Real-variable methods are used to prove the Marcinkiewicz Interpolation Theorem, boundedness of the dyadic and Hardy-Littlewood maximal operators, and the Calderón-Zygmund Covering Lemma. The Hilbert transform is defined, and its boundedness is investigated. All results lead to a final theorem on the pointwise convergence of the truncated Hilbert transform

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...

Ground moving target indication (GMTI) in foliage environment is a challenging problem, because the strong echoes from dense foliage environment and big attenuation of the radar microwave often make it difficult for traditional time frequency distributions to clearly and locally represent the Doppler frequency. This paper introduced a new approach to improve the performance of GMTI. This so-cal...

This paper describes a method of signal process applied on an end effects of Hilbert-Huang transform (HHT) to provide an improvement in the reality of spectrum. The method is based on back-propagation network (BPN). To improve the effect, the end extension of the original signal is obtained by back-propagation network. A full waveform including origin and its extension is decomposed by using em...

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...

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...

Abstrac t This paper presents a method for locating and measuring the size of cracks in beams by time of flight (ToF) of ultrasonic wave. The echo detected was processed using the stationary wavelet transform and the Hilbert transform. The accuracy of the information obtained from the processed signal depends on the selected mother wavelet. To select the best mother wavelet for signal processin...