ELEC212 Chapter 9 Computation of Discrete Fourier Transform

ELEC212 Chapter 9 Computation of Discrete Fourier Transform...

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1 The Hong Kong University of Science and Technology Department of Electronic and Computer Engineering ELEC 212 Chapter 9 Computation of the Discrete Fourier Transform 2 09-10 Fall ELEC 212 Computing the DFT Efficient Computation of DFT 3 09-10 Fall ELEC 212 Computing the DFT Efficient Computation of DFT 4 09-10 Fall ELEC 212 Computing the DFT Efficient Computation of DFT
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5 09-10 Fall ELEC 212 Computing the DFT Efficient Computation of DFT 6 09-10 Fall ELEC 212 Computing the DFT Decimation-in-Time FFT Algorithm 7 09-10 Fall ELEC 212 Computing the DFT Decimation-in-Time FFT Algorithm 8 09-10 Fall ELEC 212 Computing the DFT Decimation-in-Time FFT Algorithm ± The N /2 -point DFTs of the even- and odd-numbered sequences, G [ k ] and H [ k ] , are calculated for the range k = 0…( N /2-1) ± However, the values of the N /2 -point DFT vary periodically with period N /2 G [ k ] = G [ k + N /2] and H [ k ] = H [ k + N /2] ± Therefore, we can compute all points of the N -point DFT using two N /2 - point DFTs as follows 1 2 0 ] [ ] [ ] [ + = N k k H W k G k X k N [] [ ] [ ] 1 2 0 2 / 2 /
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This note was uploaded on 03/27/2011 for the course ELEC 212 taught by Professor Prof.matthewmckay during the Spring '11 term at HKUST.

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ELEC212 Chapter 9 Computation of Discrete Fourier Transform...

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