Ten lectures on wavelets
Signal representation using adaptive normalized Gaussian functions
Signal Processing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
The chirplet transform: physical considerations
IEEE Transactions on Signal Processing
Matching pursuits with time-frequency dictionaries
IEEE Transactions on Signal Processing
Time-frequency localization operators: a geometric phase space approach
IEEE Transactions on Information Theory
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Steady-motion-based Dopplerlet transform has been recently proposed and applied to the estimation of range and speed of moving sound source. In this paper, we develop a new Dopplerlet by introducing acceleration into its definition. Compared with the steady-motion-based Dopplerlet, the acceleration-based Dopplerlet can simultaneously exploit the information of range, speed and acceleration of a moving sound source and can better capture the true time-varying nature of the Doppler-like signals. Part I concerns the fundamentals of the proposed transform, while Part II is devoted to the implementations and applications.