On the Fourier Analysis and the Lagrange Interpolation from the Viewpoint of Signal Theory

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概要

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• The Fourier analysis is of importance not only as just one of the mathematical tools for processing signals and noise, but also for its intrinsic role in the representation of almost every informational feature of physical objects. This paper discusses some aspects related to the Fourier analysis, sampling theory, and the Lagrange interpolation from the viewpoint of signal theory. First, the intrinsic role of the Fourier analysis is clarified in relation to the wave equations and the human sensation in vision and hearing. Next, an algebraic approach to the Fourier analysis based on the Lagrange interpolation is shown as the theoretical basis of the sampling technique. The equivalence between the discrete Fourier transform (DFT) and the Lagrange interpolation on the unit circle in the complex Z-plane, on which the so-called Z-transform is defined, is shown in an algebraic way. The Fourier series expansion is derived as a limit of a Lagrange interpolation polynomial.

• 久留米工業大学の論文
• 1999-12-20

著者

• 古賀 利郎

  Department Of Electronic And Information Engineering

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