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Teaching Transforms: a vector approach

Journal article
Authors Lars Bengtsson
Published in International journal of mathematical education in science and technology
Volume 46
Issue 5
Pages 752-765
ISSN 0020-739X
Publication year 2015
Published at Department of Physics (GU)
Pages 752-765
Language en
Links dx.doi.org/10.1080/0020739X.2014.98...
https://gup.ub.gu.se/file/157245
Keywords Fourier transform, vectors, scalar product, basis vectors
Subject categories Mathematical Analysis, Learning

Abstract

This article treats the problem of introducing transform theory (Fourier, Laplace, z) to undergraduate students and we suggest a vector approach which means that signals (functions of time) should be treated as vectors from the beginning and that transforms are introduced as a scalar product; the transform should be presented as a tool to analyse the signal exactly in the same way as the dot product is used to analyse an ‘arrow’ vector in a Cartesian space. Hence, the transform becomes a tool to find the signal's magnitude in the directions of the basis vectors.

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