We develop new time-frequency analytic techniques which facilitate the detection of a person's heart and breath rates from the Doppler shift the movement of their body induces in a terahertz radar signal. One straightforward means of doing such an analysis is the following: take the spectrogram of the ridgeline of the spectrogram of the radar signal. Instead of following this approach exactly, 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 traditional problems with ridgelines, such as jump discontinuities and overquantization. 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.