An analytic signal permits unambiguous characterization of the phase and envelope of a real signal. But the analytic signal's phase-derivative i.e. the instantaneous frequency (IF) is typically a wild function and can take on values ranging fron negative in nity to positive in nity. Fortunately, any analytic signal can be decomposed into a minimum phase (MinP) signal component and an all-phase ...

The analytic signal is one of the most capable approaches in onedimensional signal processing. Two-dimensional signal theory suffers from the absence of an isotropic extension of the analytic signal. Accepting the fact that there is no odd filter with isotropic energy in higher dimensions, one tried to circumvent this drawback using the one-dimensional quadrature filters with respect to several...

The paper compares the features of three extensions of the notion of the Gabor’s analytic signal for 2-D signals: the analytic signals with single-quadrant spectra (AS), the quaternionic signals with quaternionic single-quadrant spectra (QS) and the monogenic signals (MS). A good platform of comparison are the polar representations of the AS and the QS and the spherical coordinate representatio...

The estimation of the local phase and local amplitude of 1-D signals can be realized by the construction of the analytic signal. This includes the evaluation of the signal’s Hilbert transform, which performs a phase shift. In the past, different definitions of the analytic signal of multidimensional signals have been proposed, all of which are based on different combinations of partial and tota...

This paper considers the problem of measuring and analysing the frequency and phase angle variations which occur in a power system after a fault or disturbance. This is an important problem because the results of the analysis are used in implementing control strategies to avert generat,or cutout. Commonly, the frequency is not measured directly, but is inferred from the instantaneous power at t...

We point out that the conventional de"nition of instantaneous amplitude and frequency, namely as the magnitude and derivative of the phase, respectively, of a complex representation of the signal, sometimes contains an ambiguity, even for a unique complex representation (e.g., the analytic signal). There are at least two choices for resolving this ambiguity when it arises. One choice yields a n...

For adaptive representation of nonlinear signals, the bank M of real square integrable functions that have nonlinear phases and nonnegative instantaneous frequencies under the analytic signal method is investigated. A particular class of functions with explicit expressions in M is obtained using Communicated by Qiyu Sun. Supported in part by Macau Science and Technology Fund 051/2005/A. Support...

Hilbert envelope (HE) is defined as the magnitude of the analytic signal. This work proposes HE based zero frequency filtering (ZFF) approach for the extraction of epochs in high pass filtered speech. Epochs in speech correspond to instants of significant excitation like glottal closure instants. The ZFF method for epoch extraction is based on the signal energy around the impulse at zero freque...

In this chapter, a new rotation-invariant generalization of the analytic signal will be presented to analyze intrinsic 1D and 2D local image structures. By combining differential geometry and Clifford analysis, the monogenic curvature tensor can be derived to perform a split of identity and to enable simultaneous estimation of local amplitude, phase, main orientation and angle of intersection i...

Recursive decomposition of fundamental events in the directional, one-dimensional, discrete, stationary Boolean model has resulted in analytic representation of the event probabilities and the recursive representation of clump-length and gap-length densities. This paper applies the methodology to find analytic expressions for distributions of a number of random variables, including the number o...