For many decades correlation and power spectrum have been primary tools for digital signal processing applications in the biomedical area. The information contained in the power spectrum is essentially that of the autocorrelation sequence; which is sufficient for complete statistical descriptions of Gaussian signals of known means. However, there are practical situations where one needs to look beyond autocorrelation of a signal to extract information regarding deviation from Gaussianity and the presence of phase relations. Higher order spectra, also known as polyspectra, are spectral representations of higher order statistics, i.e. moments and cumulants of third order and beyond. HOS (higher order statistics or higher order spectra) can detect deviations from linearity, stationarity or Gaussianity in the signal. Most of the biomedical signals are non-linear, non-stationary and non-Gaussian in nature and therefore it can be more advantageous to analyze them with HOS compared to the use of second-order correlations and power spectra. In this paper we have discussed the application of HOS for different bio-signals. HOS methods of analysis are explained using a typical heart rate variability (HRV) signal and applications to other signals are reviewed.

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants.

The unpredictability of the occurrence of epileptic seizures contributes to the burden of the disease to a major degree. An automatic system that detects seizure onsets would allow patients or the people near them to take appropriate precautions, and could provide more insight into these phenomena, thereby revealing important clinical information. Thus, various methods have been proposed to predict the onset of seizures based on EEG recordings. A seemingly promising approach involves nonlinear features motivated by the higher order spectra (HOS). The goal in this paper is to find the different HOS features for normal, pre-ictal (background) and epileptic EEG signals. This may help in the detection of seizure onset as early as possible with maximal accuracy. In this work, 300 EEG data, each belonging to the three classes, are studied. Our results show that the HOS based measures show unique ranges for the different classes with high confidence level (p = 0.002).

Emotion recognition using miniaturised wearable physiological sensors has emerged as a revolutionary technology in various applications. However, detecting emotions using the fusion of multiple physiological signals remains a complex and challenging task. When fusing physiological signals, it is essential to consider the ability of different fusion approaches to capture the emotional information contained within and across modalities. Moreover, since physiological signals consist of time-series data, it becomes imperative to consider their temporal structures in the fusion process. In this study, we propose a temporal multimodal fusion approach with a deep learning model to capture the non-linear emotional correlation within and across electroencephalography (EEG) and blood volume pulse (BVP) signals and to improve the performance of emotion classification. The performance of the proposed model is evaluated using two different fusion approaches – early fusion and late fusion. Specifically, we use a convolutional neural network (ConvNet) long short-term memory (LSTM) model to fuse the EEG and BVP signals to jointly learn and explore the highly correlated representation of emotions across modalities, after learning each modality with a single deep network. The performance of the temporal multimodal deep learning model is validated on our dataset collected from smart wearable sensors and is also compared with results of recent studies. The experimental results show that the temporal multimodal deep learning models, based on early and late fusion approaches, successfully classified human emotions into one of four quadrants of dimensional emotions with an accuracy of 71.61% and 70.17%, respectively.