Hilbert transform of wavelets has been used to approximate functions in L2(R) . It is proved that Hilbert transform of wavelets with many vanishing moments does a good job in approximating smooth functions in L2(R) . We also prove that Hölder continuity of a function helps in the decay of wavelet coefficients and thereby helps in approximating it. Finally, we give a result that relates the Hilb...

This paper presents the application of Hilbert transform and artificial neural network (ANN) for power quality (PQ) disturbance classification. The input features of the ANN are extracted from the envelope of the disturbance signals by applying Hilbert transform (HT). The features obtained from the Hilbert transform are distinct, understandable and immune to noise. These features after normaliz...

We obtain size estimates for the distribution function of the bilinear Hilbert transform acting on a pair of characteristic functions of sets of finite measure, that yield exponential decay at infinity and blowup near zero to the power −2/3 (modulo some logarithmic factors). These results yield all known L bounds for the bilinear Hilbert transform and provide new restricted weak type endpoint e...

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...