Formant (Vowel) Synthesis 1.2 2007/09/28 10:11:00 GMT-5 2008/03/18 09:21:37.930 GMT-5 Ed Doering doering@rose-hulman.edu Ed Doering doering@rose-hulman.edu Erik B Luther erik.luther@ni.com Sam D. Shearman sam.shearman@ni.com band-limited pulse bandpass filter formant LabVIEW speech two-pole resonator vocal tract 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. 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 screencast video develops the general approach to formant synthesis:

[video] Formant synthesis technique

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 (see Moore in the "References" section for additional details): H(z)=(1−R) 1−R z −2 1−2Rcos⁡θ z −1 + R 2 z −2 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamisaiaacIcacaWG6bGaaiykaiabg2da9iaacIcacaaIXaGaeyOeI0IaamOuaiaacMcadaWcaaqaaiaaigdacqGHsislcaWGsbGaamOEamaaCaaaleqabaGaeyOeI0IaaGOmaaaaaOqaaiaaigdacqGHsislcaaIYaGaamOuaiGacogacaGGVbGaai4CaiabeI7aXjaadQhadaahaaWcbeqaaiabgkHiTiaaigdaaaGccqGHRaWkcaWGsbWaaWbaaSqabeaacaaIYaaaaOGaamOEamaaCaaaleqabaGaeyOeI0IaaGOmaaaaaaaaaa@52CF@ where 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 MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiabg2da9iaadwgadaahaaWcbeqaaiabgkHiTiabec8aWjaadkeacaGGVaGaamOzamaaBaaameaacaWGtbaabeaaaaaaaa@3E43@ , f C MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBaaaleaacaWGdbaabeaaaaa@371A@ is the center frequency, B MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYb1uaebbnrfifHhDYfgasaacH8YjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOqaaaa@3602@ is the bandwidth, and 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 screencast video shows how to create a subVI that implements the two-pole resonator.

[video] Implementing the two-pole resonator in LabVIEW

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 :

Formant frequencies for common vowels in American English (from Peterson and Barney, 1952)

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 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.

[video] Formant synthesis LabVIEW VI

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.