Time-frequency analysis: theory and applications
Time-frequency analysis: theory and applications
Efficient numerical methods in non-uniform sampling theory
Numerische Mathematik
Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type
Mathematics of Computation
On the Behavior of the Continuous-Time Spectrogram for Arbitrarily Narrow Windows
IEEE Transactions on Signal Processing
Robust speech recognition in noisy environments based on subband spectral centroid histograms
IEEE Transactions on Audio, Speech, and Language Processing
Computationally attractive reconstruction of bandlimited images from irregular samples
IEEE Transactions on Image Processing
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The spectral centroid of a signal is the curve whose value at any given time is the centroid of the corresponding constant-time cross section of the signal's spectrogram. A spectral centroid provides a noise-robust estimate of how the dominant frequency of a signal changes over time. As such, spectral centroids are an increasingly popular tool in several signal processing applications, such as speech processing. We provide a new, fast and accurate algorithm for the real-time computation of the spectral centroid of a discrete-time signal. In particular, by exploiting discrete Fourier transforms, we show how one can compute the spectral centroid of a signal without ever needing to explicitly compute the signal's spectrogram. We then apply spectral centroids to an emerging biometrics problem: to determine a person's heart and breath rates by measuring the Doppler shifts their body movements induce in a continuous wave radar signal. We apply our algorithm to real-world radar data, obtaining heart- and breath-rate estimates that compare well against ground truth.