# Differential Entropy Analysis of the Acoustic Characteristics of a Biomimetic Dynamic Sonar Emitter

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## Abstract

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## 1. Introduction

## 2. Results

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Experimental Setup

#### 4.2. Signal Preprocessing

#### 4.3. Differential Entropy Estimation

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental design and methods for establishing 3-dimensional acoustic emission characteristics. A flexible biomimetic noseleaf model (

**a**) was simplified with five main shape features from the noseleaf of Pratt’s roundleaf bats (

**b**). A biomimetic dynamic sonar emitter (

**c**) assembled with actuation and ultrasound generation systems was mounted on a pain-tilt to scan over 1040 direction samples (

**d**). Anterior and posterior portions of the noseleaf baffle were actuated by stepper motors according to the input motion control signal (dark gray dashed line in (

**e**)). The displacement of the posterior leaf (dark gray solid line in (

**e**)) was reconstructed by a pair of high-speed video cameras. An example of time-domain signal (light gray shadow in (

**e**)) at 55 kHz was extracted from the raw received signal by a bandpass filter. The 3D acoustic characteristics were established by combining the time series of envelope amplitudes (black solid line in (

**e**)) at each fixed direction and frequency. (

**f**) Examples of beampatterns as a function of time and frequency.

**Figure 2.**Examples of differential entropy estimates taken over the dimensions of time (

**a**), frequency (

**b**), and direction (

**c**), respectively, for a set of fixed values along the remaining two dimensions.

**Figure 3.**Probability density function estimates for root-mean-square values of the amplitudes (

**a**) and differential entropy (

**b**) over time (black lines), frequency (dark gray lines), and direction (light gray lines) dimension, respectively. (

**c**) Correlation between differential entropy and standard deviation over the dimensions of time (light gray symbols, $r=0.78$, $n=1040\times 1101$), frequency (medium gray symbols, $r=0.86$, $n=1040\times 1084$), and direction (black symbols, $r=0.96$, $n=1084\times 1101$).

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**MDPI and ACS Style**

Yang, L.; Müller, R.
Differential Entropy Analysis of the Acoustic Characteristics of a Biomimetic Dynamic Sonar Emitter. *Symmetry* **2020**, *12*, 391.
https://doi.org/10.3390/sym12030391

**AMA Style**

Yang L, Müller R.
Differential Entropy Analysis of the Acoustic Characteristics of a Biomimetic Dynamic Sonar Emitter. *Symmetry*. 2020; 12(3):391.
https://doi.org/10.3390/sym12030391

**Chicago/Turabian Style**

Yang, Luhui, and Rolf Müller.
2020. "Differential Entropy Analysis of the Acoustic Characteristics of a Biomimetic Dynamic Sonar Emitter" *Symmetry* 12, no. 3: 391.
https://doi.org/10.3390/sym12030391