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Multidimensional Systolic Arrays for Computing Discrete Fourier Transforms and Discrete Cosine Transforms

  • Hyesook Lim
Part of the The Kluwer International Series in Engineering and Computer Science book series (SECS, volume 380)

Abstract

This chapter presents a new approach for computing the multidimensional discrete Fourier transform (DFT) and the multidimensional discrete cosine transform (DCT) in a multidimensional systolic array. There are extensive applications of fast Fourier transform (FFT) and fast cosine transform (FDCT) algorithms. From the basic principle of fast transform algorithms (breaking the computation in successively smaller computations), we find that the multidimensional systolic architecture is efficiently used for implementing FFT algorithms and FDCT algorithms. The essence of the multidimensional systolic array is to combine different types of semi-systolic arrays into one array so that the resulting array becomes truly systolic. This systolic array does not require any preloading of input data and it generates output data only from boundary PEs. No networks for transposition between intermediate constituent 1-D transforms are required; therefore the entire processing is fully pipelined. This approach is well suited for VLSI implementation by providing simple and regular structures. Complexity estimation of area*time 2 shows our multidimensional systolic array is within a factor of logk of the lower bound for an M-dimensional k-point DFT (k=N M ).

Keywords

Discrete Cosine Transform Discrete Fourier Transform Processing Element Systolic Array Chinese Remainder Theorem 
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.

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Hyesook Lim
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of Texas at AustinAustinUSA

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