### JPNM Physics

## Introduction to the Fourier Transform

We know that sound comes in high frequencies - squeels, and low frequencies - bass tones. We can look at a pure tone signal on an oscilloscope and observe its time response -

When we hear this, we do not hear the wave-like oscillations, but rather a pure, constant tone. If the frequency increases, we do not hear "more" oscillations per second, but rather a higher pitched pure tone.

How does this happen?

The cochlea has hairlike filaments which, when stimulated, produce a signal which is transmitted to the aural portion of the brain. Where the spiral of the cochlea is straightest, it is responsive to lowest frequencies. Where the spiral is of greatest curvature, it is responsive to highest frequencies.

### The cochlea converts time-dependent signals such as those shown in the oscilloscope trace and converts them into signals corresponding to frequencies. This conversion from time to frequency is the basis of the FOURIER TRANSFORM. The cochlea is a biological system which performs a Fourier transform.

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Douglas J. Wagenaar, Ph.D., wagenaar@nucmed.bih.harvard.edu