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Formant (Vowel) Synthesis

Module by: Ed Doering

Summary: Speech and singing contain a mixture of voiced and un-voiced sounds (sibilants like “s”). The spectrum of a voiced sound contains characteristic resonant peaks called formants caused by frequency shaping of the vocal tract. In this module, a formant synthesizer is developed and implemented in LabVIEW. The filter is implemented as a set of parallel two-pole resonators (bandpass filters) that filter a band-limited pulse source.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Table 1
LabVIEWq.png This module refers to LabVIEW, a software development environment that features a graphical programming language. Please see the LabVIEW QuickStart Guide module for tutorials and documentation that will help you:
• Apply LabVIEW to Audio Signal Processing
• Get started with LabVIEW
• Obtain a fully-functional evaluation edition of LabVIEW

Introduction

Speech and singing contain a mixture of voiced and un-voiced sounds. Voiced sounds associate with the vowel portions of words, while unvoiced sounds are produced when uttering consonants like "s." The spectrum of a voiced sound contains characteristic resonant peaks called formants, and are the result of frequency shaping produced by the vocal tract (mouth as well as nasal passage), a complex time-varying resonant cavity.

In this module, a formant synthesizer is developed and implemented in LabVIEW. The subtractive synthesis model of a wideband excitation source shaped by a digital filter is applied here. The filter is implemented as a set of parallel two-pole resonators (bandpass filters) that filter a band-limited pulse. Refer to the modules Subtractive Synthesis Concepts and Band-Limited Pulse Generator for more details.

Formant Synthesis Technique

The Figure 1 screencast video develops the general approach to formant synthesis:

Figure 1: [video] Formant synthesis technique
Figure 1 (sub_formants-technique.html)

The mathematics of the band-limited pulse generator and its LabVIEW implementation are presented in the module Band-Limited Pulse Generator.

The two-pole resonator is an IIR (infinite impulse response) digital filter defined by Equation 1 (see Moore in the "References" section for additional details):

H(z)=(1R) 1R z 2 12Rcosθ z 1 + R 2 z 2 H(z)=(1R) 1R z 2 12Rcosθ z 1 + R 2 z 2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacIcacaWG6bGaaiykaiabg2da9iaacIcacaaIXaGaeyOeI0IaamOuaiaacMcadaWcaaqaaiaaigdacqGHsislcaWGsbGaamOEamaaCaaaleqabaGaeyOeI0IaaGOmaaaaaOqaaiaaigdacqGHsislcaaIYaGaamOuaiGacogacaGGVbGaai4CaiabeI7aXjaadQhadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqGHRaWkcaWGsbWaaWbaaSqabeaacaaIYaaaaOGaamOEamaaCaaaleqabaGaeyOeI0IaaGOmaaaaaaaaaa@52CF@ (1)

where θ=2π ( f C / f S ) θ=2π ( f C / f S ) MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiUdeNaeyypa0JaaGOmaiabec8aWnaalyaabaGaaiikaiaadAgadaWgaaWcbaGaam4qaaqabaaakeaacaWGMbWaaSbaaSqaaiaadofaaeqaaaaakiaacMcaaaa@3FC1@ , R= e πB/ f S R= e πB/ f S MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiabg2da9iaadwgadaahaaWcbeqaaiabgkHiTiabec8aWjaadkeacaGGVaGaamOzamaaBaaameaacaWGtbaabeaaaaaaaa@3E43@ , f C f C MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBaaaleaacaWGdbaabeaaaaa@371A@ is the center frequency, B B MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaaaa@3602@ is the bandwidth, and f S f S MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBaaaleaacaWGdbaabeaaaaa@371A@ is the sampling frequency, all in units of Hz.

The Figure 2 screencast video shows how to create a subVI that implements the two-pole resonator.

Figure 2: [video] Implementing the two-pole resonator in LabVIEW
Figure 2 (sub_formants-twopole.html)

Formants for Selected Vowel Sounds

Peterson and Barney (see "References" section) have compiled a list of formant frequencies for common vowels in American English; refer to Figure 3:

Figure 3: Formant frequencies for common vowels in American English (from Peterson and Barney, 1952)
Figure 3 (sub_formants-voweltable.png)

Formant Synthesizer

The previous sections have laid out all of the pieces you need to create your own formant synthesizer. See if you can set up a LabVIEW VI that pulls the pieces together. The Figure 4 screencast video shows how your finished design might operate. The video also discusses how to choose the relative formant amplitudes and bandwidths, as well as the BLP source parameters.

Figure 4: [video] Formant synthesis LabVIEW VI
Figure 4 (sub_formants-formantsynth.html)

References

  • Moore, F.R., "Elements of Computer Music," Prentice-Hall, 1990, ISBN 0-13-252552-6.
  • Peterson, G.E., and H.L. Barney, "Control Methods Used in a Study of the Vowels," Journal of the Acoustical Society of America, vol. 24, 1952.

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