The performance of Hilbert spectrum (HS) in time-frequency representation (TFR) of audio signals is investigated in this paper. HS offers a fine-resolution TFR of time domain signals. It is derived by applying empirical mode decomposition (EMD), a newly developed data adaptive method for nonlinear and non-stationary signal analysis together with Hilbert transform. EMD represents any time domain...

Empirical mode decomposition is a method to decompose signals proposed by N.E.Huang et. al in 1998. It can extract adaptively the oscillatory modes at each time from a complex signal, namely it can decompose the signal into a finite (often less) number of intrinsic mode functions (IMFs). With Hilbert transform, the IMFs yield instantaneous frequencies as functions of time, that give sharp ident...

Causality verification and enforcement is of great importance for performance evaluation of electrical interconnects. We introduce a new technique based on Kramers-Krönig dispersion relations, also called Hilbert transform relations, and a construction of causal Fourier continuations using a regularized singular value decomposition (SVD) method. Given a transfer function sampled on a bandlimite...

The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

The analysis of nonlinear and nonstationary time series is still a challenge, as most classical time series analysis techniques are restricted to data that is, at least, stationary. Empirical mode decomposition (EMD) in combination with a Hilbert spectral transform, together called Hilbert-Huang transform (HHT), alleviates this problem in a purely data-driven manner. EMD adaptively and locally ...