The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal employed in various fields, such as filter design, processing, communication theory. However, it falls short representing signals generalized domains. To address this limitation, we propose novel integral transform, coined quadratic-phase transform. preliminary study encomp...

The discrete Hilbert transform (DHT) has a variety of applications in signal representation and processing [2-4]. The transform comes in a variety of forms based on assumptions on how the signal is derived from a corresponding periodic signal. The form presented by Kak [1] takes the signal to be non-periodic. Several versions of the transform for periodic signals are also known [5], [6], [7], [...

We prove L(w) bounds for the Carleson operator C, its lacunary version Clac, and its analogue for the Walsh series W in terms of the Aq constants [w]Aq for 1 q p. In particular, we show that, exactly as for the Hilbert transform, ‖C‖Lp(w) is bounded linearly by [w]Aq for 1 q < p. We also obtain L(w) bounds in terms of [w]Ap , whose sharpness is related to certain conjectures (for instance, of K...

The empirical mode decomposition (EMD) was a method pioneered by Huang et al [8] as an alternative technique to the traditional Fourier and wavelet techniques for studying signals. It decomposes a signal into several components called intrinsic mode functions (IMF), which have shown to admit better behaved instantaneous frequencies via Hilbert transforms. In this paper we propose an alternative...

The Hilbert transform is one of the most successful approaches to tracking the varying nature of vibration of a large class of nonlinear systems, thanks to the extraction of backbone curves from experimental data. Because signals with multiple frequency components do not admit a well-behaved Hilbert transform, this transform is inherently limited to the analysis of single-degree-of-freedom syst...