Understanding Harmonic Structures Through Instantaneous Frequency

The analysis of harmonics and non-sinusoidal waveform shape in neurophysiological data is growing in importance. However, a precise definition of what constitutes a harmonic is lacking. In this paper, we propose a rigorous definition of when to consider signals to be in a harmonic relationship based on an integer frequency ratio, constant phase, and a well-defined joint instantaneous frequency. We show this definition is linked to extrema counting and Empirical Mode Decomposition (EMD). We explore the mathematics of our definition and link it to results from analytic number theory. This naturally leads to us to define two classes of harmonic structures, termed strong and weak, with different extrema behaviour. We validate our framework using both simulations and real data. Specifically, we look at the harmonics structure in the FitzHugh-Nagumo model and the non-sinusoidal hippocampal theta oscillation in rat local field potential data. We further discuss how our definition helps to address mode splitting in EMD. A clear understanding of when harmonics are present in signals will enable a deeper understanding of the functional and clinical roles of non-sinusoidal neural oscillations.

Combining Evidence from Auditory, Instantaneous Frequency and Random Forest for Anti-Noise Speech Recognition

Due to the shortcomings of acoustic feature parameters in speech signals, and the limitations of existing acoustic features in characterizing the integrity of the speech information, This paper proposes a method for speech recognition combining cochlear feature and random forest. Environmental noise can pose a threat to the stable operation of current speech recognition systems. It is therefore essential to develop robust systems that are able to identify speech under low signal-to-noise ratio. In this paper, we propose a method of speech recognition combining spectral subtraction, auditory and energy features extraction. This method first extract novel auditory features based on cochlear filter cepstral coefficients (CFCC) and instantaneous frequency (IF), i.e., CFCCIF. Spectral subtraction is then introduced into the front end of feature extraction, and the extracted feature is called enhanced auditory features (EAF). An energy feature Teager energy operator (TEO) is also extracted, the combination of them is known as a fusion feature. Linear discriminate analysis (LDA) is then applied to feature selection and optimization of the fusion feature. Finally, random forest (RF) is used as the classifier in a non-specific persons, isolated words, and small-vocabulary speech recognition system. On the Korean isolated words database, the proposed features (i.e., EAF) after fusion with Teager energy features have shown strong robustness in the nosiy situation. Our experiments show that the optimization feature achieved in a speech recognition task display a high recognition rate and excellent anti-noise performance.

Switchable Instantaneous Frequency Measurement by Optical Power Monitoring Based on DP-QPSK Modulator

We propose and analyze an instantaneous frequency measurement system using optical power monitoring technique with improved resolution. The primary component employed in the proposal is a DP-QPSK modulator which is used to modulate the microwave signal with a designed time delay and phase shifting. Then the generated optical signal is sent to polarization beam splitter (PBS) via polarization controller (PC). Thanks to the complementary transmission nature of polarization interference introduced by PBS, the frequency information is converted to the optical power and the relationship between the amplitude comparison function (ACF) and microwave frequency to be measured is established. Thus, the frequency of the microwave signal could be easily measured through monitoring the optical powers of the two output ports of the PBS. Furthermore, by adjusting the DC biases of the DP-QPSK modulator instead of changing the electrical delay, the measurement range and resolution can be switched. In this paper, the basic principle of the instantaneous frequency measurement system is derived in detail, and simulation has been performed to investigate the resolution, the measurement range and the impact of imperfection devices. The proposed scheme is wavelength independent and measurement range switchable, which can avoid the laser wavelength drifting problem and greatly increase the system flexibility.

Wavelet Characterizations for Investigating Nonlinear Oscillators

This study investigates the wavelet-based system identification capabilities on determining the system nonlinearity based on the system impulse response function. Wavelet estimates of the instantaneous envelopes and instantaneous frequency are used to plot the system backbone curve. This wavelet estimate is then used to estimate the values of the parameter for the system. Two weakly nonlinear oscillators, which are the Duffing and the Van der Pol oscillators, have been analyzed using this wavelet approach. A case study based on a model of an oscillating flap wave energy converter (OFWEC) was also discussed in this study. Based on the results, it was shown that this technique is recommended for nonlinear system identification provided the impulse response of the system can be captured. This technique is also suitable when the system's form is unknown and for estimating the instantaneous frequency even when the impulse responses were polluted with noise.