Summary: Spectra of sounds and images
Pedro M. Q. Aguiar
Institute for Systems and Robotics / IST
These notes overview the spectral representation, emphasizing its
compactness for describing acoustic signals, e.g., music, and visual
patterns, e.g., textures and contours.
1 Sinusoids in Nature
We start by looking at the general class of sinusoidal signals. One of the
reasons why this class is relevant in practice is that many physical systems
produce signals that are well approximated by sinusoids. As an example,
suggested by , consider the tuning fork in Figure 1.
Figure 1: Tuning fork.
When stroked, the tuning fork produces a sound, a persistent "hum".
Figures 2 and 3 plot this sound, which is usually called a "pure tone". Is it
a coincidence that the (stationary part of the) signal looks like a sinusoid ?
Figure 2: Acoustic signal produced by a tuning fork. (From .)