Generating Waveforms with Vectors

General Instructions

This spectral simulation is an interactive Java applet. You can change parameters by clicking on the vertical arrow keys. The five control buttons at the lower right are used to start (triangle) and pause (square) the simulation, to skip forward or back one section at a time (double triangles), and to change speed (+ and -).

After the simulation is complete, the start button takes you back to the beginning of the simulation. You may experience a delay at this point.

Any waveform, from a pure sine wave to a complex cardiac waveform, can be created by adding a specific set of sine waves. This simulation shows what happens when you add in-phase harmonics to a sine wave. It also shows the equivalent rotating vectors, which, in the author's view, make the mathematical process easier to understand.

Start with a choice of "no harmonics" to see how a vector can simulate a waveform. Then add harmonics and look at the result. The sinusoidal waveform traces the tip end of the vector. If the vector starts at some phase angle other than zero, so does the sinusoid.