Wavelet based signal processing incorporating Hilbert transform pair is proved to be more efficient by many authors. The multiplier-less VLSI based architecture of wavelet filter bank for biomedical applications is being proposed in this project. The proposed architecture reduces the computational complexity and improves the performance by combining DWT, Hilbert transform and sampling. Multipli...

The Hilbert transform is essentially the only singular operator in dimension 1. This undoubtedly makes it one of the the most important linear operators in harmonic analysis. The Hilbert transform has had a profound bearing on several theoretical and physical problems across a wide range of disciplines; this includes problems in Fourier convergence, complex analysis, potential theory, modulatio...

Time-frequency distribution has received a growing utilization for analysis and interpretation of nonlinear and nonstationary processes in a variety of fields. Among them, two methods, such as, the empirical mode decomposition EMD with Hilbert transform HT which is termed as the Hilbert-Huang Transform HHT and the Hilbert spectrum based on maximal overlap discrete wavelet package transform MODW...

This paper describes a software based receiver post processor that corrects circularity and gain errors in coherent receivers. The receiver post processor additionally provides range gating capabilities, signal quality estimation, mixer non-linearity detection and various display functions. This paper will concentrate primarily on the identification of circularity errors by the receiver post pr...

The record of human brain neural activities, namely electroencephalogram (EEG), is generally known as a non-stationary and nonlinear signal. In many applications, it is useful to divide the EEGs into segments within which the signals can be considered stationary. Combination of empirical mode decomposition (EMD) and Hilbert transform, called Hilbert-Huang transform (HHT), is a new and powerful ...

We prove the following extension of the Wiener–Wintner Theorem and the Carleson Theorem on pointwise convergence of Fourier series: For all measure preserving flows (X,μ, Tt) and f ∈ L(X,μ), there is a set Xf ⊂ X of probability one, so that for all x ∈ Xf we have lim s↓0 ∫ s<|t|<1/s e f(Tt x) dt t exists for all θ. The proof is by way of establishing an appropriate oscillation inequality which ...

In joint work with C. Thiele, the author has shown that A. Calderón’s bilinear Hilbert transform extends to a bounded operator on certain products of L spaces. This article illustrates the method of proof by giving a complete proof of an inequality which is slightly weaker than the original conjecture of Calderón concerning this transform. 1991 Mathematics Subject Classification: 42A50

This paper presents random residue sequences derived from the number theoretic Hilbert (NHT) transform and their correlation properties. The autocorrelation of a NHT derived sequence is zero for all non-zero shifts which illustrates that these are self-orthogonal sequences. The cross correlation function between two sequences may be computed with respect to the moduli of the either sequence. Th...

Abstract: This paper presents several experimental findings related to the basic discrete Hilbert transform. The errors in the use of a finite set of the transform values have been tabulated for the more commonly used functions. The error can be quite small and, for example, it is of the order of 10 for the chirp signal. The use of the discrete Hilbert transform in hiding information is presented.

A speech signal can be viewed as a high frequency carrier signal containing the temporal fine structure (TFS) that is modulated by a low frequency envelope (ENV). A widely used method to decompose a speech signal into the TFS and ENV is the Hilbert transform. Although this method has been available for about one century and is widely applied in various kinds of speech processing tasks (e.g. spe...