Minimax threshold for denoising complex signals with Waveshrink
IEEE Transactions on Signal Processing
Computing the discrete-time “analytic” signal via FFT
IEEE Transactions on Signal Processing
On the analytic wavelet transform
IEEE Transactions on Information Theory
Rician noise attenuation in the wavelet packet transformed domain for brain MRI
Integrated Computer-Aided Engineering
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The idea of forming a complex-valued (analytic) signal from a real-valued one by creating an imaginary part equal to the Hilbert transform of the real part is well known in exploration geophysics for seismic character mapping via instantaneous attributes. However in this paper we consider the denoising of bivariate signals (time series) where the two real-valued components become the real and imaginary parts of a single complex-valued signal, and concentrate on the case where the two real-valued components are 'in quadrature' and also the complex signal is analytic. The Hilbert transform is applied to the noisy complex-valued signal to produce a new analytic noisy complex-valued signal with a useful noise structure. Numerical calculations show that our proposed 'complex analytic denoising' is superior to two other approaches for (i) a synthetic signal which is both in quadrature and analytic, and (ii) phase estimation for a Rayleigh wave signal which is close to analytic.