A Class of Algorithms for Time-Frequency Multiplier Estimation

Abstract

Abstract-We propose here a new approach together with a corresponding class of algorithms for offline estimation of linear operators mapping input to output signals. The operators are modelled as multipliers, i.e. linear and diagonal operator in a frame or Bessel representation of signals (like Gabor, wavelets ...) and characterized by a transfer function. The estimation problem is formulated as a regularized inverse problem, and solved using iterative algorithms, based on gradient descent schemes. Various estimation problems, which differ by a choice for the regularization function, are studied in the case of Gabor multipliers. The transfer function actually provides a meaningful interpretation of the differences between the two signals or signal classes under consideration, and examples are discussed. Furthermore, examples of signal transformations with such Gabor transfer functions are also given.

Harmonic-Aligned Frame Mask Based on Non-Stationary Gabor Transform with Application to Content-Dependent Speaker Comparison

“…The application of frame masks in musical signals was investigated in [11,12]. Based on DGT, the proposed signal model converts one sound into another by…”

“…with a (convex) regularization term d(σ − → AB ), whose influence is controlled by the parameter µ [12]. As the existence of a stable solution is assured, such approach in general can be applied to arbitrary pair of signals.…”

“…Given that f A and f B are of the same note produced by different instruments, the frame mask between the two signals was found to be effective to characterize the timbre difference between the two instruments [11,12]. Such masks were utilized as similarity measures for instrument classification and for timber morphing and conversion.…”

“…They have been used in perceptual sparsity [9], denoising [10] and signal synthesis [11]. Algorithms to estimate frame mask between audio signals were investigated in [11,12], where it was demonstrated that the frame mask between two instrumental sounds (of a same note) was an effective measure to characterize timber variations between the instruments. Such masks were used for timber morphing and instrument categorization.…”

Spectral estimation for non-stationary signal classes

“…A closer look at the right image also reveals a non-stationary behavior in the amplitude, that has not been corrected (since it was not present in the model). Accounting for such amplitude non-stationarities will require a more sophisticated model, for which one may try to use time-frequency or time-scale multipliers (as in [14]) for the estimation. The spectrum estimation (figure 2, bottom) of the underlying stationary signal shows the harmonic nature of the sound produced by the engine.…”