Vocal resonances and broad band excitation

This site introduces a technique developed in this lab for measuring the resonances of the vocal tract quickly and non-invasively, during speech or singing. We use it as a research tool and have used it as a speech trainer. The software is now available for download for Mac (also get the fig file) and download for Windows. More information about it is given in a submitted paper, which will be linked here when published. Further details will also be added to this page. ( A downloadable and installable runtime component of MATLAB is available from mathworks. It is 2GB and so slow to download.)

Vocal tract resonance measurements:

The principal use of the device is in measuring vocal tract resonances. (For the differences between resonances and formants see here.) The 'ecological' way uses a microphone and small sound source located at the lower lip. It is also possible, with suitable calibrtion, to use this software for measuring acoustic impedance spectra, but we concentrate here on the 'ecological' application.

An acoustic current is synthesised to give high resolution frequency information over the frequency range of interest. We first calibrate the system by making a measurement of sound pressure just outside the lips, with the mouth closed (pclosed). We then inject the same acoustic current into the vocal tract in parallel with the external field and again measure the pressure at the lips (popen). The ratio γ = popen/pclosed then shows the frequencies of the tract resonances.

graph showing voice harmonics and resonances independently.
This measurement of a man speaking the vowel in 'heard' shows two superposed signals. The γ = popen/pclosed ratio is the broad band signal, and the arrows show the resonances R1, R2, R3, R4. The harmonics of the voice are a frequences fo, 2fo, 3fo etc, with the 8th harmonic and above being hidden by the broad band signal. Notice that the fifth harmonic (5fo) falls close to R2, which gives it a boost in amplitude. The resonance provides impedance matching between the high impedance of the glottis and the low impedance of the radiation field at the lips.
    The vocal tract behaves is an acoustic duct about 170 mm long, nearly closed by the vocal folds and open at the mouth. A cylinder, length L, closed at one end has resonances at f0 = v/4L , at 3f0, 5f0 etc, where v is the speed of sound. (See pipes and harmonics.) For such a cylinder the resonances would fall at frequencies of about 0.5, 1.5, 2.5, 3.5 and 4.5 kHz. The vocal tract shape varies as the lips and tongue are moved in speech. So here, while R1 and R4 fall close to the values for the cylinder, R2 is lower and R3 higher than for a cylinder.
From the broad band response we can determine the resonances of the vocal tract, independently of the speech signal. The resonant frequencies are interesting for fundamental acoustical phonetic research but, if we extract and display them immediately, they can be used to drive a cursor for speech training. This is how we do it in the real time version.

diagram showing how to extract vocal tract resonances in real time

Schematic diagram. (a) shows the spectrum of the speech signal alone. This male voice has harmonic partials spaced at the pitch frequency 126 Hz. (b) The injected signal has frequencies spaced at 5Hz, whose amplitudes are calibrated (in this case) using the radiation field outside the speaker's mouth. (c) The sum of the speech signal and the broad band signal (including the effects of the resonances) goes from the microphone to the analogue-digital converter. The speech signal is used to measure pitch and amplitude; then the harmonic components below 1kHz are removed. (d) The resonances are detected from the remaining interpolated signal. Similarly, the broadband signals may be removed to leave just the speech harmonics. In the version of the device used for speech training, the resonance frequencies were used to position the cursor on the vowel plane (see below). Notice that the signal:noise ratio in these figures is greater than in the preceding figure. This is a consequence of making the measurements rapidly.


For a report of a trial experiment using a prototype system as a language trainer, see our papers:

About the hardware

    Download the .stl file for the adaptor that matches a horn driver to the hose used as a source. (The design software we used is Blender and the 3d printer was a Cubicon plus, but this should be of little importance.) The larger end is clearance diameter so that plumbing tape can be used for a good seal.

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