Teaching transforms: a vector approach

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.

Keywords:

• Fourier transform
• vectors
• scalar product
• basis vectors