An electrocardiogram (ECG) is a graph of voltage against time of the electrical activity of the heart. It’s measured by placing electrodes on the skin in a number of different places. Changes to the normal electrocardiogram pattern are an important way of diagnosing cardiac problems and diseases. Fig. 5.20 shows a recording from a single lead of an ECG; the trace is clearly periodic and shows distinct heartbeats.

We can approximate this ECG curve by taking a combination of an exponential function and multiple sine functions.

a. Let E(t) = −2.6 + 1.7 sin(t) + 1.1 sin(2t) − 2.3 sin(3t), where t has units of seconds and E has units of mV. Plot E(t). Then plot C(t) = e E(t)

(on the same graph) and compare to the ECG curve shown in Fig. 5.20.

b. What is the period of C(t)? How would you change this period so that it matches the period of the actual ECG? Write down a new function, C˜(t), that has the correct period, and check your answer by plotting C˜(t).

c. What is the amplitude of C(t)? How would you change this amplitude so that it matches the amplitude of the actual ECG?