An Analogy To Audio Signals

Most modem stereo systems are equipped with graphic equalizers that permit the

listener to tailor the frequency content of the sound. An equalizer is a set of filters that

are each responsible for manipulating a narrow frequency band of the input frequency

spectrum. In this instance, manipulation takes the form of attenuation, emphasis, or

merely allowing the input to pass through untampered. This has direct impact on the

richness of the sound. For instance, the low frequencies can be enhanced to compensate

for inadequate bass in the music. We may simultaneously attenuate the high frequencies

to eliminate undesirable noise, due perhaps to the record or tape. We may, alternatively,

wish to emphasize the upper frequencies to enhance the instruments or vocals in that

range.

The point to bear in mind is that sound is a sum of complex waveforms that each

emanate from some contributing instrument. These waveforms sum together in a linear

manner, satisfying the superposition principle. Each wax;eform is itself composed of a

wide range of sinusoids, including the fundamental frequency and overtones at the har-

monic frequencies [Pohlmann 89]. Graphic equalizers therefore provide an intuitive

interface in which to specify the manipulation of the audio signal.

An alternate design might be one that requests the user for the appropriate convolu-

tion kernels necessary to achieve the same results. It is clear that this approach would

overwhelm most users. The primary difficulty lies in the unintuitive connection between

the shape of the kernel and its precise filtering effects on the audio signal. Moreover,

considering audio signals in the frequency domain is more consistent with the signal for-

mation process.

Having established that audio signals are readily interpreted in the frequency

domain, a similar claim can be made for visual signals. A direct analogy holds between

the frequency content in music and images. In music, the transition from low- to high-

frequencies corresponds to the spectrum between baritones and sopranos, respectively.