Further Developments and Applications of the Finite Fourier Transform

  • Kurt Bernardo Wolf
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 11)


In actual applications, most mathematical methods have to deal with finite data sets. Thus it is not surprising that the finite Fourier transform is the main tool among transforms in applied research. Two topics in communication science have been selected to illustrate the use of the finite Fourier transform: signal filters and windows in Section 3.1 and signal detection in the presence of noise in Section 3.2. These make use of the operations of convolution and correlation. The implementations of these techniques would be impossible without present-day computers and an efficient algorithm for the numerical work. The fast Fourier transform (FFT) operating principles are given in Section 3.3. Finally, in Section 3.4 we let the dimension of the vector space grow without bound. In this way we arrive at the Fourier series and integral transforms which are the subjects of Parts II and III. The sections are mutually independent except for Section 3.2, which relies somewhat on concepts developed in Section 3.1. Otherwise, they can be read in any order. The References should be consulted if the reader wishes a wider picture of the applied technology.


Fourier Transform Transfer Function Fast Fourier Transform Inverse Fourier Transform Window Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Kurt Bernardo Wolf
    • 1
  1. 1.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoMéxico D.F.México

Personalised recommendations