Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Microsound
Sparse and structured decompositions of signals with the molecular matching pursuit
IEEE Transactions on Audio, Speech, and Language Processing
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As a combination of time and frequency modeling,sparse atomic representation provides a means for effective and interesting time-frequency modifications of signals. A drawback is the intensive computation required to find the representation. New tools however greatly speed the process and facilitate experimentation with real signals. We have experimented with the modification of audio signals, specifically pitch-shifting, using sparse atomic approximations found by the matching pursuit algorithm. A na ïve approach,where phase is not taken into account, produces surprisingly good results for signals having soft or no transients.An artifact sounding like amplitude modulation appears however, which we show can be reduced by a phase optimization algorithm. Finally we discuss a more sophisticated approach to time-frequency modifications in general using atomic representations.