#### Date of Award

6-3-2008

#### Document Type

Thesis

#### Degree Name

Master of Science

#### Department

Department of Mathematics and Statistics

#### First Advisor

Matthew Fickus, PhD

#### Abstract

We develop new time-frequency analytic techniques which facilitate the rapid detection of a person's heart and breath rates from the Doppler shift the movement of their body induces in a terahertz radar signal. In particular, the Doppler shift in the continuous radar return is proportional to the velocity of the person's body. Thus, a time-frequency analysis of the radar return will yield a velocity signal. This signal, in turn, may undergo a second time-frequency analysis to yield any periodic components of the velocity signal, which are often related to the heart and breath rates of the individual. One straightforward means of doing such an analysis is to take the spectrogram of the ridgeline of the spectrogram of the radar signal. Instead of exactly following this approach, we consider an alternate method in which the ridgeline of the radar signal's spectrogram is replaced with a signal computed from spectral centroids. By using spectral centroids, rather than the ridgeline, we produce a smooth signal that avoids some traditional problems with ridgelines, such as jump discontinuities and over-quantization. This new method for time-frequency analysis uses a Toeplitz matrix-based algorithm that has a fast Fourier transform-based implementation, and permits centroids of the vertical strips of the spectrogram of the radar signal to be computed without ever having to explicitly compute the spectrogram itself. This algorithm has a lower computational cost than the ridgeline method, and allows us to increase our frequency resolution. We conclude by testing these ideas on real-life data, successfully determining the heart and breath rates of a subject a distance of 10 meters from the radar aperture.

#### AFIT Designator

AFIT-GAM-ENC-08-05

#### DTIC Accession Number

ADA483261

#### Recommended Citation

Massar, Melody L., "Time-Frequency Analysis of Terahertz Radar Signals for Rapit Heart and Breath Rate Detection" (2008). *Theses and Dissertations*. 2662.

https://scholar.afit.edu/etd/2662