# Micro-Doppler Signal Time-Frequency Algorithm Based on STFRFT

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## Abstract

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## 1. Introduction

## 2. STFRFT-Based Time-Frequency Analysis Technique

#### 2.1. Basic Principle of STFRFT

_{ω}have $N/2\pi m$ discrete sampling points in frequency domain. Substituting them into Equation (3) gets the following discrete form:

#### 2.2. Quick Order Selection for STFRFT Domain Transformation

#### 2.2.1. Order Selection

#### 2.2.2. Analysis of Frequency Resolution Error

#### 2.3. STFRFT’s Time-Frequency Analysis Capability of Time-Varying Signal

#### 2.3.1. One-Component Signal Analysis

#### 2.3.2. Computation Load Analysis

#### 2.3.3. Analysis of a Sinusoidal Signal

#### 2.3.4. Multi-Component Signal Analysis

## 3. Multi-Order STFRFT Time-Frequency Analysis Technique

## 4. Experiment Analysis

#### 4.1. Actual Signals from a Rocket Projectile Target

#### 4.2. Signals from a Real Model Helicopter Target

#### 4.3. Signals from the Bird Target

#### 4.4. Actual Fan Target Signals

#### 4.4.1. Dual-Blade Fan

#### 4.4.2. Three-Blade Fan

## 5. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Comparison of time-frequency analysis for different algorithms. (

**a**) Theoretical time-frequency relation results; (

**b**) STFT results; (

**c**) STFRFT results.

**Figure 5.**Analysis of sinusoidal time-frequency signal using different techniques. (

**a**) Original signal; (

**b**) Result of STFT processing; (

**c**) Result of STFRFT processing.

**Figure 6.**Micro-doppler time-frequency spectrum for two-blade helicopter. (

**a**) Theoretical time-frequency relation results; (

**b**) STFT results; (

**c**) STFRFT results.

**Figure 7.**Micro-doppler time-frequency spectrum for three-blade helicopter. (

**a**) Theoretical time-frequency relation results; (

**b**) STFT results; (

**c**) STFRFT results.

**Figure 9.**Comparison of STFT and STFRFT analysis results. (

**a**) STFT results; (

**b**) STFRFT (p = 0.93) results; (

**c**) STFRFT (p = 1.05) results; (

**d**) STFRFT results after comprehensive processing.

**Figure 10.**Comparisons of STFT and STFRFT local time-frequency analysis results. (

**a**) STFT; (

**b**) STFRFT.

**Figure 12.**Time-frequency analysis of helicopter echo signals. (

**a**) STFT results; (

**b**) STFRFT (p = 0.9) results; (

**c**) STFRFT (p = 1.1) results; (

**d**) STFRFT results after comprehensive processing.

**Figure 14.**Micro Doppler time-frequency analysis of flapping wings. (

**a**) Bird target model; (

**b**) STFT; (

**c**) STFRFT.

Time Point (s) | A(0) | B(0.2) | C(0.4) | D(0.6) | E(0.8) |
---|---|---|---|---|---|

Order of matching | 0.99 | 1.0 | 1.02 | 1.03 | 1.05 |

STFT | 1.0094 | 0.9520 | 1.1650 | 1.3858 | 1.9287 |

STFRFT | 0.9520 | ||||

Time-frequency resolution ratio | 1.1 | 1.1 | 1.4 | 1.7 | 2.3 |

SNR | Technique 1 | Technique 2 | Technique 3 | T2/T1 | T3/T1 |
---|---|---|---|---|---|

−4 dB | 18,0096 | 11,340 | 11,310 | 15.90 | 15.88 |

−6 dB | 18,0096 | 12,430 | 12,400 | 14.52 | 14.48 |

−8 dB | 18,0096 | 13,570 | 13,540 | 13.33 | 13.27 |

Parameter | Value |
---|---|

Carrier frequency | 3 GHz (continuous wave) |

Baseband sampling rate | 78 kHz |

Frame signal accumulation time | 72.1 ms |

Target | Rocket projectile |

Parameter | Time-Frequency Resolution Ratio |
---|---|

A | 1.27 |

B | 1.25 |

C | 1.23 |

Parameter | Value |
---|---|

Frequency | 674 MHz |

Baseband sampling rate | 5 kHz |

Signal accumulation time | 1 s |

Target | Align 750e |

Parameter | Value |
---|---|

Frequency | 3 GHz (continuous wave) |

Baseband sampling rate | 20 kHz |

Accumulation time | 0.15 s |

Target | Fan |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pang, C.; Han, Y.; Hou, H.; Liu, S.; Zhang, N. Micro-Doppler Signal Time-Frequency Algorithm Based on STFRFT. *Sensors* **2016**, *16*, 1559.
https://doi.org/10.3390/s16101559

**AMA Style**

Pang C, Han Y, Hou H, Liu S, Zhang N. Micro-Doppler Signal Time-Frequency Algorithm Based on STFRFT. *Sensors*. 2016; 16(10):1559.
https://doi.org/10.3390/s16101559

**Chicago/Turabian Style**

Pang, Cunsuo, Yan Han, Huiling Hou, Shengheng Liu, and Nan Zhang. 2016. "Micro-Doppler Signal Time-Frequency Algorithm Based on STFRFT" *Sensors* 16, no. 10: 1559.
https://doi.org/10.3390/s16101559