相关论文: Instantaneous frequency and amplitude of complex s…
The concept of the analytic signal is extended from the case of a real signal with a complex analytic signal to a complex signal with a hypercomplex analytic signal (which we call a hyperanalytic signal) The hyperanalytic signal may be…
The hyperanalytic signal is the straight forward generalization of the classical analytic signal. It is defined by a complexification of two canonical complex signals, which can be considered as an inverse operation of the Cayley-Dickson…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. As the starting point, we abandon Gabor's complex extension and re-evaluate fundamental principles of time-frequency…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
A novel approach towards the spectral analysis of stationary random bivariate signals is proposed. Using the Quaternion Fourier Transform, we introduce a quaternion-valued spectral representation of random bivariate signals seen as…
In this work we extend analytic signal theory to the multidimensional case when oscillations are observed in the $d$ orthogonal directions. First it is shown how to obtain separate phase-shifted components and how to combine them into…
An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…
In this study, we experimentally investigate the application of a transient signal with complex frequencies to the absorption and transmission of sound waves. Indeed, the emission of a wave with an exponentially varying amplitude in time is…
We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between…
In this work, a quaternion-valued model is proposed in lieu of the Clarke's \alpha, \beta transformation to convert three-phase quantities to a hypercomplex single-phase signal. The concatenated signal can be used for harmonic distortion…
In this letter, based on the variational model, we propose a novel time-frequency post-processing technique to approximate the ideal time-frequency representation. Our method has the advantage of modularity, enabling "plug and play",…
A subject's heart beat can be nearly invisible in a spectrum, when that spectrum is generated using conventional methods of Fourier analysis. The phenomenon has been observed in records of both electrocardiography type and…
Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology…
This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…