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

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):

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

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)

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

References