EECE 301 Note Set 24 DFT Definition

EECE 301 Note Set 24 DFT Definition - EECE 301 Signals &...

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1/15 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #24 • D-T Signals: Definition of DFT – Numerical FT Analysis • Reading Assignment: Sections 4.2 of Kamen and Heck
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2/15 Ch. 1 Intro C-T Signal Model Functions on Real Line D-T Signal Model Functions on Integers System Properties LTI Causal Etc Ch. 2 Diff Eqs C-T System Model Differential Equations D-T Signal Model Difference Equations Zero-State Response Zero-Input Response Characteristic Eq. Ch. 2 Convolution C-T System Model Convolution Integral D-T System Model Convolution Sum Ch. 3: CT Fourier Signal Models Fourier Series Periodic Signals Fourier Transform (CTFT) Non-Periodic Signals New System Model New Signal Models Ch. 5: CT Fourier System Models Frequency Response Based on Fourier Transform New System Model Ch. 4: DT Fourier Signal Models DTFT (for “Hand” Analysis) DFT & FFT (for Computer Analysis) New Signal Model Powerful Analysis Tool Ch. 6 & 8: Laplace Models for CT Signals & Systems Transfer Function New System Model Ch. 7: Z Trans. Models for DT Signals & Systems Transfer Function New System Model Ch. 5: DT Fourier System Models Freq. Response for DT Based on DTFT New System Model Course Flow Diagram The arrows here show conceptual flow between ideas. Note the parallel structure between the pink blocks (C-T Freq. Analysis) and the blue blocks (D-T Freq. Analysis).
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3/15 4.2 Discrete Fourier Transform (DFT) (DTFT) ] [ ) ( Namely −∞ = Ω = Ω n n j e n x X can be computed analytically (at least in principle) when we have an equation model for x [ n ] -The first one (“infinite # of terms”)… isn’t a problem if x [ n ] has “finite duration” -The second one (“infinitely many points”)… is always a problem!! We’ve seen that the DTFT is a good analytical tool for D-T signals (and systems – as we’ll see later when we return to Ch. 5) Q: Well… why can’t we use a computer to compute the DTFT from Data ? A: There are two reasons why we can’t !!
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This note was uploaded on 02/29/2012 for the course EECE 301 taught by Professor Fowler during the Fall '08 term at Binghamton University.

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EECE 301 Note Set 24 DFT Definition - EECE 301 Signals &...

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