Good Approximations

Howard L. Resnikoff () and Raymond O. Wells ()
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Howard L. Resnikoff: Future WAVE Inc.
Raymond O. Wells: Rice University, Department of Mathematics

Chapter 2 in Wavelet Analysis, 1998, pp 12-29 from Springer

Abstract: Abstract Every measurement, whether the naked result of an impression on the human eye or ear, or the product of a sophisticated measuring instrument, is merely an approximation. We can know, and our computing machines can know, only a finite number of decimal places in the numerical representation of a distance or a weight or a force or a temperature.1 The eye has limited resolving power, the ear a limited frequency response, and comparable limitations hold for all other instruments whether biological or “mechanical.”These limitations are not merely due to poor “manufacturing technique”; as Heisenberg’s Uncertainty Principle tells us, they are inherent in the essence of things. Life and the universe depend on approximations. And so, too, does technology.

Keywords: Fourier Series; Rational Number; Discrete Fourier Transform; Information Gain; Digital Computer (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-0593-7_2

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