m11 - discrete fourier transform

8/18/2019 M11 - Discrete Fourier Transform

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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.

•

•

•

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.

•

Frequency DomainTime Domain

n − discrete k − discrete


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Relationship of DFT to DTFS (cont.)

10

5

00 10

n

Aperiodic signal with length 10 samples

10

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).

m11 - discrete fourier transform

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