## Literature

### The Instantaneous Spectrum: A General Framework for Time-Frequency Analysis (2018)

## Copyright Notice

The following work is copyrighted by the IEEE.

S. Sandoval and P. L. De Leon “The Instantaneous Spectrum: A General Framework for Time-Frequency Analysis,” *IEEE Trans. Sig. Proc*, 2018

The official version can be obtained at DOI: 10.1109/TSP.2018.2869121.

Click here to access a copy of this work.This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. We review the fundamental Hilbert transform relationship in systems analysis and argue that the dual relationship assumed in signal analysis, i.e.~spectral single-sidedness is not necessarily justifiable. Therefore, we abandon the analytic signal and utilize a carefully parameterized signal model composed of a superposition of complex, AM--FM components that enables rigorous definition of instantaneous amplitude and instantaneous frequency. We then propose the instantaneous spectrum (IS) and prove that it exactly localizes signal components in an instantaneous bandwidth sense. The relation of the IS to traditional time-frequency distributions is discussed and comparative examples are provided. It is shown that under certain conditions the IS specializes to the Fourier spectrum and properties of the IS, similar to standard Fourier transform properties, are given.

### Advances in Empirical Mode Decomposition for Computing Instantaneous Amplitudes and Instantaneous Frequencies (2017)

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The following work is copyrighted by the IEEE.

S. Sandoval and P. L. De Leon “Advances in Empirical Mode Decomposition for Computing Instantaneous Amplitudes and Instantaneous Frequencies,” * The IEEE International Conference on Acoustics, Speech and Signal Processing *, Mar. 2017.

The official version can be obtained at DOI: 10.1109/ICASSP.2017.7952970.

Click here to access a copy of this work.In this paper, we propose improvements to the Complete Ensemble Empirical Mode Decomposition (CEEMD) aimed at the resolution of closely-spaced Intrinsic Mode Functions (IMFs), reproducible and consistent decompositions, reduction in estimation error, numerical stability, and faster decompositions through fewer ensemble trials. We focus on three areas to achieve these goals: 1) use of complimentary masking signals applied at the IMF level, 2) use of narrowband tones instead of white noise for masking signals, and 3) ensuring a true IMF is obtained after ensemble averaging. We propose a numerically stable Instantaneous Frequency (IF) demodulation approach that together with a previously-reported Instantaneous Amplitude (IA) demodulation, allows estimation of the IA/IF parameters of the IMFs and hence a time-frequency representation. Using biomedical signal examples, we compare our results with CEEMD and Improved CEEMD (ICEEMD).

### Analysis of Vowels using Intrinsic Mode Functions (2015)

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The following work is copyrighted by the IEEE.

S. Sandoval, P. L. De Leon, and J. M. Liss “Instantaneous spectral analysis of vowels using intrinsic mode functions,” *2015 IEEE Workshop on Automatic Speech Recognition and Understanding (ASRU)*, pp.569-575, Dec. 2015.

The official version can be obtained at DOI: 10.1109/ASRU.2015.7404846.

Click here to access a copy of this work.In recent work, we presented mathematical theory and algorithms for time-frequency analysis of non-stationary signals. In that work, we generalized the definition of the Instantaneous spectrum by using a superposition of complex AM--FM components parameterized by the Instantaneous Amplitude (IA) and Instantaneous Frequency (IF). Using our Instantaneous Spectral Analysis (ISA) approach, the IA and IF estimates can be far more accurate at revealing underlying signal structure than prior approaches to time-frequency analysis. In this paper, we have applied ISA to speech and compared to both narrowband and wideband spectrograms. We demonstrate how the AM--FM components, assumed to be intrinsic mode functions, align well with the energy concentrations of the spectrograms and highlight fine structure present in the Instantaneous spectrum. As an example, we show never before seen intra-glottal pulse phenomena that are not readily apparent in other analyses. Such fine-scale analyses may have application in speech-based medical diagnosis and automatic speech recognition (ASR) for pathological speakers.