You are a biomedical engineer working in a seizure clinic. The clinicians have observed a strange phenomenon. When the EEG signal is low pass filtered, there is a recurring peak in the signal that occurs sporadically before a seizure and this peak increases every few seconds but is not periodic. They have asked you to see if you can detect, measure and track this peak every time it occurs.
What circuits that you have learned about so far would you use to perform these mathematical functions?
The trace below is a representative recording from one of the affected patients, cycling through normal behaviour, a pre-state, a seizure, and a brief recovery. The feature of interest is the band shaded yellow: a small number of brief, sporadic spikes whose amplitude grows in the lead-up to the seizure.
Two facts matter for the design that follows. First, the spikes are not periodic, so a fixed sampling clock cannot decide when a spike has occurred. Second, the amplitude is the quantity of clinical interest, not the count alone, because a rising envelope during the pre-state is what predicts the seizure.
The clinicians ask for three things from the circuit: detect each spike, measure its peak amplitude, and track the trend.
The clinic's brief reduces to three mathematical operations: a binary detection, an analog amplitude measurement, and a slow trend over many events. Pick the blocks from this course that you would assemble to perform those three operations.
Multiple selections are allowed. Some choices are correct, some are partially useful, and some belong to a different problem.
The simplest detector is an op-amp comparator with its non-inverting input tied to the EEG and its inverting input held at a reference voltage $V_\mathrm{th}$. Whenever the EEG crosses upwards through $V_\mathrm{th}$, the output flips to the positive rail and a spike is registered.
Plain comparators chatter on noisy inputs because the signal can wander across the threshold several times within one true spike. A Schmitt trigger replaces the single threshold with a hysteretic pair $V_{T+} > V_{T-}$. The output goes high only when the input rises above $V_{T+}$ and only resets when the input falls back below $V_{T-}$, so each spike yields exactly one pulse.
The simplest peak detector is a diode in series with a hold capacitor. While the input rises, the diode conducts and the capacitor charges to the input voltage minus the diode forward drop, $V_C = V_\mathrm{in} - V_D$. When the input falls back, the diode blocks and the capacitor holds the most recent peak.
An ideal hold would freeze the reading forever and confuse the next measurement. A leak resistor is added across the capacitor, giving a decay time constant $\tau_\mathrm{leak} = R_\mathrm{leak} C$, so the held voltage tracks the envelope of the spike train rather than freezing on the first peak.
The filtered EEG is in millivolts and is too small to drive the analog peak detector directly. A pre-amp lifts the signal above the diode forward drop, then a parallel pair of blocks supplies the two outputs the brief requires: a Schmitt trigger plus monostable produce one clean pulse per spike for counting, and a diode with a hold capacitor and leak resistor produce a held envelope that tracks the spike amplitude over time.