As was defined in a previous chapter, the discrete Fourier transform (DFT) is the sampled version of the discrete-time Fourier transform (DTFT), with a finite number of samples taken around the unit circle in the Z-domain. DFT is very useful in the analysis of discrete-time signals and linear time-invariant discrete-time systems. It is, therefore, necessary to determine the computational complexity in performing an N-point DFT of a sequence so that we may be able to come up with a more efficient computational algorithm. To this end, let us first evaluate the computational complexity of computing an N-point DFT using brute-force method. Consider an N-point discrete-time sequence {x[n]}, 0 ≤ n ≤ N − 1, N ∈ Z. Its DFT is given by

Supplementary material (1.3 mb)


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • K. S. Thyagarajan
    • 1
  1. 1.Extension ProgramUniversity of California, San DiegoSan DiegoUSA

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