Abstract: This paper introduces a new instantaneous frequency
computation approach -Counting Instantaneous Frequency for a
general class of signals called simple waves. The classsimple wave
contains a wide range of continuous signals for which the concept
instantaneous frequency has a perfect physical sense. The concept of
-Counting Instantaneous Frequency also applies to all the discrete data.
For all the simple wave signals and the discrete data, -Counting
instantaneous frequency can be computed directly without signal
decomposition process. The intrinsic mode functions obtained through
empirical mode decomposition belongs to simple wave. So
-Counting instantaneous frequency can be used together with
empirical mode decomposition.
Abstract: In this paper, a new adaptive Fourier decomposition
(AFD) based time-frequency speech analysis approach is proposed.
Given the fact that the fundamental frequency of speech signals often
undergo fluctuation, the classical short-time Fourier transform (STFT)
based spectrogram analysis suffers from the difficulty of window size
selection. AFD is a newly developed signal decomposition theory. It is
designed to deal with time-varying non-stationary signals. Its
outstanding characteristic is to provide instantaneous frequency for
each decomposed component, so the time-frequency analysis becomes
easier. Experiments are conducted based on the sample sentence in
TIMIT Acoustic-Phonetic Continuous Speech Corpus. The results
show that the AFD based time-frequency distribution outperforms the
STFT based one.
Abstract: There have been different approaches to compute the
analytic instantaneous frequency with a variety of background reasoning
and applicability in practice, as well as restrictions. This paper presents an adaptive Fourier decomposition and (α-counting) based
instantaneous frequency computation approach. The adaptive Fourier
decomposition is a recently proposed new signal decomposition
approach. The instantaneous frequency can be computed through the so called mono-components decomposed by it. Due to the fast energy
convergency, the highest frequency of the signal will be discarded by the adaptive Fourier decomposition, which represents the noise of
the signal in most of the situation. A new instantaneous frequency
definition for a large class of so-called simple waves is also proposed
in this paper. Simple wave contains a wide range of signals for which
the concept instantaneous frequency has a perfect physical sense.
The α-counting instantaneous frequency can be used to compute the highest frequency for a signal. Combination of these two approaches one can obtain the IFs of the whole signal. An experiment is demonstrated the computation procedure with promising results.