Arbitrary tilings of the time-frequency plane using local bases

Abstract

Abstract-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 their simplicity (all filters are obtained from a single prototype) and low computational complexity. We show examples of design, in particular, that of a critical-band system for use in audio coding.

Quilted Gabor frames – A new concept for adaptive time-frequency representation

“…We prove the existence of an upper frame bound for quilted frames as defined in (4). Note that the Bessel property alone allows for interesting conclusions about operators associated with the respective sequence, compare [2].…”

“…For quilted Gabor frames we give up this restriction and introduce systems constructed from globally defined frames by restricting these to certain, possibly compact, regions in the timefrequency or time-scale plane. The idea of realizing tilings of the time-frequency plane has been suggested in [4] and [29], however, these authors stick to the construction of orthogonal bases. In this case, every basis function corresponds to a particular tile.…”

Time-Frequency Mean and Variance Sequences of Orthonormal Bases

“…The question of finding prescribed tilings of the time-frequency plane has been studied in the engineering literature by Bernardini and Kovačević, [4]. They use local bases to construct filters which realize a wide class of tilings of the time-frequency plane, and give applications to audio coding.…”

Nonuniform oversampled filter banks for audio applications

“…On the other hand, if v satisfies the looser form of the perfect reconstruction condition, given by (2), the distortions in the subband components and the distortion in the synthesized signal are related as…”

“…Iterated filter banks, however, impose considerable structure on the equivalent filters which results in inferior time-frequency localization compared to direct designs. -Recently, critically sampled nonuniform filter banks have been studied by Princen [ 13 and Bemardini and KovaEevi6 [2]. Nonuniform filter banks studied by Princen are obtained by joining pseudo QMF filter bank sections, that are nearly perfect reconstruction a t e r banks based on cosine modulation and the principle of adjacent channel aliasing cancellation.…”