BME I5100: Biomedical Signal Processing and Signal Modeling

Course overview and schedule:
Syllabus

Office Hours Fall 2025:
Sam Tran: Wednesday 11:00am - 12:00pm (ST403E), Tuesday and Thursday 11:00am - 11:30am (ST403E), and Friday 9:30am - 10:30pm (Zoom)

Lectures:
1. Introduction
2. Linear Systems, Impulse Response, ARMA filter
3. z-transform, fourier transform, filter design, circular convolution, sampling theorem
4. Random Variables
5. Jointly Distributed Random Variables
6. Stochastic Processes, Power Spectrum, ARMA model, linear prediction
7. Probablistic Estimation, Harmonic process
8. Linear discrimnation, Single trial detection in EEG/MEG
9. Linear Mixtures, ICA, PCA
10. Kalman Filter, Hidden Markov Model
11. Causal Inference, introduction
12. EEG linear decoding and spatial filtering

Data files:

• Steam engine data for ARX estimation: SteamEng.mat
• Heart rate during rest and a Stroop task: hr_rest_stroop.mat
• ECG signal: ECG.mat
• EMG data measured on tongue muscle: tonguemg.mat
• Error Related Negativity & Scalp Data: eeg-ern.mat, scalp.m.
• Eye blinks (EEG): EEG.mat
• Spike trains: spike.mat
• Speech (start the day on the right foot: speech.wav
• Sine Frequency Estimate: sinefreq.mat
• Local field potentials from hippocampal slice (first channel recorded in CA1, second channel recorded outside the slice as noise reference): gamma.mat
• Local field potentials from hippocampal in-vivo recodings (first 60 second are baseling activity, remaining time includes responses to electrical stimulation, time markers indicate start of electrical stimulation): lfp.mat
• Bird song recorded in the wild in stereo: bird-stereo.wav
• EEG Visual evoked responses: eeg-vep.mat. To display this data you may use topoplot() and this location file. (The version of topotplot() posted here is VERY old, but has the distinct advantage of not requiring enything else other that this one single file. If you want a newer, significantly more complicated version of topoplot you will have to install the complete EEGLAB toolbox from UCSD..)
• EEG to analyze apha power: eeg_128Hz.txt (recorded at 128 Hz)
• EEG to analyze apha power, 2nd example: alpha.mat
• EEG and audio sound files to analyze the response of EEG to sound envelope: audio_eeg.mat
• Simulated data to practice idendtifying cause while contolling for condounding: cause_or_confound.mat
• Simulated data to practice computing LATE, ITT, PP estimates in RCT with imperfect compliance: LATE_example.mat
• Simulated data to practice estimating direction of forcasting using Granger "causality": granger_example.mat

Tutorials:

• Matlab tutorials: several courses from Mathworks, and Open Course Work from MIT
• Linear Algebra: Open Course Work from MIT
• Linear Algebra: Compact review and nice visualization of liner algebra
• Digital Signal Processing: graphic demonstrations in matlab
• Andrew Ng's lectures on machine learning: videos and course page.
• Geoffrey Hinton's neural networks for machine learning: Coursera class
• Digital signals processing: Coursera class

Tools:

• A fair number of good algorithms: netlab (Logistic regression, mixture EM, PCA, ...)
  
• Filter Design toolbox for python (similar to filterDesigner in matlab): pyFDA

Homework Instructions:
1. Batch LMS ARMA modeling
2. Linear System Responses
3. Source separation