Adapted Bases of Time-Frequency Local Cosines

Adapted Bases of Time-frequency Local Cosines

We develop and analyze a best basis algorithm for orthonormal bases of local cosines which satisfy a uniform bound on their time-frequency concentration. All waveforms are obtained from three elementary window functions by shifts, rescaling, and modulation. For a discrete signal of length N, the complexity is of order N(logN) 2 .

Arbitrary Tilings of the Time-Frequency Plane Using Local Bases

We show how to design filters given a prescribed tiling of the time–frequency plane. Moreover, we impose on these filters the structure of local orthogonal bases. These bases were recently constructed as a generalization of the cosinemodulated filter banks in discrete time and local trigonometric bases in continuous time. They have been found to be of considerable practical importance due to th...

Time-frequency analysis with best local cosine bases

We propose new best basis search algorithms for local cosine dictionaries. We provide several algorithms for dictionaries of various complexity. Our framework generalizes the classical best local cosine basis selection based on a dyadic tree [1].

Computation With Adapted Time-Frequency Atoms

Time-frequency representation adapted to perception

The human auditory system performs a time-frequency analysis with a frequency dependent spectral resolution. We will illustrate the basics of this phenomenon and show how to apply this knowledge to a linear transform, the ERB-let transform. In particular this transform is a special case of a large class of transforms which we call generalized Gabor-wavelet transform. For this class we derive im...