# Ultrasonic Signal Time-Expansion Using DAC Frequency Modulation

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- A sampled sinusoidal ultrasonic signal is time-expanded with the calculation of its spectrum.
- The process is generalized to a generic band-limited signal.

#### 2.1. Sinusoidal Input

#### 2.2. Extension to Passband Ultrasonic Signals

#### 2.3. Simulations Results

## 3. Experimental Results

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

DAC | digital-to-analog converter |

Ksps | kilo samples per second |

MDPI | Multidisciplinary Digital Publishing Institute |

## References

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**Figure 5.**Spectrum of the Time-Expanded of Gaussian ultrasonic pulse (orange) and Sinc Envelope (blue).

fo (KHz) | fs (KHz) | n | f_out (KHz) | |
---|---|---|---|---|

100 | 333.33 | 0 | 5 | |

100 | 333.33 | 1 | 11.66 | 21.66 |

100 | 333.33 | 2 | 28.33 | 38.33 |

100 | 333.33 | 3 | 44.99 | 54.99 |

100 | 333.33 | 4 | 61.66 | 71.66 |

fo (KHz) | fs (KHz) | n | f_out (KHz) | |
---|---|---|---|---|

100 | 333.3 | 0 | 5 | |

100 | 333.3 | 1 | 11.7 | 21.7 |

100 | 333.3 | 2 | 38.3 | 45.1 |

100 | 333.3 | 3 | 55.1 | 61.8 |

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**MDPI and ACS Style**

Rossi, M.; Frasca, M.
Ultrasonic Signal Time-Expansion Using DAC Frequency Modulation. *Vibration* **2023**, *6*, 466-476.
https://doi.org/10.3390/vibration6030029

**AMA Style**

Rossi M, Frasca M.
Ultrasonic Signal Time-Expansion Using DAC Frequency Modulation. *Vibration*. 2023; 6(3):466-476.
https://doi.org/10.3390/vibration6030029

**Chicago/Turabian Style**

Rossi, Massimiliano, and Marco Frasca.
2023. "Ultrasonic Signal Time-Expansion Using DAC Frequency Modulation" *Vibration* 6, no. 3: 466-476.
https://doi.org/10.3390/vibration6030029