Fourier Analysis of Harmonics

The waveform from an EKG machine.
••• Oleg Shipov/iStock/Getty Images

You can think of any kind of waveform as being made of a set of sine waves, each of which contributes to the overall wave shape. A mathematical tool called Fourier analysis describes exactly how these sine waves add together to produce waves of different shapes.


Every wave begins with a sine wave called the fundamental. The fundamental serves as the backbone for the wave shape and determines its frequency. The fundamental has greater energy, or amplitude, than the harmonics.


Sine waves called harmonics determine a complex wave’s final shape. Harmonics always have frequencies which are exact multiples of the fundamental’s frequency. While a wave always has a fundamental, the number and amount of harmonics varies. Sharp-edged waves, such as square and sawtooth, have stronger harmonics than waves with few sharp transitions, such as the triangle.

Infinite Series

Mathematically ideal waveforms may have an infinite number of harmonics. For example, the sawtooth waveform has all harmonics. The strength of each one is the reciprocal of its harmonic number. Its third harmonic has one-third the energy of the fundamental, the fourth, has one-fourth, and so on. You add the odd harmonics to the fundamental and subtract the even ones.

Related Articles

How to Calculate a Wavenumber
What Is the Formula for Velocity of a Wave?
How to Calculate Photons Per Second
Infrared Vs. Visible Light
How do I Measure Ocean Wave Energy?
What Is a Swell in the Ocean?
How to Read Oscilloscopes
How to Calculate Hertz to Joules
How to Calibrate Oscilloscope Probes
How to Calculate the First Ionization Energy of the...
How to Calculate Frequency
How to Calculate Frequency in Hertz
What Are Some Differences Between P & S Waves?
How to Calculate the Phase Shift

Dont Go!

We Have More Great Sciencing Articles!