In terms of forward and backward shift invariant subspaces, we characterize functions in Hardy spaces, or, analytic signals in the terminology of signal analysis, through multiplications between analytic and conjugate analytic signals. As applications, we give some necessary and sufficient conditions for solutions of the Bedrosian equation HðfgÞ 1⁄4 f ðHgÞwhen f or g is a bandlimited signal. We...

In general, the problem of determining the amplitude and frequency modulations ~AM and FM! of a signal is ill posed because there is an unlimited number of combinations of AM and FM that will generate a given signal. Although Gabor proposed a method for uniquely defining the AM and FM of a signal, namely via the analytic signal, the results obtained are sometimes physically paradoxical. In this...

The fundamental property of the analytic signal is the split of identity, meaning the separation of qualitative and quantitative information in form of the local phase and the local amplitude, respectively. Especially the structural representation, independent of brightness and contrast, of the local phase is interesting for numerous image processing tasks. Recently, the extension of the analyt...

The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as function of the orientation two vectors; one representing optimal signal-to-noise ratio, and other maximised or F-statistic. Analytic marginalisation over angle between vectors yields marginalised which Further analytic explored using different choices prior. Monte-Carlo simulations show that ratios had i...

A new simple and efficient dual tree analytic wavelet transform based on Discrete Cosine Harmonic Wavelet Transform DCHWT (ADCHWT) has been proposed and is applied for signal and image denoising. The analytic DCHWT has been realized by applying DCHWT to the original signal and its Hilbert transform. The shift invariance and the envelope extraction properties of the ADCHWT have been found to be ...