# Acoustic reflectometry using Gaussian-modulated sinusoidal waves and the Ware-Aki algorithm

#### Abstract

Acoustic reflectometry, a non invasive technique, consists of solving, the inverse problem of estimating the cross sectional area as function of the distance of a cylindrical cavity by impacting an audible acoustic pulse of high amplitude and short duration, and analyzing the reflected wave. The technique has been applied in Biomedical Engineering to estimate both the area of a human upper airway and the patency of endotracheal tubes as a function of distance. Several ways have been tested to improve the quality of an acoustic pulse and different algorithms have been tested to reduce the losses. However, an acoustic pulse is difficult to generate with a broad frequency bandwidth and the reconstruction algorithms require robust mathematical procedure to compensate the losses within the system. The solution of the inverse problem in this dissertation consists of sweeping the frequency bandwidth by using Gaussian-modulated sinusoidal packets. A long source tube is used not only to propagate and identify the acoustic waves generated, but also it is used to compute the frequency impulse response by using a least mean square algorithm. The Ware-Aki algorithm is recalled to compute the reflection coefficients, which are directly related with the bore profile. A computational model was developed to evaluate the quadratic error of several acoustic parameters used on acoustic reflectometry. The results obtained by the simulation model show that axial resolution depends on the frequency step size used to sweep a broad frequency bandwidth. The present study utilized an in vitro model that replaced a human upper airway to validate this method. It is based on a calibration of the reflectometer to compensate for the losses along the source tube. This work made of acoustic reflectometry a versatile technique, because the frequency response is obtained by using only one loudspeaker, and the signal-to-noise ratio is increased at high frequencies by using match filter. Therefore, the use of Gaussian-modulated sinusoidal waves and the Ware-Aki algorithm can be used to estimate a cylindrical cavity with an appropriate axial resolution.

#### Subject Area

Electrical engineering

#### Recommended Citation

Vazquez Ceron, Ernesto Rodrigo, "Acoustic reflectometry using Gaussian-modulated sinusoidal waves and the Ware-Aki algorithm" (2010). *ETD Collection for University of Texas, El Paso*. AAI3426872.

https://scholarworks.utep.edu/dissertations/AAI3426872