed using a Hamming windowover 256 values ofg (ρ) at fixedρ, for all values ofρ shownin panel (c). The modulation spectrum indicates how fre-quently specific ratesρ of F0 variation (along they-axis)appear, expressed in Hertz along thex-axis. As the dark-est region in panel (d) suggests, rates of approximately+1octave per second (along they-axis), corresponding to notetransitions, appear at a rate of just over 1 Hz (along thex-axis). The remaining modulation frequencies, for positiverates ofF0 change, are harmonics of this 1 Hz frequency.

6.3. A Scale with Vibrato

Finally, we show a similar scale sung by the same vocal-ist, this time with vibrato, in Figure 5. This is an effect ofsmall-scaleF0 variation, superimposed on the underlyingnote. As for our previous two examples,F0 variation com-puted from pitch tracker output, in Figure 5(b), exhibits thesame features as that expressed directly by theffv output(Figure 5(c)).

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−1

−0.5

0

0.5

1

(a) (b)

0 1 2 3 4

−1

−0.5

0

0.5

1

(c)

Figure 3: Glissando. Clockwise from the upper left: (a)p [t], the output of a pitch tracker, in absolute frequency along they-axis, as a function of time in seconds along thex-axis. (b)p [t], computed fromp [t] using Equation 10, in octaves persecond along they-axis, as a function of time in seconds along thex-axis. (c) Bird’s eye view of consecutive FFV spectragt (ρ), with timet in seconds along thex-axis, and rate ofF0 variation in octaves per second along they-axis; darker shadesof gray indicate larger magnitudes ofgt (ρ).

The modulation spectrum in Figure 5(d) indicates that ratesof F0 change in the range(+0.5,+1.0) octaves per secondappear at a frequency of just over 1 Hz, as observed also inFigure 4(d). However, in addition, there is a dark patch atρ values of approximately±0.5 octaves per second, whichappears at the much higher modulation frequency of 3.5 Hz.This up and down change, symmetric aboutρ = 0 and dis-tinct from the mostly positive rates of change at approxi-mately 1 Hz, is due to vibrato.

7. Applications in Automatic SpeechProcessing

FFV processing has been applied to a number of tasks inspeech understanding, and in a limited few cases a com-parison has been made with information available from astandard pitch trajectory. It is important to note, how-ever, that the computational flexibility afforded by adopt-ing FFV features cannot be duplicated when using their

pitch-trajectory-derived counterparts. This section enumer-ates several applications in which FFV processing has beenshown to be beneficial and/or enabling in that regard.

7.1. Text-Independent Speaker Change Prediction

Speaker change prediction is the task of deciding whether acurrently vocalizing speaker is signaling the intent to con-tinue, following an incipient pause. It is an important func-tionality in dialogue systems which aim to exhibit human-like response times, avoiding long hold-over waits beforeinitiating a turn (Edlund and Heldner, 2005). From a sys-tem design perspective, real-time speaker change predictionwould ideally be incorporated into speech activity detec-tion; this calls for frame-level acoustic features characteriz-ing instantaneous intonation sub-phrases.The FFV representation was designed primarily with thistask in mind, and was tested (Laskowski et al., 2008a) onthe Swedish Map Task Corpus (Helgason, 2006). Graph-

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5 10 15 20

−1

−0.5

0

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1

0 1 2 3 4 5 6

−1

−0.5

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(d) (c)

Figure 4: A scale. Clockwise from the upper left: (a)p [t], the output of a pitch tracker; (b)p [t], change in pitch computedfrom p [t]; (c) consecutive FFV spectragt (ρ); axes as in Figure 3. (d) Modulation spectrum ofgt (ρ) for specific values ofratesρ of F0 variation, shown along they-axis as for panel (c); modulation frequency shown alongx-axis in Hertz; darkershades of gray indicate larger magnitudes.

ical depiction of what HMMs learn for this task, namelythat speakers employ predominantly flat intonation con-tours to signal a desire to continue speaking, was shownin (Laskowski et al., 2008b). In (Heldner et al., 2008),it was additionally shown that intonation contours prior tospeaker change differ as a function of speaker role; instruc-tion givers employ more falls than rises, whilefollowersuse the opposite strategy. Finally, (Laskowski et al., 2008c)considered several refinements to the FFV representationfor the speaker change prediction task.

7.2. Text-Independent Dialogue Act Recognition

The FFV representation has also been applied in multi-party conversational settings (Laskowski et al., 2009a), ini-tially to detect floor mechanism dialog acts in the ICSIMeeting Corpus (Janin et al., 2003). We reported thatfloorholdersand holds, signaling floor reservation (and there-fore quite similar to the phenomena in Section 7.1.), canbe separated from all other dialog act types with a dis-

crimination of 70.6 to 72.2%. FFV model analysis re-vealed that talkspurts implementing these dialog acts areinitiated with flat intonation contours, and terminated withslower speech. Several modifications, and augmentationwith other prosodic features, are presented in (Laskowskiet al., 2009b).

Most recently, the acoustic prosodic vector defined in(Laskowski et al., 2009b) has been implemented ina full-scale text-independent HMM dialog act decoder(Laskowski and Shriberg, 2010), which segments and clas-sifies audio into 8 types of dialog acts, with 3 types of dia-log act termination. The decoder operates without relianceon word boundaries, typically used for inferring models ofintonation, and is therefore deployable in privacy-sensitivesettings in which spectral envelopes may not be computed.For several dialog act types and termination types, its per-formance approaches that of a contrastive lexical systemwhich uses human-transcribed words.

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(d) (c)

Figure 5: A scale with vibrato. Clockwise from the upper left: (a) p [t], the output of a pitch tracker; (b)p [t], change inpitch computed fromp [t]; (c) consecutive FFV spectragt (ρ); (d) modulation spectrum ofgt (ρ); axes as in Figure 4.

7.3. Pitch Detection

An approach which appears conceptually identical to FFVprocessing and which may be computationally quite similarwas proposed for the purposes of improving pitch estima-tion in (Martin, 2008). Harmonic similarity between adja-cent spectra was shown to benefit pitch tracking in severalexamples of utterances with low signal-to-noise ratios.

7.4. Text-Independent Speaker Recognition

Finally, the FFV representation has also been shown toaid in the task of speaker recognition, in both nearfield(Laskowski and Jin, 2009) and farfield (Jin et al., 2010)scenarios. The temporal locality of the FFV features makespossible the construction of single-state Gaussian mixturemodel systems, such as those used with standard Mel-frequency cepstral coefficient systems. Because these sys-tems do not model trajectories, the observed improvementsin baseline speaker recognition system performance sug-gest that speakers differ in their preferences of rate ofF0

change, in addition to differences in absoluteF0 (whichFFV features, and therefore the systems in (Laskowski and

Jin, 2009; Jin et al., 2010), do not model).

8. ConclusionsWe have implemented and presented an interface to thecomputation of a novel representation of macro- and micro-intonation, the fundamental frequency variation (FFV)spectrum, within the popular and publicly available SnackSound Toolkit. The interface exposes the majority ofparameters governing FFV behavior, and our descriptionmakes it possible for speech researchers, practitioners andvoice pathologists to explore its potential use in their workwithout needing to understand and to re-implement the sig-nal processing internals.This work has also compared the FFV representation to theslope of theF0 trajectory, as estimated via a frequently usedpitch-tracking method. For relatively clean signals of ex-tended intervals of continuous voicing, the representationmaximum appears to contain the same information as dosuch slopes, over a wide range of magnitudes of rate ofF0

change. This fidelity is achieved without reliance on dy-namic programming, as employed in most pitch trackers,

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making FFV suitable for deployment in HMM decodingscenarios, such as speech recognition for tonal languages.

9. Acknowledgments

We would like to thank Marietta Fischesser and FlorianMetze for contributing their voices and recording expertise,as well as Timo Baumann who implemented the first stageof the FFV port to Snack.

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