DSP (2015 Spring) Discrete Fourier Transform NCTU EE 1 Discrete Fourier Transform What is Discrete Fourier Transform (DFT)? (Note: It’s not DTFT – discrete-time Fourier transform) A linear transformation (matrix) Samples of the Fourier transform (DTFT) of an aperiodic (with finite duration) sequence Extension of Discrete Fourier Series (DFS) Review: FT, DTFT, FS, DFS Time signal Transform Coeffs. (periodic/aperiodic) Coeffs. (con- ti./discrete) Analog aperiodic FT Aperiodic Continuous Analog periodic FT FS Aperiodic Aperiodic Continuous (impulse) Discrete Discrete aperiodic DTFT Periodic Continuous Discrete periodic DFS Periodic Discrete Discrete finite-duration DFT The Discrete Fourier Series Properties of N W k N j k N N j N e W e W 2 2 thus , -- N W is periodic with period N. (It is essentially cos and sin) : N k N N k N k N W W W 2 -- 1 0 if , 0 if , N k lk N mN l mN l N W (Pf) (i) 1 , If 0 N N mk N lk N W W W N m l N W N k N k lk N 1 0 1 0 1 (ii) 1 , If l N W N m l 0 1 1 1 1 1 1 0 l N l N N l N N k lk N W W W W -- 1 0 1 N k m lk N mN l W N l Y
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Discrete Fourier Transform - VLSI Signal Processing …twins.ee.nctu.edu.tw/courses/dsp_16/Class note/dsp8.pdf · What is Discrete Fourier Transform (DFT)? ... Linear Convolution
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DSP (2015 Spring) Discrete Fourier Transform
NCTU EE 1
Discrete Fourier Transform
What is Discrete Fourier Transform (DFT)?
(Note: It’s not DTFT – discrete-time Fourier transform)
A linear transformation (matrix)
Samples of the Fourier transform (DTFT) of an aperiodic (with finite duration) sequence
Extension of Discrete Fourier Series (DFS)
Review: FT, DTFT, FS, DFS Time signal Transform Coeffs.
(periodic/aperiodic) Coeffs. (con-ti./discrete)
Analog aperiodic FT Aperiodic Continuous Analog periodic FT