A linear programming approach to the tracking of partials
This work addresses a specific signal processing problem for audio or communication applications, but it is incremental as it builds on existing tracking methods.
The paper tackles the problem of tracking sinusoidal chirps by proposing a linear programming approach, which outperforms the classical McAulay and Quatieri algorithm in high noise levels with lower complexity.
A new approach to the tracking of sinusoidal chirps using linear programming is proposed. It is demonstrated that the classical algorithm of McAulay and Quatieri is greedy and exhibits exponential complexity for long searches, while approaches based on the Viterbi algorithm exhibit factorial complexity. A linear programming (LP) formulation to find the best $L$ paths in a lattice is described and its complexity is shown to be less than previous approaches. Finally it is demonstrated that the new LP formulation outperforms the classical algorithm in the tracking of sinusoidal chirps in high levels of noise.