Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L2(0, 1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the Hilbert space of square-integrable functions on the unit-interval, both with respect to Lebesgue measure, and also with respect to a wider class of self-similar me...

Motivated by problems on Brownian motion, we introduce a recursive scheme for a basis construction in the Hilbert space L2(0, 1) which is analogous to that of Haar and Walsh. More generally, we find a new decomposition theory for the Hilbert space of square-integrable functions on the unit-interval, both with respect to Lebesgue measure, and also with respect to a wider class of self-similar me...

This paper presents a new method for designing two-band orthonormal IIR wavelet "lter banks using allpass "lters. It is well known that orthonormal wavelet bases can be generated by paraunitary "lter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary "lter banks. In this paper, two-band orthonormal IIR wavelet "lter banks using a parallel connection ...

In this paper, we study the properties of the transform which approximates a signal at a given resolution. We show that the difference of a signal at different resolutions can be extracted by decomposing the signal on a wavelet orthonormal basis. In wavelet orthonormal basis is a family of functions, which is built by dilating and translating a unique function. The development of orthonormal wa...

It is a well known fact that any orthonormal basis in L 2 can produce a \random density". If fng is an orthonormal basis and fang is a sequence of random variables such that a 2 n = 1 a.s., then f(x) = jann(x)j 2 is a random density. In this note we deene a random density via orthogonal bases of wavelets and explore some of its basic properties.

The proportional-bandwidth and constant-bandwidth timefrequency signal decompositions of the wavelet, Gabor, and Wilson Manuscript received August 21, 1992; revised May 26, 1993. The Guest Editor coordinating the review of this paper and approving it for publication was Dr. Patrick Flandrin. This work was supported in part by the Sound Group of the computer-based Education Research Laboratory, ...

The deconvolution of signals is studied with thresholding estimators that decompose signals in an orthonormal basis and threshold the resulting coefficients. A general criterion is established to choose the orthonormal basis in order to minimize the estimation risk. Wavelet bases are highly sub-optimal to restore signals and images blurred by a low-pass filter whose transfer function vanishes a...

We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. We next show that this result is best possible by including a result of N.J. Kalton: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two...