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SKEL4223 Digital Signal Processing
Discrete Fourier Transform
Nor Aini Zakaria
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Introduction
In digital system, all values must be in discrete.
However, discrete signal in time-domain that undergoes DTFT will
produce a continuous frequency value in frequency-domain.
Thus, it is impossible to compute Fourier Transform in a digitalsystem.
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Frequency DomainTime Domainn − discrete f − continuous
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Introduction (cont.)
To overcome the problem, Discrete Fourier Transform (DFT) is
introduced where both time and frequency are in discrete form.
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Frequency DomainTime Domain
n − discrete k − discrete
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Relationship of DFT to DTFS (cont.)
10
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00 10
n
Aperiodic signal with length 10 samples
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5
0-20 -10 0 10 20
n
Periodic signal with 10 samples in each period
x
x
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References
John G. Proakis, Dimitris K Manolakis, “Digital Signal Processing:1)
4thPrinciple, Algorithm and Applications”, Prentice-Hall,
(2006).
edition
2) Sanjit K. Mitra, “Digital Signal Processing-A Computer Based
3rdApproach”, McGraw-Hill Companies, edition (2005).
3) Alan V. Oppenheim, Ronald W. Schafer, “Discrete-Time Signal
3rdProcessing”, Prentice-Hall, edition (2009).