Fourier Transform

  • Apurba Das
Part of the Signals and Communication Technology book series (SCT)


In the previous chapter of Fourier series, we have already seen how any periodic signal can be represented in terms of its single tone components. The understanding of unique frequency present in any periodic signal has been changed there to fundamental frequency of principle frequency component. In the present chapter we'll extend our idea of spectral representation for aperiodic signals also to get a feel of frequency response characteristics of natural systems as well as frequency domain distribution of natural signals. We have extended our idea of Fourier series to Fourier transform in a logical and smooth way. The mathematical formulation helps us to understand the physical significance of Fourier transform. Signals which have finite phase response can often be defined as complex function of time. These types of complex signals with evenness and oddness are addressed and studied in transformed domain. Convergence of Fourier transform into cosine or sine transform has also been studied. From different properties of Fourier transform we have also discussed the method of modulation, verified the realizability of ideal filters and searched the reason to be the phase response of a filter to be negative linear.


Fourier Series Phase Response Frequency Response Characteristic Single Tone Introductory Chapter 
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.


  1. 1.
    Bracewell, R.N.: The Fourier Transform and its Applications, 2nd edn. McGraw-Hill Book Company, New York (1987)Google Scholar
  2. 2.
    Lathi, B.P.: Modern Digital and Analog Communication Systems, 3rd edn. Oxford Universal Press, Oxford (2005)Google Scholar
  3. 3.
    Hardy, G.H., Rogosinski, W.W.: Fourier Series. Dover Publications Inc, New York (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Image Processing Lab CDAC, KolkattaMinistry of Communication and ITKolkattaIndia
  2. 2.Imaging Tech Lab, Engineering and R&DHCL Technologies Ltd.ChennaiIndia

Personalised recommendations