Nonlinear Energy Operator Research Articles

A Power-and-Area-Efficient Channel-Interleaved Neural Signal Processor for Wireless Brain-Computer Interfaces with Unsupervised Spike Sorting.

Next generation of wireless brain-computer-interface (BCI) devices require dedicated neural signal processors (NSPs) to extract key neurological information while operating within given power consumption and transmission bandwidth limits. Spike detection and clustering are important signal processing steps in neurological research and clinical applications. Computational-friendly spike detection and feature extraction algorithms are first systematically evaluated in this work. The nonlinear energy operator (NEO) and the first-and-second-derivative (FSDE) together with the 'perturbed' K-mean clustering achieve the highest accuracy performance. An NSP ASIC is implemented in a channel-interleaved architecture and the folding ratio of 16 leads to the minimum power-and-area product. As the result, the NSP consumes 2-μW power consumption and occupies 0.0057 mm2 for each channel in a 65-nm CMOS technology. The proposed system achieves the unsupervised spike classification accuracy of 92% and a data-rate reduction of 98.3%, showing the promise for realizing high-channel-count wireless BCIs.

Analysing heart rate variability in preterm infants: the effect of temporal adjustment of NN peaks and missing data.

The measurement of heart rate variability (HRV) in preterm infants provides important information on function to clinicians. Measuring the underlying electrocardiogram (ECG) in the neonatal intensive care unit is a challenge and there is a trade off between extracting accurate measurements of the HRV and the amount of ECG processed due to contamination. Knowledge on the effects of 1) quantization in the time domain and 2) missing data on the calculation of HRV features will inform clinical implementation. In this paper, we studied multiple 5 minute epochs from 148 ECG recordings on 56 extremely preterm infants. We found that temporal adjustment of NN peaks improves the estimate of the NN interval resulting in HRV features (m = 9) that are better correlated with age (median percentage increase in correlation of individual features: 0.2%, IQR: 0.0 to 5.6%; correlation with age predictor and age from 0.721 to 0.787). Improved (sub-sample) quantization of the NN intervals (via interpolation) reduced the overall value of HRV features (median percentage reduction in feature value: -1.3%, IQR: -18.8 to 0.0; m = 9), primarily through a reduction in the energy of high-frequency oscillations. HRV features were also robust to missing data, with measures such as mean NN, fractal dimension and the smoothed nonlinear energy operator (SNEO) less susceptible to missing data than features such as VLF, LF, and HF. Furthermore, age predictions derived from a combination of HRV measures were more robust to missing data than individual HRV measures.Clinical Relevance-Poor quantization in time when estimating the NN peak and the presence of missing data confound HRV measures, particularly spectral measures.

Abnormal discharge detection using adaptive neuro-fuzzy inference method with probability density-based feature and modified subtractive clustering

Abnormal discharge (AD) is a discharge mode in electroencephalogram (EEG) with sharp outlines. Lack of related open-access datasets and insufficient annotation hamper the development of AD detection, while cognitive neuroscience, clinical research and pilots’ neural screening demand stable and reliable AD detection methods. An adaptive neuro-fuzzy inference method for AD detection is proposed in this work. First, a probability-density-based (PD) method is proposed to extract lognormal amplitude features from EEG envelopes. Second, the subtractive clustering method (SCM) is modified so that clustering radii can adapt to cluster shapes for each dimension instead of using identical radii for each cluster. The outputs of modified SCM (mSCM), coordinates of cluster centers and adjusting rates for radius components are used to automatically initialize Gaussian membership functions of adaptive-network-based fuzzy inference system (ANFIS). Finally, we conducted multiple experiments to validate mSCM-based ANFIS, comparing it with traditional machine learning classifiers (support vector machines, multi-layer perceptrons, decision trees, and random forests) and the state-of-the-art deep learning-based time-series classification methods InceptionTime and Minirocket, using synthetic data, small-size datasets and a private EEG dataset. Results show that combining PD features with features proposed in previous studies, such as smoothed nonlinear energy operator features and discrete wavelet transform features, achieved higher accuracy (95.13 ± 0.86%) and recall (89.17 ± 3.06%) than other feature combinations. mSCM created more suitable cluster boundaries than SCM on small-size datasets, and its clustering results demonstrated potential in helping interpretation of classification rules built in the ANFIS network. Results of comparison experiments showed that mSCM-based ANFIS produced competitive results in accuracy and recall for AD detection, with lower computational cost, compared to the top 2 results obtained by InceptionTime and Minrocket.

Low-Power Energy-Based Spike Detector ASIC for Implantable Multichannel BMIs

Advances in microtechnology have enabled an exponential increase in the number of neurons that can be simultaneously recorded. To meet high-channel count and implantability demands, emerging applications require new methods for local real-time processing to reduce the data to transmit. Nonlinear energy operators are widely used to distinguish neural spikes from background noise featuring a good tradeoff between hardware resources and accuracy. However, they require an additional smoothing filter, which affects both area occupation and power dissipation. In this paper, we investigate a spike detector, based on a series of two nonlinear energy operators, and a simple and adaptive threshold, based on a three-point median operator. We show that our proposal provides good accuracy compared to other energy-based detectors on a synthetic dataset at different noise levels. Based on the proposed technique, a 1024-channel neural signal processor was designed in a 28 nm TSMC CMOS process by using latch-based static random-access memory (SRAM), demonstrating a total power consumption of 1.4 μW/ch and a silicon area occupation of 230 μm2/ch. These features, together with a comparison with the state of the art, demonstrate that our proposal constitutes an alternative for the development of next-generation multichannel neural interfaces.

Artefact-Suppressing Analog Spike Detection Circuit for Firing-Rate Measurements in Closed-Loop Retinal Neurostimulators

The aim of this research is to investigate low-power circuit concepts for the hardware implementation of an adaptively controlled stimulator for future retinal implants. For this specific application purpose, the circuit complexity must be low, while at the same time the functionality is extended. This paper presents the implementation of an analog spike detection circuit to detect spikes from extracellular recordings and to perform electrode individual firing-rate measurements in a spatially high-density electrode array, which has a reduced circuit complexity compared to the widely-used nonlinear energy operator (NEO) and allows stronger suppression of local oscillations following the retinal remodeling. The module is verified by emulating extracellular activities using the Hodgkin-Huxley model. This recording-unit is integrated into an eight-channel closed-loop-neurostimulator prototype. It dissipates <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$11.4 ~\mu \text{W}$ </tex-math></inline-formula> and requires an area of 0.066 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> by using a 350 nm CMOS process.

Analysis of out-of-breath speech for assessment of person’s physical fitness

In this work, a novel method is proposed for the assessment of a person’s physical fitness from out-of-breath speech using Gaussian posteriorgram. Based on physical fitness, we consider two categories of persons, physically-active and physically-non-active. A physically-active person is somebody who regularly does physical exercises like jogging, running, cycling, and playing sports. Out-of-breath speech is recorded from a person immediately after he/she undergoes jogging or physical exercise, and it contains higher breath-emission level than normal speech. It is expected that the breath-emission level will be different for physically-active people than the physically-non-active person in the out-of-breath speech. Due to this, speech characteristics of out-of-breath between physically-active and physically-non-active person categories may differ. To capture this variation, posteriorgram-based features are evaluated on Fourier parameters from out-of-breath speech. Performance is evaluated using recordings of out-of-breath speech from 30 persons. In terms of classification rate, the new feature shows an average classification rate of 91.7% using out-of-breath speech, and it outperforms linear prediction coefficients (LPC), mel frequency cepstral coefficients (MFCC) and non-linear Teager energy operator (TEO) based TEO-CB-Auto-Env features.

Cardiac Artifact Noise Removal From Sleep EEG Signals Using Hybrid Denoising Model

Sleep is one of the prime natural activities for human well-being in physical, emotional, and mental aspects. The assessment of sleep Electroencephalography (EEG) signals is required to diagnose sleep-related neurological disorders. It is found that sleep EEG signals are extremely vulnerable to highly energetic electrocardiogram (ECG) signals. The intermixing of ECG into EEG, commonly known as cardiac artifacts, might severely affect the sleep EEG data. In order to have artifact-free EEG signal, a hybrid signal denoising methodology which includes empirical wavelet transforms (EWT), adaptive threshold-based nonlinear Teager-Kaiser energy operator (TEO), and customized morphological filter in accompanying with modified ensemble average subtraction (MEAS) is proposed for automatic detection and suppression of cardiac artifact from a single-channel EEG. The efficacy of the proposed methodology presented in the paper has been evaluated over standard public datasets such as CinC Challenge 2014 dataset (synthetic), and MIT-BIH polysomnography data (clinical). It has been observed that the proposed method outperforms other state-of-the-art automated EEG artifact elimination methods in terms of few popular denoising performance indexes such as signal to artifact ratio, percentage root mean square difference, percentage distortion in power spectral density, structural similarity index measure, and execution time. The proposed method is robust, time-efficient, and preserves the majority of EEG data with minimal loss, making it suitable for neuro clinical EEG analysis.

Multidimensional Feature Optimization Based Eye Blink Detection Under Epileptiform Discharges.

Eye blink artifact detection in scalp electroencephalogram (EEG) of epilepsy patients is challenging due to its similar waveforms to epileptiform discharges. Developing an accurate detection method is urgent and critical. In this paper, we proposed a novel multi-dimensional feature optimization based eye blink artifact detection algorithm for EEGs containing rich epileptiform discharges. An unsupervised clustering algorithm based on smoothed nonlinear energy operator (SNEO) and variational mode extraction (VME) is proposed to detect epileptiform discharges in the frontal leads. Then, multi-dimensional time/frequency EEG features extracted from forehead electrodes (FP1 and FP2 channels) combining with the improved VME (IVME) threshold are derived for EEG representation. A variance filtering method is further applied for discriminative feature selection and a machine learning model is finally learned to perform detection. Experiments on EEGs of 16 subjects from the Children's Hospital of Zhejiang University School of Medicine (CHZU) show that our method achieves the highest average sensitivity, specificity and accuracy of 95.04, 89.52, and 93.01, respectively. That outperforms 5 recent and state-of-the-art (SOTA) eye blink detection algorithms. The proposed method is robust in eye blink artifact detection for EEGs containing high-frequency epileptiform discharges. It is also effective in dealing with individual differences in EEGs, which is usually ignored in conventional methods.

A Low Power 1024-Channels Spike Detector Using Latch-Based RAM for Real-Time Brain Silicon Interfaces

High-density microelectrode arrays allow the neuroscientist to study a wider neurons population, however, this causes an increase of communication bandwidth. Given the limited resources available for an implantable silicon interface, an on-fly data reduction is mandatory to stay within the power/area constraints. This can be accomplished by implementing a spike detector aiming at sending only the useful information about spikes. We show that the novel non-linear energy operator called ASO in combination with a simple but robust noise estimate, achieves a good trade-off between performance and consumption. The features of the investigated technique make it a good candidate for implantable BMIs. Our proposal is tested both on synthetic and real datasets providing a good sensibility at low SNR. We also provide a 1024-channels VLSI implementation using a Random-Access Memory composed by latches to reduce as much as possible the power consumptions. The final architecture occupies an area of 2.3 mm2, dissipating 3.6 µW per channels. The comparison with the state of art shows that our proposal finds a place among other methods presented in literature, certifying its suitability for BMIs.

Novel feature representation using single frequency filtering and nonlinear energy operator for speech emotion recognition

In this paper, the intrinsic characteristics of speech modulations are estimated to propose the instant modulation spectral features for efficient emotion recognition. This feature representation is based on single frequency filtering (SFF) technique and higher order nonlinear energy operator. The speech signal is decomposed into frequency sub-bands using SFF, and associated nonlinear energies are estimated with higher order nonlinear energy operator. Then, the feature vector is realized using cepstral analysis. The high-resolution property of SFF technique is exploited to extract the amplitude envelope of the speech signal at a selected frequency with good time-frequency resolution. The fourth order nonlinear energy operator provides noise robustness in estimating the modulation components. The proposed feature set is tested for the emotion recognition task using the i-vector model with the probabilistic linear discriminant scoring scheme, support vector machine and random forest classifiers. The results demonstrate that the performance of this feature representation is better than the widely used spectral and prosody features, achieving detection accuracy of 85.75%, 59.88%, and 65.78% on three emotional databases, EMODB, FAU-AIBO, and IEMOCAP, respectively. Further, the proposed features are found to be robust in the presence of additive white Gaussian and vehicular noises.

CVAR-Seg: An Automated Signal Segmentation Pipeline for Conduction Velocity and Amplitude Restitution.

BackgroundRate-varying S1S2 stimulation protocols can be used for restitution studies to characterize atrial substrate, ionic remodeling, and atrial fibrillation risk. Clinical restitution studies with numerous patients create large amounts of these data. Thus, an automated pipeline to evaluate clinically acquired S1S2 stimulation protocol data necessitates consistent, robust, reproducible, and precise evaluation of local activation times, electrogram amplitude, and conduction velocity. Here, we present the CVAR-Seg pipeline, developed focusing on three challenges: (i) No previous knowledge of the stimulation parameters is available, thus, arbitrary protocols are supported. (ii) The pipeline remains robust under different noise conditions. (iii) The pipeline supports segmentation of atrial activities in close temporal proximity to the stimulation artifact, which is challenging due to larger amplitude and slope of the stimulus compared to the atrial activity.Methods and ResultsThe S1 basic cycle length was estimated by time interval detection. Stimulation time windows were segmented by detecting synchronous peaks in different channels surpassing an amplitude threshold and identifying time intervals between detected stimuli. Elimination of the stimulation artifact by a matched filter allowed detection of local activation times in temporal proximity. A non-linear signal energy operator was used to segment periods of atrial activity. Geodesic and Euclidean inter electrode distances allowed approximation of conduction velocity. The automatic segmentation performance of the CVAR-Seg pipeline was evaluated on 37 synthetic datasets with decreasing signal-to-noise ratios. Noise was modeled by reconstructing the frequency spectrum of clinical noise. The pipeline retained a median local activation time error below a single sample (1 ms) for signal-to-noise ratios as low as 0 dB representing a high clinical noise level. As a proof of concept, the pipeline was tested on a CARTO case of a paroxysmal atrial fibrillation patient and yielded plausible restitution curves for conduction speed and amplitude.ConclusionThe proposed openly available CVAR-Seg pipeline promises fast, fully automated, robust, and accurate evaluations of atrial signals even with low signal-to-noise ratios. This is achieved by solving the proximity problem of stimulation and atrial activity to enable standardized evaluation without introducing human bias for large data sets.

Comparison of Sneo-Based Neural Spike Detection Algorithms for Implantable Multi-Transistor Array Biosensors

Real-time neural spike detection is an important step in understanding neurological activities and developing brain-silicon interfaces. Recent approaches exploit minimally invasive sensing techniques based on implanted complementary metal-oxide semiconductors (CMOS) multi transistors arrays (MTAs) that limit the damage of the neural tissue and provide high spatial resolution. Unfortunately, MTAs result in low signal-to-noise ratios due to the weak capacitive coupling between the nearby neurons and the sensor and the high noise power coming from the analog front-end. In this paper we investigate the performance achievable by using spike detection algorithms for MTAs, based on some variants of the smoothed non-linear energy operator (SNEO). We show that detection performance benefits from the correlation of the signals detected by the MTA pixels, but degrades when a high firing rate of neurons occurs. We present and compare different approaches and noise estimation techniques for the SNEO, aimed at increasing the detection accuracy at low SNR and making it less dependent on neurons firing rates. The algorithms are tested by using synthetic neural signals obtained with a modified version of NEUROCUBE generator. The proposed approaches outperform the SNEO, showing a more than 20% increase on averaged sensitivity at 0 dB and reduced dependence on the neuronal firing rate.

FPGA Design Integration of a 32-Microelectrodes Low-Latency Spike Detector in a Commercial System for Intracortical Recordings

Numerous experiments require low latencies in the detection and processing of the neural brain activity to be feasible, in the order of a few milliseconds from action to reaction. In this paper, a design for sub-millisecond detection and communication of the spiking activity detected by an array of 32 intracortical microelectrodes is presented, exploiting the real-time processing provided by Field Programmable Gate Array (FPGA). The design is embedded in the commercially available RHS stimulation/recording controller from Intan Technologies, that allows recording intracortical signals and performing IntraCortical MicroStimulation (ICMS). The Spike Detector (SD) is based on the Smoothed Nonlinear Energy Operator (SNEO) and includes a novel approach to estimate an RMS-based firing-rate-independent threshold, that can be tuned to fine detect both the single Action Potential (AP) and Multi Unit Activity (MUA). A low-latency SD together with the ICMS capability, creates a powerful tool for Brain-Computer-Interface (BCI) closed-loop experiments relying on the neuronal activity-dependent stimulation. The design also includes: A third order Butterworth high-pass IIR filter and a Savitzky-Golay polynomial fitting; a privileged fast USB connection to stream the detected spikes to a host computer and a sub-milliseconds latency Universal Asynchronous Receiver-Transmitter (UART) protocol communication to send detections and receive ICMS triggers. The source code and the instruction of the project can be found on GitHub.

A new method for accurate detection of movement intention from single channel EEG for online BCI

Low frequency readiness potential (RP) is elicited in electroencephalograms (EEGs) as one intends to perform an imagery (IMI) or real movement (RMI). While in most brain-computer-interface (BCI) applications the challenge is to classify RPs of different limbs from the given EEG trials, the objective of this study is fast and automatic detection of RPs from the entire single channel EEG signal. The proposed algorithm has two threshold blocks based on the nonlinear Teager-Kaiser energy operator (TEO) in the first block and the morphological properties of the RP waveform as constraints in the second block. The performance is strongly influenced by the abrupt energy changes due to transients and artefacts. As the major contribution, the proposed nonlinear convex optimization algorithm enables separation of transients from low frequency components by providing a fast thresholding mechanism. Application of the proposed method to Physionet RMI dataset, BCI competitionIV-1 IMI dataset and our own left hand movement datasets of healthy subjects led to true positive rates (TPRs) of 76.5±8.27%, 83.85±11.4%, and 81.1±5.23%, number of FPs/min of 2.4±1.07, 1.4±0.7, and 1.6±0.69 and accuracy rates of 85.4±3.83%, 90±3.56%, and 91.2±2.04%. Movement onset detection latency from our automatic RP detector was -384.9±296.5 ms.As a conclusion, the proposed method outperforms state-of-the-art techniques using as low as single channel EEG making it suitable for real-time neuro-rehabilitation of paralyzed subjects suffering from stroke.

Eye Blink Artifact Detection With Novel Optimized Multi-Dimensional Electroencephalogram Features.

Accurate eye blink artifact detection is essential for electroencephalogram (EEG) analysis and auxiliary analysis of nervous system diseases, especially in the presence of the frontal epileptiform discharges. In this paper, we develop a novel eye blink artifact detection algorithm based on optimally selected multi-dimensional EEG features. Specific efforts have been paid to filtering the frontal epileptiform discharges, where an unsupervised learning exploiting the EEG signal physiological characteristics and smooth nonlinear energy operator (SNEO) based on the K-means clustering has been firstly proposed. Multiple statistical EEG features derived from the frontal electrodes and other electrodes are then extracted to characterize eye blink artifacts. Discriminative feature selection scheme based on the variance filtering and Relief algorithms has been respectively studied, and the average correlation coefficient (ACC) is applied for feature optimization evaluation. The eye blink artifact detection is finally achieved based on the support vector machine (SVM) trained on the optimized EEG features. The effectiveness of the proposed algorithm is demonstrated by experiments carried out on the EEG database of 11 subjects recorded from the Children's Hospital, Zhejiang University School of Medicine (CHZU). Comparisons to several state-of-the-art (SOTA) eye blink artifact detection methods are also presented.

Evaluation of In Vivo Spike Detection Algorithms for Implantable MTA Brain—Silicon Interfaces

This work presents a comparison between different neural spike algorithms to find the optimum for in vivo implanted EOSFET (electrolyte–oxide-semiconductor field effect transistor) sensors. EOSFET arrays are planar sensors capable of sensing the electrical activity of nearby neuron populations in both in vitro cultures and in vivo experiments. They are characterized by a high cell-like resolution and low invasiveness compared to probes with passive electrodes, but exhibit a higher noise power that requires ad hoc spike detection algorithms to detect relevant biological activity. Algorithms for implanted devices require good detection accuracy performance and low power consumption due to the limited power budget of implanted devices. A figure of merit (FoM) based on accuracy and resource consumption is presented and used to compare different algorithms present in the literature, such as the smoothed nonlinear energy operator and correlation-based algorithms. A multi transistor array (MTA) sensor of 7 honeycomb pixels of a 30 μm2 area is simulated, generating a signal with Neurocube. This signal is then used to validate the algorithms’ performances. The results allow us to numerically determine which is the most efficient algorithm in the case of power constraint in implantable devices and to characterize its performance in terms of accuracy and resource usage.

ACTIVITY COMMAND ENCODING OF CEREBRAL CORTEX M1-EVOKED POTENTIALS OF THE SPRAGUE DAWLEY RAT USING TIME DELAY NEURAL NETWORKS

Understanding the neurons that transmit messages in the brain while we thinking, feeling, or acting is critical for research on the causes of neurological disease and treatment strategies. This research focuses on the primary motor cortex M1 region, which is involved in human motor function as an activity command center. Understanding this region can help us to determine the mechanism of movement control by the brain, with applicability to other activity mechanisms. A time delay neural network (TDNN) is a suitable model for studying brain signals. TDNN can analyze comprehensive information for a period of successive signals, which is similar to the transmission mechanism of the M1 region. Therefore, this study used a TDNN to build a three-stage encoding system corresponding to the signal type, type arrangement, and time sequence of the brainwave signal from the M1 region and the encoded results were defined as codes, symbols, and commands, respectively. This study aimed to understand the relationship between movement and the M1 region by decoding the signal when the rat undertakes an action. First, we recorded the M1 signal from three rat action types (walk, stand up, and shift head) and performed signal processing. This included using a nonlinear energy operator to find the response points of each action signal. The signals were separated into several sections according to the response time points and independent component analysis was then used to extract the features of the signal (the signal of interest). Finally, we found 16 representative sample signals through a dynamic dimension increasing algorithm to train a three-stage TDNN. We then input the remaining feature signals of interest into the three-stage TDNN for encoding and classification. The results showed an accuracy rate for the three actions of 51.4%, 80.0%, and 54.3%, which means that it is feasible to explain the brain signal of M1 from the free-moving animal using a three-stage TDNN encoding model.

New algorithm based on group sparsity for correcting wideband noise in ECG recordings

A new algorithm for denoising ECG data contaminated by wideband noise signals (e.g., muscle artifacts and instrumentation noise) is proposed in this paper. In contrast to the wideband noise, a clean ECG signal s(t) has the property that its pth order difference sp(t) (with p≥3) and the nonlinear energy operator h(t) associated with it are both group-sparse signals that have common support, which coincides with that of the QRS-complex. Accordingly, the main idea of the proposed algorithm is to estimate the clean ECG signal s(t) by encouraging the group sparsity of both sp(t) and h(t), and also encouraging their supports to coincide with that of the QRS-complex. A modified partial whitening technique is also proposed in this paper to handle the practical situations of having colored noise. The proposed algorithm depends on two regularization parameters, and their values are selected automatically in the proposed algorithm. Simulation results on real and simulated ECG data show that the proposed algorithm can be successfully utilized to denoise ECG data contaminated by wideband noise signals. In addition, the proposed algorithm is also shown to produce significantly improved results compared to existing techniques used for performing similar tasks.

Instantaneous modal identification under varying structural characteristics: A decentralized algorithm

One of the latest trends in structural health monitoring involves the use of wireless decentralized sensing systems, developed to reduce costs and speed up the whole monitoring process. The main purpose of this paper is to present a novel decentralized procedure for the instantaneous modal identification of time-varying structures, also suitable in the presence of environmental variations and non-stationary ambient excitation. In particular, a modal assurance criterion (MAC)-based clustered filter bank (CFB) is obtained, capable of decomposing structural responses into modal components for the evaluation of time-varying natural frequencies and modal shapes through a nonlinear energy operator. The proposed algorithm is relatively simple and usable with low-cost smart sensing systems, as it requires low computational effort and works with few data at a time. To prove the effectiveness of the presented method, a simulated near-real-time modal identification procedure has been performed on a full-scale bridge under progressive damage scenarios. The estimated modal parameters have then been used for damage diagnosis. The results reveal a good correspondence between identified modal parameters and reference values, showing also promising outcomes for both damage detection and localization.

Charge-Redistribution Based Quadratic Operators for Neural Feature Extraction.

This paper presents a SAR converter based mixed-signal multiplier for the feature extraction of neural signals using quadratic operators. After a thorough analysis of design principles and circuit-level aspects, the proposed architecture is explored for the implementation of two quadratic operators often used for the characterization of neural activity, the moving average energy (MAE) operator and the nonlinear energy operator (NEO). Programmable chips for both operators have been implemented in a HV-180nm CMOS process. Experimental results confirm their suitability for energy computation and action potential detection and the accomplished area×power performance is compared to prior art. The MAE and NEO prototypes, at a sampling rate of 30kS/s, consume 116nW and 178nW, respectively, and digitize both the input neural signal and the operator outcome, with no need for digital multipliers.