IN THE REALM OF FOURIER

transform computer sound to a fractal domain which is effective for interactive communication, it is necessary to: one, fine tune the creative input; and two apply fourier filtering to sound sampled to the computer. A way of dealing with the filtering is to develop a technique of mapping time-domain signals into frequency domain representations. In this way, the harmonic analysis of musical tones becomes the process of isolating a frequency and then attenuating the other frequencies. [Bateman, INTRODUCTION TO COMPUTER MUSIC]. The fourier transform becomes a type of frequency controller.

Fourier analysis is a process that can be used for the conversion of values into sine and cosine values in the frequency domain. My interst in Fourier transforms began during graduate studies in photography when I was first introduced to a Fourier transform camera. Upon photographing slides of artist paintings with the camera, the resulting images became patterns of waveform values transformed to the frequency domain. Some images transformed to spirals, some to cubes, or circles, but each painting transformed to a unique pattern. The complexity and composition of the original paintings, as well as the color values associated with the paintings, directly affected the resulting pattern.

Roughly speaking, what Fourier developed was a mathematical way of converting any pattern, no matter how complex, into a language of simple waves. [Talbot, Michael, THE HOLOGRAPHIC UNIVERSE] . The Fourier filtering method can be explained as a spectral synthesis method. My fascination with these fourier abstractions of light inspired a portfolio of photographs where I worked with light sources trying to artificially create the illusion of an abstracted universe similar to that of an image transformed into the frequency domain. Just as the complexity of image patterns taken with the fourier camera was altered relative to the qualities of the painting being transformed, a photograph of light trails becomes more compelex depending on the complexity of the event marked in light, and, similarly, the quality of sound output from a computer is directly related to the sound complexity of the sound data sampled to the computer.

In general, sound which has been computer generated in the fractal domain has been recognized as being unpleasant to human perception. Richard Voss says sound input of the one over f order has the most positive effect on the human. Spectral density gives an estimate of vibratory energy at frequency f, and of the variations in vibratory levels over a time scale of one over f order. [Richard Voss, SCIENCE OF FRACTALS]

Voss explains that patterns made by each of these one over f noises occur as a fractal curve, and there is a direct relationship between the fractal dimension and the logarithmic slope of the spectral density. Balance seems to exist between the low frequencies and the high frequencies, and there is also a balanced blend of randomness and predictability in the sound output. One over f noise is the most common type of sound in nature. [Voss, SCIENCE OF FRACTALS]

In regard to fourier filtering as applied to the picture image, Walter Bender, from MIT, presented a paper at SIGGRAPH 1990 called Image and Motion which suggested that noise which is particularly irritating to the human's visual perception results from energy not uniformly distributed in the frequency domain. Visual systems are more sensitive to noise in the low frequency domain, so by bumping up values in the frequency domain, low range frequency noise is filtered out without altering the bandwidth. He also suggests using the inverse fourier transform to further filter the noise from the picture image, and in doing this, suggests the process as being sub-band coding of the picture image. [Bender, CONFERENCE PROCEEDINGS, SIGGRAPH 1990]

As interactive communications need to be reversable, the need for a similar process of sub-band coding, through inverse fourier transforms, exists for sound, as quite possibly the sound having the most positive effect on the human would be low frequency sound. Possibly high frequency sound carry the most information with the highest definition; however high frequency sound needs to be compressed into a lower range that can be interpreted by the human and decompressed again to transfer back to the originating source.

COLOR/FREQUENCY, AN INTERACTIVE PROCESS

During a brief study with Steven Halpern in Detroit, he spoke extensively on the effect of sound on the nervous system, revealing the fact that different frequencies affect each of the seven nerve centers of the body. Some frequecies would have positive effects and others negative. With positive sounds, literally, The oscillation of the music vibration usually massages tissues and cells which in turn effect a balance that improves blood circulation, metabolism, and the pulsation of endocrine glands. [MacClain, GOING WITHIN]

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