SSVEP Extraction Based on the Similarity of Background EEG

Steady-state Visual Evoked Potential (SSVEP) outperforms the other types of ERPs for Brain-computer Interface (BCI), and thus it is widely employed. In order to apply SSVEP-based BCI to real life situations, it is important to improve the accuracy and transfer rate of the system. Aimed at this target, many SSVEP extraction methods have been proposed. All these methods are based directly on the properties of SSVEP, such as power and phase. In this study, we first filtered out the target frequencies from the original EEG to get a new signal and then computed the similarity between the original EEG and the new signal. Based on this similarity, SSVEP in the original EEG can be identified. This method is referred to as SOB (Similarity of Background). The SOB method is used to detect SSVEP in 1s-length and 3s-length EEG segments respectively. The accuracy of detection is compared with its peers computed by the widely-used Power Spectrum (PS) method and the Canonical Coefficient (CC) method. The comparison results illustrate that the SOB method can lead to a higher accuracy than the PS method and CC method when detecting a short period SSVEP signal.     

Simultaneous Detection of P300 and Steady-State Visually Evoked Potentials for Hybrid Brain-Computer Interface

Objective

We study the feasibility of a hybrid Brain-Computer Interface (BCI) combining simultaneous visual oddball and Steady-State Visually Evoked Potential (SSVEP) paradigms, where both types of stimuli are superimposed on a computer screen. Potentially, such a combination could result in a system being able to operate faster than a purely P300-based BCI and encode more targets than a purely SSVEP-based BCI.

Approach

We analyse the interactions between the brain responses of the two paradigms, and assess the possibility to detect simultaneously the brain activity evoked by both paradigms, in a series of 3 experiments where EEG data are analysed offline.

Main Results

Despite differences in the shape of the P300 response between pure oddball and hybrid condition, we observe that the classification accuracy of this P300 response is not affected by the SSVEP stimulation. We do not observe either any effect of the oddball stimulation on the power of the SSVEP response in the frequency of stimulation. Finally results from the last experiment show the possibility of detecting both types of brain responses simultaneously and suggest not only the feasibility of such hybrid BCI but also a gain over pure oddball- and pure SSVEP-based BCIs in terms of communication rate.     

A Comparison Study of Canonical Correlation Analysis Based Methods for Detecting Steady-State Visual Evoked Potentials

Canonical correlation analysis (CCA) has been widely used in the detection of the steady-state visual evoked potentials (SSVEPs) in brain-computer interfaces (BCIs). The standard CCA method, which uses sinusoidal signals as reference signals, was first proposed for SSVEP detection without calibration. However, the detection performance can be deteriorated by the interference from the spontaneous EEG activities. Recently, various extended methods have been developed to incorporate individual EEG calibration data in CCA to improve the detection performance. Although advantages of the extended CCA methods have been demonstrated in separate studies, a comprehensive comparison between these methods is still missing. This study performed a comparison of the existing CCA-based SSVEP detection methods using a 12-class SSVEP dataset recorded from 10 subjects in a simulated online BCI experiment. Classification accuracy and information transfer rate (ITR) were used for performance evaluation. The results suggest that individual calibration data can significantly improve the detection performance. Furthermore, the results showed that the combination method based on the standard CCA and the individual template based CCA (IT-CCA) achieved the highest performance.     

A Dynamic Selection Method for Reference Electrode in SSVEP-Based BCI

In SSVEP-based Brain-Computer Interface (BCI), it is very important to get an evoked EEG with a high signal to noise ratio (SNR). The SNR of SSVEP is fundamentally related to the characteristics of stimulus, such as its intensity and frequency, and it is also related to both the reference electrode and the active electrode. In the past, with SSVEP-based BCI, often the potential at ‘Cz’, the average potential at all electrodes or the average mastoid potential, were statically selected as the reference. In conjunction, a certain electrode in the occipital area was statically selected as the active electrode for all stimuli. This work proposed a dynamic selection method for the reference electrode, in which all electrodes can be looked upon as active electrodes, while an electrode which can result in the maximum sum relative-power of a specific frequency SSVEP can be confirmed dynamically and considered as the optimum reference electrode for that specific frequency stimulus. Comparing this dynamic selection method with previous methods, in which ‘Cz’, the average potential at all electrodes or the average mastoid potential were selected as the reference electrode, it is demonstrated that the SNR of SSVEP is improved significantly as is the accuracy of SSVEP detection.     

Multiple frequencies sequential coding for SSVEP-based brain-computer interface

Background

Steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI) has become one of the most promising modalities for a practical noninvasive BCI system. Owing to both the limitation of refresh rate of liquid crystal display (LCD) or cathode ray tube (CRT) monitor, and the specific physiological response property that only a very small number of stimuli at certain frequencies could evoke strong SSVEPs, the available frequencies for SSVEP stimuli are limited. Therefore, it may not be enough to code multiple targets with the traditional frequencies coding protocols, which poses a big challenge for the design of a practical SSVEP-based BCI. This study aimed to provide an innovative coding method to tackle this problem.

Methodology/Principal Findings

In this study, we present a novel protocol termed multiple frequencies sequential coding (MFSC) for SSVEP-based BCI. In MFSC, multiple frequencies are sequentially used in each cycle to code the targets. To fulfill the sequential coding, each cycle is divided into several coding epochs, and during each epoch, certain frequency is used. Obviously, different frequencies or the same frequency can be presented in the coding epochs, and the different epoch sequence corresponds to the different targets. To show the feasibility of MFSC, we used two frequencies to realize four targets and carried on an offline experiment. The current study shows that: 1) MFSC is feasible and efficient; 2) the performance of SSVEP-based BCI based on MFSC can be comparable to some existed systems.

Conclusions/Significance

The proposed protocol could potentially implement much more targets with the limited available frequencies compared with the traditional frequencies coding protocol. The efficiency of the new protocol was confirmed by real data experiment. We propose that the SSVEP-based BCI under MFSC might be a promising choice in the future.     

Influence of Stimuli Spatial Proximity on a SSVEP-Based BCI Performance

Objective: Steady-State Visual Evoked Potentials based Brain-Computer Interfaces (SSVEP-based BCIs) systems have been shown as promising technology due to their short response time and ease of use. SSVEP-based BCIs use brain responses to a flickering visual stimulus as an input command to an external application or device, and it can be influenced by stimulus properties, signal recording, and signal processing. We aim to investigate the system performance varying the stimuli spatial proximity (a stimulus property).Material and methods: We performed a comparative analysis of two visual interface designs (named cross and square) for an SSVEP-based BCI. The power spectrum density (PSD) was used as feature extraction and the Support Machine Vector (SVM) as classification method. We also analyzed the effects of five flickering frequencies (6.67, 8.57, 10, 12 e 15 Hz) between and within interfaces.Results: We found higher accuracy rates for the flickering frequencies of 10, 12, and 15 Hz. The stimulus of 10 Hz presented the highest SSVEP amplitude response for both interfaces. The system presented the best performance (highest classification accuracy and information transfer rate) using the cross interface (lower visual angle).Conclusion: Our findings suggest that the system has the highest performance in the spatial proximity range from 4° to 13° (visual angle). In addition, we conclude that as the stimulus spatial proximity increases, the interference from other stimuli reduces, and the SSVEP amplitude response decreases, which reduces system accuracy. The inter-stimulus distance is a visual interface parameter that must be chosen carefully to increase the efficiency of an SSVEP-based BCI.     

Investigating the Effect of Flickering Frequency Pair and Mother Wavelet Selection in Steady-State Visually-Evoked Potentials on Two-Command Brain-Computer Interfaces

IntroductionSteady-state visually evoked potentials (SSVEPs) have become popular in brain-computer interface (BCI) applications in addition to many other applications on clinical neuroscience (neurodegenerative disorders, schizophrenia, epilepsy, etc.), cognitive (visual attention, working memory, brain rhythms, etc.), and use of engineering researches. Among available methods to measure brain activities, SSVEPs have advantages like higher information transfer rate, simplicity in structure, and short training time. SSVEP-based BCIs use flickering stimuli at different frequencies to discriminate distinct commands in real life. Some features are extracted from the SSVEP signals before these commands are classified. The wavelet transform (WT) has attracted researchers among feature extraction methods since it utilizes the non-stationary signals well. In the WT, a sample function (named mother wavelet) represents the SSVEP signal in both time and frequency domains. Unfortunately, there is no universal mother wavelet function that fits all the signals. Therefore, choosing an appropriate mother wavelet function may be a challenge in WT-related studies. Although there are such studies in three- and seven-command SSVEP-based studies, there is no study for two-command systems in our knowledge.Materials and MethodsIn this study, two user commands flickered at the combinations of seven different frequencies were tested to determine which frequency pairs give the highest performance. For this purpose, three well-known wavelet features (energy, entropy, and variance) were calculated for each of derived EEG frequency bands from the discrete WT coefficients of SSVEP signals. The WT was repeated for six different mother wavelet functions (Haar, Db4, Sym4, Coif1, Bior3.5, and Rbior2.8). Then, four feature sets (every three features, and all together) were applied to seven commonly-used machine learning algorithms (Decision Tree, Discriminant Analysis, Logistic Regression, Naive Bayes, Support Vector Machines, Nearest Neighbors, and Ensemble Classifiers).Results and DiscussionWe achieved 100% accuracies among these 3,528 runs (7 classifiers x 4 feature sets x 6 mother wavelets x 21 flickering frequency pairs) using the mother wavelet function of Haar and the Ensemble Learner classifier. The highest classifier performances are 100% when two commands have the flickering frequency pairs of (6.0 and 10 Hz), (6.5 and 8.2 Hz), or (6.5 and 10.0 Hz).ConclusionWe obtained three main outcomes from this study. First, the most representative mother wavelet function was Haar, while the worst one was Symlet 4. Second, the Ensemble Learner classifier gave the maximum classifier performance in a two-command SSVEP-based BCI system. Besides, two user commands from SSVEP should be one of the frequency pairs of (6.0 and 10.0 Hz), (6.5 and 8.2 Hz), and (6.5 and 10.0 Hz) to achieve the maximum accuracy.     

Robust frequency recognition for SSVEP-based BCI with temporally local multivariate synchronization index

Multivariate synchronization index (MSI) has been proved to be an efficient method for frequency recognition in SSVEP-BCI systems. It measures the correlation according to the entropy of the normalized eigenvalues of the covariance matrix of multichannel signals. In the MSI method, the estimation of covariance matrix omits the temporally local structure of samples. In this study, a new spatio-temporal method, termed temporally local MSI (TMSI), was presented. This new method explicitly exploits temporally local information in modelling the covariance matrix. In order to evaluate the performance of the TMSI, we performs a comparison between the two methods on the real SSVEP datasets from eleven subjects. The results show that the TMSI outperforms the standard MSI. TMSI benefits from exploiting the temporally local structure of EEG signals, and could be a potential method for robust performance of SSVEP-based BCI.     

基于节律性脑电信号的脑-机接口

脑-机接口系统是一个不依靠外周神经和肌肉组织等而实现大脑和外界装置之间直接的交流和控制的通道。它为那些运动障碍的残疾人表达自己的意愿和实现对外部设备的控制提供了一种新的强大的技术支持。基于脑电的脑-机接口作为一种非侵入型的技术引起了该领域很多人的关注。基于脑电的脑-机接口采用了很多种类型的脑电信号。其中,振荡性的脑电图由于有较高的幅值和对噪声不敏感等特性而体现出极大的优势。也是由于这些原因,振荡性的脑电图变成了脑-机接口的应用中非常成功的设计之一。本文要介绍主要的基于脑电的脑-机接口中的两种,分别是稳态视觉诱发电位和基于运动本体感觉节律的脑-机接口。作者将详细的叙述该研究的生理背景、脑-机接口的参数,以及该系统的构造及信号处理的方法,并且会演示一些具有潜在应用价值的科研成果。     

Classification of Motor Imagery EEG Based on Time-Domain and Frequency-Domain Dual-Stream Convolutional Neural Network

Background and objectiveAn important task of the brain-computer interface (BCI) of motor imagery is to extract effective time-domain features, frequency-domain features or time-frequency domain features from the raw electroencephalogram (EEG) signals for classification of motor imagery. However, choosing an appropriate method to combine time domain and frequency domain features to improve the performance of motor imagery recognition is still a research hotspot.MethodsIn order to fully extract and utilize the time-domain and frequency-domain features of EEG in classification tasks, this paper proposed a novel dual-stream convolutional neural network (DCNN), which can use time domain signal and frequency domain signal as the inputs, and the extracted time-domain features and frequency-domain features are fused by linear weighting for classification training. Furthermore, the weight can be learned by the DCNN automatically.ResultsThe experiments based on BCI competition II dataset III and BCI competition IV dataset 2a showed that the model proposed by this study has better performance than other conventional methods. The model used time-frequency signal as the inputs had better performance than the model only used time-domain signals or frequency-domain signals. The accuracy of classification was improved for each subject compared with the models only used one signals as the inputs.ConclusionsFurther analysis shown that the fusion weight of different subject is specifically, adjusting the weight coefficient automatically is helpful to improve the classification accuracy.     

Enhancing P300 Detection Using a Band-Selective Filter Bank for a Visual P300 Speller

Background: An open challenge of P300-based BCI systems focuses on recognizing ERP signals using a reduced number of trials with enough classification rate.Methods: Three novel methods based on Filter Bank and Canonical Correlation Analysis (CCA) are proposed for the recognition of P300 ERPs using a reduced number of trials. The proposed methods were evaluated with two freely available EEG datasets based on 6x6 speller and were compared with five standard methods: Mean-Amplitude, Step-Wise, Principal Component Analysis, Peak, and CCA.Results: The proposed methods outperform significantly standard algorithms for P300 identification with a maximum AUC of 0.93 and 0.98, and an average of 0.73 and 0.76, using a single trial.Conclusion: Proposed methods based on Filter Bank are robust for the identification of P300 using a reduced number of trials, which could be used in real-time BCI spellers for rehabilitation engineering.     

Brain-Computer Interface Controlled Cyborg: Establishing a Functional Information Transfer Pathway from Human Brain to Cockroach Brain

An all-chain-wireless brain-to-brain system (BTBS), which enabled motion control of a cyborg cockroach via human brain, was developed in this work. Steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI) was used in this system for recognizing human motion intention and an optimization algorithm was proposed in SSVEP to improve online performance of the BCI. The cyborg cockroach was developed by surgically integrating a portable microstimulator that could generate invasive electrical nerve stimulation. Through Bluetooth communication, specific electrical pulse trains could be triggered from the microstimulator by BCI commands and were sent through the antenna nerve to stimulate the brain of cockroach. Serial experiments were designed and conducted to test overall performance of the BTBS with six human subjects and three cockroaches. The experimental results showed that the online classification accuracy of three-mode BCI increased from 72.86% to 78.56% by 5.70% using the optimization algorithm and the mean response accuracy of the cyborgs using this system reached 89.5%. Moreover, the results also showed that the cyborg could be navigated by the human brain to complete walking along an S-shape track with the success rate of about 20%, suggesting the proposed BTBS established a feasible functional information transfer pathway from the human brain to the cockroach brain.     

Towards an Optimization of Stimulus Parameters for Brain-Computer Interfaces Based on Steady State Visual Evoked Potentials

Efforts to construct an effective brain-computer interface (BCI) system based on Steady State Visual Evoked Potentials (SSVEP) commonly focus on sophisticated mathematical methods for data analysis. The role of different stimulus features in evoking strong SSVEP is less often considered and the knowledge on the optimal stimulus properties is still fragmentary. The goal of this study was to provide insight into the influence of stimulus characteristics on the magnitude of SSVEP response. Five stimuli parameters were tested: size, distance, colour, shape, and presence of a fixation point in the middle of each flickering field. The stimuli were presented on four squares on LCD screen, with each square highlighted by LEDs flickering with different frequencies. Brighter colours and larger dimensions of flickering fields resulted in a significantly stronger SSVEP response. The distance between stimulation fields and the presence or absence of the fixation point had no significant effect on the response. Contrary to a popular belief, these results suggest that absence of the fixation point does not reduce the magnitude of SSVEP response. However, some parameters of the stimuli such as colour and the size of the flickering field play an important role in evoking SSVEP response, which indicates that stimuli rendering is an important factor in building effective SSVEP based BCI systems.     

Estimating the mutual information of an EEG-based Brain-Computer Interface.

An EEG-based Brain-Computer Interface (BCI) could be used as an additional communication channel between human thoughts and the environment. The efficacy of such a BCI depends mainly on the transmitted information rate. Shannon's communication theory was used to quantify the information rate of BCI data. For this purpose, experimental EEG data from four BCI experiments was analyzed off-line. Subjects imaginated left and right hand movements during EEG recording from the sensorimotor area. Adaptive autoregressive (AAR) parameters were used as features of single trial EEG and classified with linear discriminant analysis. The intra-trial variation as well as the inter-trial variability, the signal-to-noise ratio, the entropy of information, and the information rate were estimated. The entropy difference was used as a measure of the separability of two classes of EEG patterns.     

On the Quantification of SSVEP Frequency Responses in Human EEG in Realistic BCI Conditions

This article concerns one of the most important problems of brain-computer interfaces (BCI) based on Steady State Visual Evoked Potentials (SSVEP), that is the selection of the a-priori most suitable frequencies for stimulation. Previous works related to this problem were done either with measuring systems that have little in common with actual BCI systems (e.g., single flashing LED) or were presented on a small number of subjects, or the tested frequency range did not cover a broad spectrum. Their results indicate a strong SSVEP response around 10 Hz, in the range 13–25 Hz, and at high frequencies in the band of 40–60 Hz. In the case of BCI interfaces, stimulation with frequencies from various ranges are used. The frequencies are often adapted for each user separately. The selection of these frequencies, however, was not yet justified in quantitative group-level study with proper statistical account for inter-subject variability. The aim of this study is to determine the SSVEP response curve, that is, the magnitude of the evoked signal as a function of frequency. The SSVEP response was induced in conditions as close as possible to the actual BCI system, using a wide range of frequencies (5–30 Hz, in step of 1 Hz). The data were obtained for 10 subjects. SSVEP curves for individual subjects and the population curve was determined. Statistical analysis were conducted both on the level of individual subjects and for the group. The main result of the study is the identification of the optimal range of frequencies, which is 12–18 Hz, for the registration of SSVEP phenomena. The applied criterion of optimality was: to find the largest contiguous range of frequencies yielding the strong and constant-level SSVEP response.     

Improving the separability of multiple EEG features for a BCI by neural-time-series-prediction-preprocessing

A recently proposed method for EEG preprocessing is extended and analyzed in this work via a range of different tests in combination with various other BCI components. Neural-time-series-prediction-processing (NTSPP) is a predictive approach to EEG preprocessing where prediction models (PMs) are trained to perform one-step-ahead prediction of the EEG times-series which reflect motor imagery induced alterations in neuronal activity. Due to the specialization of distinct PMs, the predicted signals (Ys) and error signals (Es) are distinctly different from the original (Os) signals. The PMs map the Os signals to a higher dimension which, in the majority of cases, produces features that are more separable than those produced by the Os signals. Four feature extraction procedures, ranging in complexity and in terms of the information which is extracted i.e., time domain, frequency domain and time–frequency (t–f) domain, are used to determine the separability enhancements which are verified by comparative statistical tests and brain–computer interface (BCI) tests on six subjects. It is shown that, in the majority of the tests, features extracted from the NTSPP signals are more separable than those extracted from the Os signals, in terms of increased Euclidean distance between class means, reduced inter-class correlations and intra-class variance, and higher classification accuracy (CA), information transfer (IT) rate and mutual information (MI).     

Motor Imagery EEG Spectral-Spatial Feature Optimization Using Dual-Tree Complex Wavelet and Neighbourhood Component Analysis

BackgroundFrequency band optimization improves the performance of common spatial pattern (CSP) in motor imagery (MI) tasks classification because MI-related electroencephalograms (EEGs) are highly frequency specific. Many variants of CSP algorithm divided the EEG into various sub bands and then applied CSP. However, the feature dimension of MI-EEG data increases with addition of frequency sub bands and requires efficient feature selection algorithms. The performance of CSP also depends on filtering techniques.MethodIn this study, we designed a dual tree complex wavelet transform based filter bank to filter the EEG into sub bands, instead of traditional filtering methods, which improved the spatial feature extraction efficiency. Further, after filtering EEG into different sub bands, we extracted spatial features from each sub band using CSP and optimized them by a proposed supervised learning framework based on neighbourhood component analysis (NCA). Subsequently, a support vector machine (SVM) is trained to perform classification.ResultsAn experimental study, conducted on two datasets (BCI Competition IV (Dataset 2b), and BCI competition III (Dataset IIIa)), validated the MI classification effectiveness of the proposed method in comparison with standard algorithms such as CSP, Filter bank CSP (CSP), and Discriminative FBCSP (DFBCSP). The average classification accuracy obtained by the proposed method for BCI Competition IV (Dataset 2b), and BCI Competition III (Dataset IIIa) are 84.02 ± 12.2 and 89.1 ± 7.50, respectively and found significant than that achieved by standard methods.ConclusionAchieved superior results suggest that the proposed algorithm can improve the performance of MI-based Brain-computer interface devices.     

Regularized common spatial patterns with subject-to-subject transfer of EEG signals

In the context of brain-computer interface (BCI) system, the common spatial patterns (CSP) method has been used to extract discriminative spatial filters for the classification of electroencephalogram (EEG) signals. However, the classification performance of CSP typically deteriorates when a few training samples are collected from a new BCI user. In this paper, we propose an approach that maintains or improves the recognition accuracy of the system with only a small size of training data set. The proposed approach is formulated by regularizing the classical CSP technique with the strategy of transfer learning. Specifically, we incorporate into the CSP analysis inter-subject information involving the same task, by minimizing the difference between the inter-subject features. Experimental results on two data sets from BCI competitions show that the proposed approach greatly improves the classification performance over that of the conventional CSP method; the transformed variant proved to be successful in almost every case, based on a small number of available training samples.     

A Deep Learning Architecture for P300 Detection with Brain-Computer Interface Application

In this paper, a brain-computer interface (BCI) system for character recognition is proposed based on the P300 signal. A P300 speller is used to spell the word or character without any muscle movement. P300 detection is the first step to detect the character from the electroencephalogram (EEG) signal. The character is recognized from the detected P300 signal. In this paper, sparse autoencoder (SAE) and stacked sparse autoencoder (SSAE) based feature extraction methods are proposed for P300 detection. This work also proposes a fusion of deep-features with the temporal features for P300 detection. A SSAE technique extracts high-level information about input data. The combination of SSAE features with the temporal features provides abstract and temporal information about the signal. An ensemble of weighted artificial neural network (EWANN) is proposed for P300 detection to minimize the variation among different classifiers. To provide more importance to the good classifier for final classification, a higher weightage is assigned to the better performing classifier. These weights are calculated from the cross-validation test. The model is tested on two different publicly available datasets, and the proposed method provides better or comparable character recognition performance than the state-of-the-art methods.     

Model analyses of visual biofeedback training for EEG-based brain-computer interface

The primary goal of this study was to construct a simulation model of a biofeedback brain-computer interface (BCI) system to analyze the effect of biofeedback training on BCI users. A mathematical model of a man-machine visual-biofeedback BCI system was constructed to simulate a subject using a BCI system to control cursor movements. The model consisted of a visual tracking system, a thalamo-cortical model for EEG generation, and a BCI system. The BCI system in the model was realized for real experiments of visual biofeedback training. Ten sessions of visual biofeedback training were performed in eight normal subjects during a 3-week period. The task was to move a cursor horizontally across a screen, or to hold it at the screen’s center. Experimental conditions and EEG data obtained from real experiments were then simulated with the model. Three model parameters, representing the adaptation rate of gain in the visual tracking system and the relative synaptic strength between the thalamic reticular and thalamo-cortical cells in the Rolandic areas, were estimated by optimization techniques so that the performance of the model best fitted the experimental results. The serial changes of these parameters over the ten sessions, reflecting the effects of biofeedback training, were analyzed. The model simulation could reproduce results similar to the experimental data. The group mean success rate and information transfer rate improved significantly after training (56.6 to 81.1% and 0.19 to 0.76 bits/trial, respectively). All three model parameters displayed similar and statistically significant increasing trends with time. Extensive simulation with systematic changes of these parameters also demonstrated that assigning larger values to the parameters improved the BCI performance. We constructed a model of a biofeedback BCI system that could simulate experimental data and the effect of training. The simulation results implied that the improvement was achieved through a quicker adaptation rate in visual tracking gain and a larger synaptic gain from the visual tracking system to the thalamic reticular cells. In addition to the purpose of this study, the constructed biofeedback BCI model can also be used both to investigate the effects of different biofeedback paradigms and to test, estimate, or predict the performances of other newly developed BCI signal processing algorithms.