On the Apparent Propagation Speed in Transmission Line Matrix Uniform Grid Meshes

(a) Volume of interest (VOI) selection and (b) attribute setting to TLM nodes through the ModaVox interface

Numerical dispersion in TLM (adapted from Ref. [2])

TLM meshes for tubes with 12 mm in diameter and 170 mm in length. Numbers from 0 to 3 define the boundary value code at Sec. 4.1. (a) and (b) 2D open and closed tubes (c) and (d) 3D open and closed tubes.

Frequency response functions for the one-section tube models with 12 mm in diameter and 170 mm in length. TLM simulations considering 2D and 3D cases D = 1 and c = 343.1 m/s at Eq. (2). (a) Open tube and (b) closed tube.

Frequency response functions for the one-section tube models with 12 mm in diameter and 170 mm in length. The analytical resonance values are given according to Eqs. (3) and (4). Simulations considering c = 343.1 m/s at Eq. (2) with D = 2.238704168 and D = 3.35805625 for 2D and 3D TLM, respectively. (a) Open tube and (b) closed tube.

Two-tube concatenation for the /a/ vowel. Numbers from 0 to 3 define the boundary value code at Sec. 4.1. (a) 2D model and (b) 3D model.

Frequency response functions for the two-tube model representing the /a/ vowel. The analytical resonance values are the poles of Eq. (5). Simulations considering c = 343.1 m/s at Eq. (2) with (a) D = 2 and D = 2.238704168 for 2D TLM and (b) D = 3 and D = 3.35805625 for 3D TLM.

Human VT TLM meshes for the /a/ vowel. Numbers from 0 to 3 define the boundary value code at Sec. 4.1. The indexes of the chosen output nodes are shown (the source node values are also stored in output files). The sagittal plane shows a slice from the MRI sequence. (a) 2D mesh and (b) 3D mesh shown translucent.

3D TLM simulation on the /a/ vowel shaped VT mesh with piriform fossa considering soft walls, the GS as input and c = 343.1 m/s at Eq. (2) with D = 3.35805625. (a) Time-domain output signal, (b) zoom in the segment of (a) from 0.3 to 0.4 s, and (c) FFT comparison (human voice versus TLM).

A filter based on the frequency response of Fig. 12(b) is applied to the TLM simulation output signal of Fig. 13(a). Applying this filter to the GS of Fig. 12(a) and using it as input in a new simulation at the human 3D VT mesh gives the same result. (a) Time-domain signal in the 0 to 0.2 s interval and (b) FFT comparison (human voice versus TLM).

(a) Glottal sound after average removal and amplitude enhancement and (b) frequency envelope of the glottal sound (note the harmonic reduction ratio of −4 dB/Oct)

2D TLM simulation on the /a/ vowel shaped VT mesh considering soft walls, the signal at Eq. (1) as input and c = 343.1 m/s at Eq. (2) with D = 2.23870416. (a) Time-domain output signal and (b) FFT comparison (human voice versus TLM).

FFT plots (with versus without piriform fossa) for the 3D TLM simulation on the /a/ vowel shaped human VT mesh considering soft walls, the signal at Eq. (1) as input and c = 343.1 m/s at Eq. (2) with D = 3.35805625. (a) 4–6 kHz range and (b) 6–10 kHz range.

3D TLM simulation on the /a/ vowel shaped VT meshes considering soft walls, the signal at Eq. (1) as input and c = 343.1 m/s at Eq. (2) with D = 3.35805625 (a) and (b) time-domain output signal, (c) and (d) FFT comparison (human voice versus TLM), (a) and (c) mesh with piriform fossa, (b) and (d) mesh without piriform fossa.