PE2-3.5 Event Detection & Waveform Analysis
You can detect the QRS complex using derivative-based approaches and the Pan-Tompkins algorithm, detect the dicrotic notch, and analyse waveforms using correlation, envelope extraction and activity measures.
Pan-Tompkins is the algorithm to know cold — it has been running in cardiac monitors since 1985, and its pipeline of bandpass, derivative, squaring, integration and adaptive threshold is a masterclass in stacking simple operations to solve a hard problem. Once R-peaks are detected, everything clinical follows: heart rate, variability, arrhythmia. The activity measures at the end (RMS, zero-crossing rate, turns count, form factor) are cheap features that still carry real diagnostic information, particularly in EMG.
Work through these
Example events: P, QRS and T waves in the ECG
What you are looking for in the heart's signal, named part by part. The rest of the topic is methods for finding these automatically.
Derivative-based approaches for QRS detection
The first family of detectors, using the fact that one part of the waveform is much steeper than the rest. Noise sensitivity is the weakness the next item addresses.
The Pan-Tompkins algorithm for QRS detection
The standard algorithm, still used decades later. Working through its stages is the most valuable single exercise in this subject.
Dicrotic notch detection
Finding a feature in the arterial pressure waveform, which marks the closing of a valve. It is a good second example of the same detection ideas.
Correlation analysis of EEG
Comparing brain signals between channels, which is how synchrony is assessed. It uses the correlation machinery in a different setting.
Morphological analysis of the ECG; correlation coefficient
Comparing the shape of one beat with a template, which is how abnormal beats are flagged. The correlation coefficient is the measure and its limitations are worth knowing.
The minimum phase correspondent; signal length
Two more analytical ideas that come up when comparing waveforms of different lengths. They are technical and they matter for making comparisons fair.
Envelope extraction, amplitude demodulation and the envelogram
Extracting the outline of a signal that varies in amplitude, which is how heart sounds are analysed. It reduces a complicated waveform to something interpretable.
Analysis of activity: RMS value, zero-crossing rate, turns count, form factor
Four simple measures of how much is happening, used for muscle signals. They are cheap to compute and surprisingly informative, which is why they survive.
Periodogram and averaged periodogram
Estimating the frequency content, and why averaging several estimates is necessary. The variance of the raw estimate does not fall with more data, which is a genuinely surprising fact.
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