Complete neural signal processing and analysis: Zero to hero

Explore the origins, advantages, and limits of EEG as a noninvasive tool, including how scalp electrodes capture synchronized large-scale neural activity and its rich temporal dynamics.

Explore practical preprocessing steps for neural signal data, including importing data into Matlab, filtering, epoching, baseline correction, trial rejection, electrode referencing, and ICA cleanup.

Apply independent components analysis (ica) to clean EEG data, identify blink and EMG artifacts, and decide which components to remove while preserving brain signal.

Learn to identify and clean EEG data by removing artifacts, using visual rejection, ICA for eye blink removal, selective interpolation, and edge management.

Explore topographical mapping for visualizing EEG activity across the scalp with interpolation between electrodes. Understand electrode labeling, montage conventions, and the difference between flat maps and head plots.

Introduce the event related potential (ERP) as a time-domain analysis in cognitive electrophysiology, and contrast its simple computation with time-frequency analysis that reveals phase-locked and non phase locked activity.

Apply rhythm-based spectral analysis to brain signals, distinguishing phase locked and non phase locked, evoked and induced activities, and using trial-based time-frequency powers to reveal rhythmic neural activity.

Learn the basics of spectral analysis and time-frequency plots, and apply a five-step plan to interpret results from the Fourier-based power spectrum to experiment design and statistics.

Present two empirical datasets: a human EEG with 64 electrodes during a color circle task, and a mouse cortex recording with 16 depths in V1, using a checkerboard stimulus.

Explore MATLAB scripts to load and inspect a 64-channel EEG dataset, identify data structure fields, and compute ERP and topographical maps for time-domain analysis.

Load the MATLAB V1 laminar dataset, clear the workspace, and inspect a 16-channel, 1,527-time-point current source density. Plot channel 7 ERP and a depth-by-time contour to visualize gamma activity.

Access the EEG data set, the V1 laminar data set, and the simulated data for this course. Note caveats of free data: incomplete data, poor documentation, and missing metadata.

Learn to simulate biophysically and cognitively constrained neural data to evaluate analysis methods, exploring white and pink noise, stationary and nonstationary signals, and Gaussian–based transients.

The lecture introduces the problem set structure with MATLAB code, eight challenges, and the separate problem and solution scripts, plus two videos solving problems 1–4 and 5–8.

Learn to simulate EEG time series data in EEG Lab format, visualize with plotts, and compare white and pink noise, plus phase locked and non phase locked signals.

We simulate realistic EEG-like data by shaping random frequency-domain coefficients with Gaussian tapers to produce narrowband, non stationary signals, then explore transients, phase locking, and pink noise in time-frequency analysis.

Investigate the Planck length, neuron, and observable universe to compare spatial scales across around 30 orders of magnitude and reveal the surprising mid-scale position of a brain cell.

Explore why simulating neural data tests data analysis methods and constrains models by biology, providing ground-truth validation, robustness to noise, and deeper intuition for brain signals.

Generate white and pink noise using Gaussian and uniform distributions, adjust with shift and stretch, and synthesize pink noise via frequency-domain shaping and inverse Fourier transform in Matlab.

Explore three equations in time series analysis—the sine wave, the Gaussian, and Euler's formula—and learn how their parameters (amplitude, frequency, phase, center, width) drive simulations, spectral analysis, and synchronization analyses.

Learn to simulate brain-like narrowband, non-stationary signals by filtering noise in the frequency domain, applying a Gaussian spectrum, and using inverse Fourier transform to observe bandwidth effects.

Learn to create transient oscillations by multiplying a gaussian envelope with a sine or cosine, generating Morleigh wavelets for time-frequency analysis and EEG data simulation.

Explore the eeglab eeg structure, including data layout (channels by time by trials), key fields such as data and channel locations, and event related potentials (erp) computation.

Learn to simulate channel-level EEG data in matlab by generating sine waves and noise across channels, trials, and time, plotting ERP and time–frequency results, and exploring phase-locked versus non-phase-locked signals.

Explore solving project one with simulated neural signals, using random phase offsets and non phase-locked sine waves, and compare ERP time-domain and time-frequency analyses to illustrate limitations.

Simulate brain activity by generating signals at dipoles, then project them onto the scalp using the lead field and gain matrices across 64 channels, illustrating dipole orientation and topography.

Simulate dipole-level EEG data and project it to the scalp, using the preloaded 64-channel data structure to explore signal amplitude, noise, and dipole topographies.

Study practical neural signal simulations by generating sine waves over many trials with noise, and explore dipole projections onto the scalp via lead fields, including cross-dipole contamination.

Learn about event-related potentials (ERPs) as time-domain neural signals, showing how trial averaging reveals the signal amid noise, with simulation and 16-channel V1 data.

Study low-pass filtering of event-related potentials to emphasize low-frequency components using an FBAR filter with a 20 Hz cutoff, comparing ERP averaging, trial-wise filtering, and a super-trial approach.

Compute the common average reference for scalp EEG by subtracting the mean across channels, referencing to ear lobe data, and compare double-loop and vectorized methods with deal.

Explore butterfly plots and topographical variance time series to quantify scalp energy, compare ear lobe and average references, and relate variance to root mean square in EEG data.

Plot topographies over time from EEG data and convert milliseconds to indices for time selection. Compare time-point topographies with time-window averaged maps, and explore color limits and average reference options.

Simulate two dipole sources to generate ERP-like neural signals and project them to the scalp, analyzing channel mixing and spatial source separation to understand electrode projections.

Quantify ERP features by computing peak to peak and mean around the peak measures from both unfiltered and low-pass filtered ERP, using time windows and robust averaging to compare results.

Master neural signal processing through a peak-to-peak ERP solution and extracting peak times. Learn double-precision filtering, a low-pass sink function, and a hand window to produce robust peak estimates.

Identify peak latency for each channel in the 100–400 ms window to create ERP peak-latency topoplots; repeat on the low-pass filtered ERP (15 Hz) and compare fronto-central differences.

Load data, set time boundaries in milliseconds, convert to indices, compute ERP peaks across channels with max, and compare unfiltered versus 15 Hz windowed filtered ERPs with topographical maps.

Explore self-accountability in online learning and how motivation governs progress, balancing the benefits of accessible, repeatable lectures with the challenge of minimal external accountability.

Explore how time and frequency domains reveal spectral features of time series, perform spectral analyses, and build intuition for the Fourier transform from sine waves, complex numbers, and dot products.

Explore sine waves by examining amplitude, frequency, and phase, and see how changing each parameter reshapes the wave and its energy for data analysis and orthogonality of sine and cosine.

Build and analyze sine waves in MATLAB by summing multiple waves with defined frequencies, amplitudes, and phases at a 1000 Hz sampling rate, then fix code and explore parameter recovery.

Explore complex numbers by extending the real line to the complex plane, describing magnitude and phase, and linking conjugates to the power of Fourier coefficients.

Uncover Euler's formula e^(iθ) = cos θ + i sin θ on the unit circle and extend it with magnitude to connect to Fourier coefficients, amplitude, and phase.

Explore creating complex numbers in MATLAB, extract real and imaginary parts, and apply Euler's formula to plot magnitude and phase on the complex plane.

Explore the dot product as a scalar mapping between two equal-length vectors, illustrated by its algebraic formula and geometric meaning, including orthogonal and linear cases.

Explore how to compute the dot product in Matlab between a signal and a series of sine waves, comparing element-wise multiplication and dot(), and noting phase effects on the spectrum.

Embed sine waves in complex numbers with Euler's formula e^{i(2 pi f t + theta)} to form complex sine waves; visualize 3d corkscrew of time, real, and imaginary parts, theta=0.

Create a complex sine wave in MATLAB using Euler's formula, and visualize it in 2D and 3D with real and imaginary parts, plot3, and phase rotation.

Learn how to compute the complex dot product between complex vectors by element-wise multiplication and summation, then extract magnitude and phase from the real and imaginary parts.

Demonstrate the complex dot product and its magnitude with complex valued sine waves. Show phase invariance and how this relates to the Fourier transform, contrasting with real valued sine waves.

Explore how the Fourier coefficients arise from correlating a signal with complex sine waves, producing amplitude and phase spectra across frequencies, including the DC component.

Learn how MATLAB code implements the discrete-time Fourier transform on a multi-sine signal, using a normalized time vector, frequency in Hz, and amplitude spectrum versus FFT, with Nyquist notes.

Explore Fourier coefficients as complex numbers, visualize them on the complex plane with a polar plot, and extract amplitude, power, and phase from real and imaginary parts.

Convert Fourier indices to hertz, define the lower and upper frequency bounds, and understand Nyquist frequency and frequency resolution; recognize the DC component and aliasing in sampling.

Explore positive and negative frequencies in the Fourier transform, including why a real-valued signal yields a mirrored spectrum around Nyquist and how the DC component remains on the left.

Learn how to correctly scale Fourier coefficients to recover original units, using division by n and doubling positive frequencies for real signals, while understanding zero and Nyquist handling.

Explore MATLAB implementation of complex sine waves for the positive/negative spectrum and apply two amplitude normalization factors to correctly scale Fourier coefficients, including handling DC mean and mean offsets.

Examine resting-state EEG with spectral analysis, converting time-domain data to amplitude and power spectra. Observe 1/f decline, 50 Hz line noise, and alpha activity near 10 Hz.

Perform spectral analysis on resting-state EEG data in MATLAB to quantify alpha power (8–12 Hz) across epochs and create a scalp topography of average power.

Explain the Fourier transform as a lossless, exact time-to-frequency domain conversion, using statistics and linear algebra perspectives to show no information is lost.

Explore how the inverse Fourier transform reconstructs time-domain signals from frequency-domain coefficients and why pairing forward and inverse transforms enables spectral filtering and faster analysis via the convolution theorem.

Learn how to implement the inverse Fourier transform in code with a loop to reconstruct a time-domain signal from forward Fourier coefficients, including normalization and small rounding errors.

Zero padding increases frequency resolution by appending zeros to the signal end, while keeping the sampling rate fixed; use it to target frequencies, smooth spectra, and align convolution lengths.

Explore how sampling rate and signal length set temporal and frequency resolution in the Fourier transform, and examine zero padding's effect on spectrum via FFT.

Learn how estimation errors from noisy measurements affect Fourier coefficients of brain signals. Explore how amplitude and phase relate under uncertainty, noting phase independence except when amplitude is zero.

Explore nonstationary signals and why Fourier transform results, including the amplitude spectrum, are only easily interpretable for stationary data, with time-frequency analyses and brain signal examples.

Explore how sharp nonstationarities in time-domain signals distort the power spectrum via the Fourier transform, using abrupt amplitude and frequency transitions.

Explore how non-stationary signals affect power and amplitude spectra, using amplitude and frequency modulation and chirps to illustrate harmonics. The lecture contrasts stationary versus non-stationary signals and motivates time-frequency analyses.

Explore Welch's method for smooth spectral decomposition of non stationary signals, comparing it with the full FFT, using windowing, tapering, and averaging to reveal robust, time-averaged power spectra.

Apply Welch's method to phase-slip data using overlapping windows and tapering to estimate the spectrum, illustrating non-stationarity and how phase flips affect the 10 Hz component.

Learn how to apply Welch's method to resting-state EEG data in MATLAB, comparing manual implementation with pwelch, and explore window length, overlap, and linear versus dB power spectra.

Apply Welch's method to the V1 LFG laminar dataset in MATLAB, exploring single versus double precision data, computing the power spectrum with pwelch, and examining gamma activity around 40–60 Hz.

Walk through eight problems on spectral analyses of real and simulated neural data, comparing time-domain and fft power spectra and contrasting trial-averaged vs single-trial gamma activity.

Develop a discrete time Fourier transform from scratch, compare with the FFT, and analyze zero padding, power spectra, and frequency-domain filtering for 50 Hz line noise.

Program the Fourier transform from scratch by looping frequencies, constructing a complex sine wave via Euler's formula, computing the dot product with the signal, and normalizing by N.

Program the inverse Fourier transform from scratch by building template sine waves per frequency, multiplying by Fourier coefficients, and summing to reconstruct the signal, then compare to Matlab’s inverse.

Explore spectral analysis to separate two overlapping EEG dipole signals, revealing distinct 9 Hz and 14 Hz components even when time-domain signals are inseparable.

Study stationary and non-stationary signals and their Fourier spectra to learn how amplitude changes affect the spectrum. See why non-stationarity broadens energy and why narrow filters may miss key features.

Analyze resting state EEG using FFT and Welch's method with windowed segments, tapering, and overlap to estimate stable power spectra, highlighting alpha rhythm and nonstationarity.

Explore tapering as a pre processing step in spectral analyses, using Gaussian, Hann, and Hamming windows to reduce edge effects and influence the power spectrum, and consider when it's needed.

Extract average power from a frequency band by converting Hz boundaries to indices and averaging the power spectrum within that band, enabling comparisons across channels or conditions.

Compute the Fourier-based power spectrum for each trial and for the ERP-based trial average, then compare to reveal non phase-locked versus phase-locked activity across time windows.

Compute channel power spectra to separate two nearby brain dipole sources using spectral features, generate topographical power maps, and quantify fit to the ground truth dipole projections with r-squared.

Review and implement project 3-1 solutions by computing the FFE across EEG channels, extracting spectral power in defined windows, and assessing fit with correlation and R-squared, with Matlab tips.

Compute alpha to theta power ratio per electrode in two windows (−800 to 0 ms, 0 to 800 ms) using 3–8 Hz theta and 8–13 Hz alpha, and map topographically.

Walks through solving a neural time series analysis project in Matlab, extracting theta and alpha power. Includes building a power spectrum, upsampling, frequency bins, and comparing pre and post ratios.

Discover Morlet wavelet convolution for time-frequency analysis of non-stationary neural signals, and how Gaussian tapering creates a Gaussian frequency spectrum.

Experiment with Morleigh wavelets in Matlab by simulating the wavelets, visualizing their time and frequency domains, and adjusting parameters like frequency and full width at half maximum for convolution analysis.

Discover how time-domain convolution blends a signal with a kernel via sliding dot products, and compare with frequency-domain convolution through the convolution theorem, including padding, edge effects, and kernel flipping.

Learn time-domain convolution in Matlab by building Gaussian kernels with unit energy, applying them to signals to visualize smoothing, and exploring full versus same padding and edge-detection kernels.

Explore the convolution theorem, linking time-domain convolution to frequency-domain multiplication, and see why Morleigh Wavelet Convolution enables time-frequency analysis.

Implement the convolution theorem in MATLAB by spectral multiplying the signal and kernel, using zero padding, a Fourier transform, and inverse transform, then trim wings to match MATLAB's conv results.

Convolve real data with a Gaussian in Matlab to smooth the ERP and examine how full width at half maximum shapes the spectrum and temporal precision.

Explore MATLAB-based complex Morlet wavelets in time and frequency domains, constructing a complex sine with a Gaussian window and visualizing its real and imaginary parts and spectrum.

Learn complex Morleigh wavelet convolution with complex-valued kernels. Extract amplitude, phase, and power from complex coefficients to build time-frequency plots and Narrabeen filtered signals, and explore phase synchronization.

Learn practical convolution tips to boost time-frequency analysis efficiency in neural signals by concatenating trials, minimizing redundant fft computations, and leveraging wavelets for faster computation.

Explore MATLAB-based complex Morlet wavelet convolution to perform time-frequency analysis of signals, including spectrum normalization, power envelopes, phase dynamics, and phase slips.

perform wavelike convolution across all trials in Matlab using a complex Morlet wavelet, reshape data to time by trial, and average across 200 trials to reveal time-frequency power.

Create a full time-frequency power plot in MATLAB by applying Morlet wavelet convolution, computing the spectrum, and averaging power across trials to reveal gamma dynamics.

Learn to assess phase consistency across trials by averaging unit vectors in the complex plane using Euler's formula, revealing intertrade phase clustering in neural signals.

Explore inter-trial phase clustering (ITPC/ITC) and how to interpret phase-locking results in time-frequency data, including robustness to trial count, temporal jitter, and its relation to the ERP.

Learn MATLAB ITPC by visualizing inter trial phase clustering from simulated to real data, computing average vector magnitude from phase angles, and exploring Morleigh wavelets in time frequency analysis.

Explore how Morlet wavelets balance temporal and frequency precision through the number of cycles, shaping the time-frequency trade-off in EEG data analysis.

Examine how the Morleigh wavelet's number of cycles shapes the time-frequency trade-off in EEG analysis, comparing 2, 6, 8, and 15 cycles with baseline normalization.

Explain how wavelet convolution interpretation hinges on stationarity within the wavelet's time window. Relate window width and cycle count to the data's non-stationarity in brain signals.

Explore the one over f structure in spectral brain dynamics, its impact on short time frequency features, and how decibel normalization and baseline corrections help reveal fast brain responses.

Discover baseline normalization of time-frequency power using decibels to compare across individuals and frequencies. Learn how to select a baseline window that precedes stimulus onset and enhances interpretability.

Demonstrates MATLAB baseline normalization of time-frequency plots using multiple baseline windows, exploring wavelet convolution and decibel normalization across 2–30 Hz for data.

Explore scale-free brain dynamics through detrended fluctuation analysis (DFA), revealing long-range temporal correlations and criticality by mapping RMS scaling with log-log plots across multiple time scales.

load the dfa data and apply the filter hilbert method, compare to morley wavelet output, and compute the detrended fluctuation exponent across scales for 1–40 hz.

Explore four time-frequency analysis methods, with a focus on the filter-Hilbert approach. Learn how the Hilbert transform creates an analytic signal, magnitude, and phase after narrowband FIR filtering.

In MATLAB, design a 20–25 Hz fbar filter, apply it to random noise, compare spectra, then use the Hilbert transform to extract magnitude and phase of the signal.

Explore the short time Fourier transform for time frequency analysis by sliding a tapered window across the signal to build a time frequency plane, balancing window size, overlap, and resolution.

Explore the short time Fourier transform by using a chirp signal and MATLAB spectrogram to reveal its time-frequency evolution, with windowing, overlap, and zero padding.

Compare Morleigh wavelet convolution, the filter Hilbert method, and the short-time Fourier transform for time-frequency analysis and learn that, with proper parameters, they yield highly similar results.

The multi-taper method uses discrete prolate spheroidal tapers to robustly estimate power spectra by averaging across multiple tapered time series, smoothing the spectrum and highlighting broad time-frequency features.

Learn how to perform within-subject, cross-trial regression on EEG data using the general linear model and least squares, linking trial-by-trial brain activity to behavior.

Explore cross-trial regression using linear least squares on EEG power. Relate trial-wise EEG frequencies to reaction time and interpret beta coefficients via time-frequency maps.

Define temporal resolution and temporal precision; show that wavelet convolution preserves temporal resolution but reduces temporal precision; advocate downsampling the time-frequency results to save space without losing information.

Demonstrates downsampling time-frequency results from a complex Morlet wavelet convolution (10–100 Hz) for one V1 channel, comparing full temporal resolution with 40 Hz downsampled maps in MATLAB.

Explore MATLAB approaches to linear versus logarithmic frequency scaling by building and comparing plots of linearly spaced and log spaced frequencies from 10 to 100.

Learn to separate phase locked and non phase locked EEG components by subtracting the ERP from the total signal and analyzing time-frequency power.

Explore MATLAB time-frequency analysis of EEG by separating total and non-phase-locked components into phase-locked power and ERP-based non-phase-locked power using wavelet convolution and baseline normalization.

Prevent edge effects in time-frequency EEG analysis by using buffer zones and, if needed, clipping unused data, ensuring artifacts do not contaminate target epochs.

Solve a time-frequency analysis problem set using complex Morlet wavelets to compute power and phase from 10–100 Hz data, and visualize depth-by-time gamma patterns.

Explore time-frequency analysis of a square wave and boxcar impulse, study edge effects, and learn how Morlet wavelets shape power and phase spectra.

Explore time-frequency analysis by comparing complex wavelet convolution and filter Hilbert on ERP data, tune parameters, and assess how spectra align at 42 hertz before Welch-style fast Fourier transform comparison.

Explore time-frequency analysis with wavelet convolution by constructing a family of complex morleigh wavelets, combining sine waves with gaussian envelopes across 2-54 Hz, with real and imaginary parts and magnitude.

Create a nonlinear chirp from 5 to 17 Hz and perform time-frequency analysis with a lipless distribution using wavelet convolution to reveal instantaneous frequency and power changes over time.

Compare wavelet-derived spectrum and the fast Fourier transform using a non-stationary chirp; show how time-frequency analysis, averaged over time, approximates the FFT while trading temporal precision for spectral detail.

Explore the limits of wavelet convolution when two close frequencies are hard to separate in time-frequency analysis. See how wavelet width trades temporal precision for spectral precision using simulated data.

Perform time-frequency power analyses on multitrial EEG data by computing single-trial spectra with wavelets and then averaging power across trials.

Compare baseline normalization methods for time-frequency power, including decibel and percent change, using simulated data and EEG examples to reveal their similarities, differences, and baselining effects.

Explore how wavelet parameters shape real EEG analysis by varying the Gaussian width and the number of cycles in Morleigh wavelets, balancing temporal and spectral precision in time-frequency power analysis.

Explore how varying Morlet wavelet parameters affects time-frequency power in simulated data, comparing ground-truth signals with amplitude envelopes and highlighting the trade-off between temporal and spectral precision.

Explore inter-trial phase clustering before and after removing the ERP to compare phase-locked and non-phase-locked components in time-frequency analysis.

Demonstrate downsampling time-frequency power to reduce memory usage while preserving information, and recommend downsampling the results of time-frequency analysis for multi-channel data.

Explore visualizing time-frequency power across all channels and many time points using a three-dimensional time-frequency matrix, with down-sampled post-analysis data and an interactive graphical user interface for channel-based exploration.

Learn to compute instantaneous frequency from simulated neural signals using the Hilbert transform and phase derivative, explore noise effects, edge artifacts, and frequency sliding with smoothing.

Analyze instantaneous frequency in real resting-state EEG data using a narrowband alpha filter (8–12 Hz), Welch method estimates, and median filtering to smooth outliers.

Generate three time-frequency maps—total power, non-phase-locked power, and phase-locked power—by subtracting the ERP from each trial and baseline normalize.

Explore hands-on neural data analysis by loading the laminar dataset, computing ERP and non-phase-locked activity, applying morleigh wavelet time-frequency analysis, and visualizing baseline-normalized power with ERP overlays.

Design a narrowband filter to isolate 10–15 Hz activity with the FLIR one function, then apply the Hilbert transform to obtain the analytic envelope.

Create a time-frequency power plot using the filter-Hilbert method on the SPG EEG data, electrode 30, and analyze the power spectrum across frequencies.

The lecture walks through solving project two in section four, building time–frequency power plot for channel 30 with a filter–Hilbert approach, including data loading, 5–40 Hz analysis, and zero padding.

Explore core concepts in neural connectivity, including univariate vs multivariate measures, volume conduction, connectivity over time versus over trials, and directional measures such as Granger causality.

Examine how volume conduction can create spurious synchronization, yielding zero or pi phase lag and distance-based decay, and learn ten mitigation strategies from spatial filters to phase-based tests.

Explore the intuition of phase synchronization and the terminology around phase clustering. See how timing, not amplitude, indicates functional connectivity and how synchronization dynamically varies with brain activity.

Explore inter-site phase clustering (ISPC) to quantify phase synchronization between two electrodes by averaging unit vectors of phase differences and using the mean vector length as a clustering metric.

Learn to compute interstate phase clustering (ISPC) in MATLAB by implementing Morlet wavelets, analytic signals, phase differences, and mean vector magnitude to quantify phase synchronization between neural signals.

Explore how the surface Laplacian, a second spatial derivative on the head model, reduces volume conduction confounds in EEG connectivity analyses by highlighting local electrode activity.

Demonstrate MATLAB-based Laplacian analysis on simulated EEG data by creating low- and high-spatial-frequency Gaussian features across two channels. Visualize their topographical maps and explore channel distances and Euclidean distance relations.

In MATLAB, apply laplacian filtering to EEG data, compare voltage and laplacian topographies and ERPs, and normalize with z-scores to reveal local versus distant sources and phase lag index.

Learn how phase lag based connectivity measures ignore zero or pi phase differences to reduce volume conduction artifacts, focusing on the phase lag index (PLI).

Explore MATLAB simulations of phase angles to compute the phase lag index and compare it with phase clustering and imaginary coherence.

Compare phase-lag based measures and phase clustering for electrophysiological connectivity, highlighting when to prefer PLI or phase clustering and the impact of volume conduction. Guide exploratory versus hypothesis-driven analyses.

Investigate phase synchronization between two EEG channels using phase clustering and phase lag index, comparing voltage and Laplacian data and how Laplacian filtering affects volume conduction across 2-40 Hz.

Compare connectivity over time and over trials in phase synchronization analyses. Apply each approach for resting-state data, long tasks, or trial-based experiments, noting windowing effects on temporal resolution.

Compute 44 Hz phase synchronization between V1 channels one and seven using Morleigh wavelet, store phase angles across time and trials, and compare synchronization over trials versus over time.

Simulate time-series neural data in MATLAB to test connectivity methods, using phase lag, noise levels, and wavelet-based analysis to compare phase clustering and phase lag indices on EEG-like signals.

Explore two power-based connectivity methods—amplitude envelope correlations and trial-to-trial power coupling—using time–frequency power series, with guidance on same-frequency focus and hypothesis-driven windows.

Explore Granger prediction, using autoregressive models to forecast one neural signal from another's past, revealing directional connectivity and covering univariate, multivariate, and spectral analyses with cautions about causality.

Apply univariate and multivariate autoregressive modeling to implement time-domain Granger causality, using variance ratios and sliding three-hundred-millisecond windows to reveal directional connectivity between prefrontal and occipital channels.

Learn how multivariate brain synchronization reveals hubness in neural networks using graphs and connectivity matrices. Thresholding and binarization identify hubs as highly connected nodes across EEG channels.

Learn to compute connectivity hubs in EEG scout data using all-to-all phase lag index and 10 Hz time-frequency analysis, including data preparation, thresholding, and topographical hub maps.

Evaluate connectivity methods for electrophysiology data by considering volume conduction, physiological constraints, and replication. Motivate one method by theory or report multiple analyses with cross-validation to avoid bias.

Learn pairwise synchronization analysis of neural signals using two-frequency wavelets at 8 hz and 55 hz to build phase connectivity matrices across time windows and trials.

Examine pairwise EEG synchronization using seed-to-all phase data from wavelet convolution (2–40 Hz), compare phase clustering vs phase lag index, and build baseline-subtracted time–frequency maps for FCZ and OZ.

Explore phase synchronization in simulated noisy oscillators by comparing two filtered sine waves, extracting phase angles via the Hilbert transform, and assessing robustness to noise.

See how narrowband filtered noise can produce apparent phase synchronization, risking misinterpretation as genuine connectivity in brain data, and highlighting edge effects that can create spurious peaks in spectral analyses.

Showcases all-to-all phase synchronization matrices for a 16-channel V1 laminar dataset at 40 Hz across two time windows, using Hilbert-derived phase angles to reveal symmetric connectivity.

Explore power time series correlations across channels to map all-to-all connectivity across frequencies from 10 to 80 hertz using a gaussian filter and animate the results.

Explore power correlations over trials within a time frequency window, revealing cross trial correlation and cross frequency coupling using EEG data and seed region power measures.

Apply the scalp Laplacian spatial filter to attenuate low spatial frequency activity, reducing volume conduction confounds and improving electrode-level connectivity estimates, demonstrated with simulated dipole data.

Explore all-to-all EEG connectivity and graph-theory concepts by computing Hubner measures, applying phase synchronization via the Hilbert transform, then thresholding the matrix to reveal inter-electrode hubness.

Explore interstate phase clustering and phase synchronization in voltage and policy data, with and without the surface of the plastic, and learn to attenuate volume conduction using the phase-like index.

Explore project solutions for neural signal processing, including separating data fields to avoid overwriting, constructing symmetric wavelets, and evaluating phase-based connectivity methods robust to volume conduction.

Compute power correlations and phase synchronization in the same data set to compare the networks that emerge from each metric, with figures showing both measures across channels at 50 Hz.

Walk through the project 2 solutions in section five, detailing modifications to power and phase synchronization code using the Hilbert transform. Discuss matrix expansion to four dimensions.