Harmonic Analysis Lecture is Music to Mathematicians

Erica White

On March 22 math aficionados from around the GCC campus gathered in room 243 in the Santa Barbara building to hear Dr. Ashot Djrbashian lecture on harmonic analysis and its real-world applications.

It’s lunchtime. An audience of GCC students, faculty and staff are milling around in the semi-circular lecture room eating their lunches and talking among themselves.

Harmonic analysis or Fourier analysis, named so after founder Jean Fourier its, is a branch of mathematics that studies the representation of basic sound waves or “harmonics.”

Fourier discovered harmonic analysis while working as a prefect. It wasn’t until Fourier’s death that his contributions to math and science were acknowledged.

“It’s one of the most advanced and important branches of mathematics,” Djrbashian said.
Djrbashian went through a brief PowerPoint presentation showcasing the history of harmonics.

“It involves a vast variety of problems having one underlying theme: how to present complicated objects as combinations of simpler objects,” Djrbashian said.

The early days of harmonics were focused on the trigonometric functions sine and cosine. As harmonics evolved and once simple sine and cosine functions became more complicated, harmonics made these functions easier to compute, Djrbashian said.

An everyday example of harmonics is in music sampling. Harmonics analysis gives correct limits for the number of samples per second that should be taken from each sound wave, Djrbashian said.

“If not enough samples are taken the sound will be distorted,” Djrbashian said.

The same method holds true for the digital imaging technology used in MRI and CT machines. Harmonic analysis generates the calculations to determine the number of sample cuts that need to be taken to produce a clear image.

A lack of samples produces an inferior image Djrbashian said.

Djrbashian stressed the practicality of mathematics in everyday situations.

“Mathematics always finds applications even when that is not the intention,” Djrbashian said.
This was the second lecture in the series of four science lecture. There are two remaining lectures.

“Beautiful Science: Ideas that changed the world” will feature speaker Dr. Daniel Lewis, senior curator of the history of science at the Huntington Library, on April 26 at 12:15 p.m.
“The Science of Making Chocolate” will feature speaker Ray Fischbach, director of technical services at Nestle, on May 24 at 12:15 p.m.