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5 pages in length. Mathematician Fourier was instrumental in establishing a more detailed understanding of vision and audition; his findings not only revolutionized all previous scientific thinking, but it also set a precedent for further exploration from that point forward. In short, the importance of Fourier's findings revolves around his proven assertion that continuous function could be produced as an infinite sum of sine and cosine waves; as such, this weighty and comprehensive declaration became the fundamental basis of sight/sound reproduction and synthesis. Bibliography lists 5 sources.
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File: LM1_TLCFouri.rtf
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set a precedent for further exploration from that point forward. In short, the importance of Fouriers findings revolves around his proven assertion that "continuous function could be produced as
an infinite sum of sine and cosine waves" (Fourier Analysis and Synthesis); as such, this weighty and comprehensive declaration became the fundamental basis of sight/sound reproduction and synthesis. Converting a
pure sine wave is as simple as utilizing a loudspeaker to convert the sound; when this occurs, the speaker will emit a "steady, pure tone of a single pitch" (Fourier
Analysis and Synthesis). An example of this scenario might be a collection of orchestral instruments, inasmuch as their standard composition is that of a "fundamental and a complement of
harmonics" (Fourier Analysis and Synthesis), which constitutes a laying over of sorts with regard to sine waves "of a fundamental frequency f and integer multiples of that frequency" (Fourier Analysis
and Synthesis). One might gain a better perspective of this by examining what one of those instruments would sound like if its resonance were broken down into constituent sine
or cosine waves, a formula for which Fouriers findings were wholly responsible. The Fourier Analysis allows one to distinguish various sound waves as
amplitudes of the existing constituent sine waves, a collection of numbers that provides information about the sounds harmonic composition, which is from time to time called the harmonic spectrum of
the sound. Comprehending the importance of this aspect of Fouriers Analysis enables one to understand how and why a musical notes sound timbre is based primarily upon the harmonic
content, inasmuch as this allows for the "capability of synthesizing that sound from a series of pure tone generators by properly adjusting their amplitudes and adding them together" (Fourier Analysis
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