frequency 
FrequencyDomain Bounds for Nonnegative, Unsharply BandLimited Functions


In this paper we give a further investigation of the method introduced by the author in [1, Frequencydomain bounds for nonnegative unsharply bandlimited functions] for proving bounds for functions with nonnegative Fourier transforms.


We present twosided singular value estimates for a class of convolutionproduct operators related to timefrequency localization.


This paper presents an expansion for radial tempered distributions on ${\bf R}^n$ in terms of smooth, radial analyzing and synthesizing functions with spacefrequency localization properties similar to standard wavelets.


The BalianLow theorem (BLT) is a key result in timefrequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(tna)\}_{m,n \in \mbox{\bf Z}}$


Gabor TimeFrequency Lattices and the WexlerRaz Identity


Gabor timefrequency lattices are sets of functions of the form $g_{m \alpha , n \beta} (t) =e^{2 \pi i \alpha m t}g(tn \beta)$ generated from a given function $g(t)$ by discrete translations in time and frequency.


HighOrder Orthonormal Scaling Functions and Wavelets Give Poor TimeFrequency Localization


For a fairly general class of orthonormal scaling functions and wavelets with regularity exponents n, we prove that the areas of the timefrequency windows tend to infinity as n → ∞.


We present an explicit, straightforward construction of smooth integrable functions with prescribed gaps around the origin in both time and frequency domain.


Smoothing Minimally Supported Frequency Wavelets: Part II


The main purpose of this paper is to give a procedure to "mollify" the lowpass filters of a large number of Minimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also lowpass filters for an MRA.


Smoothing minimally supported frequency wavelets: Part II


The main purpose of this paper is to give a procedure to "mollify" the lowpass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also lowpass filters for an MRA.


From the original framer to presentday timefrequency and timescale frames


The lowfrequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series.


The wavelets fill in the gaps and provide the necessary high frequency corrections.


Finally, we consider the spline of order 2; we investigate numerically the region of the timefrequency plane where it generates a frame and we compute the dual function for some values of the parameters.


Such systems play an important role in timefrequency analysis and digital signal processing.


We study timecontinuous Gabor frame generating window functions g satisfying decay properties in time and/or frequency with particular emphasis on rational timefrequency lattices.

