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Frequency-Domain Bounds for Nonnegative, Unsharply Band-Limited Functions
      
In this paper we give a further investigation of the method introduced by the author in [1, Frequency-domain bounds for nonnegative unsharply band-limited functions] for proving bounds for functions with nonnegative Fourier transforms.
      
We present two-sided singular value estimates for a class of convolution-product operators related to time-frequency localization.
      
This paper presents an expansion for radial tempered distributions on ${\bf R}^n$ in terms of smooth, radial analyzing and synthesizing functions with space-frequency localization properties similar to standard wavelets.
      
The Balian-Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(t-na)\}_{m,n \in \mbox{\bf Z}}$
      
Gabor Time-Frequency Lattices and the Wexler-Raz Identity
      
Gabor time-frequency lattices are sets of functions of the form $g_{m \alpha , n \beta} (t) =e^{-2 \pi i \alpha m t}g(t-n \beta)$ generated from a given function $g(t)$ by discrete translations in time and frequency.
      
High-Order Orthonormal Scaling Functions and Wavelets Give Poor Time-Frequency Localization
      
For a fairly general class of orthonormal scaling functions and wavelets with regularity exponents n, we prove that the areas of the time-frequency 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 low-pass filters of a large number of Minimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass 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 low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA.
      
From the original framer to present-day time-frequency and time-scale frames
      
The low-frequency 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 time-frequency 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 time-frequency analysis and digital signal processing.
      
We study time-continuous Gabor frame generating window functions g satisfying decay properties in time and/or frequency with particular emphasis on rational time-frequency lattices.
      
 

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