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A-A+ B-B+ C-C+ F

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Week 11. Chapter 10 Fourier Transforms 1.The Four Fourier transforms CTFT DTFT FS DFT/S 2.Relationships 3.Important properties

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1.The Four Fourier transforms The signal spaces The transform definitions 2.Relationships 3.Important properties

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The 4 Signal Spaces CTFT is defined for ContSignals DTFT is defined for DiscSignals FS is defined for ContPeriodic p DFT (DFS) defined for DiscPeriodic p

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CTFT

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CTFT Intuition

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Properties 1 Sinusoids

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Example FS & FT of periodic signals

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Properties 2 Time change

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Example

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Properties 3 Symmetry

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Properties 4 More symmetry

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Example

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Properties 5 Duality

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Example

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Properties 6 Convolution

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Properties 7Delay

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Properties 8Modulation

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Discrete-time Fourier Transform (DTFT)

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Example Rectangle

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Example Upsampling

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Fourier series 012 1

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Discrete Fourier Transform (DFT) 07 1

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Fourier series and DTFT

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SummaryDefinitions CTFT InvCTFT DTFT InvDTFT

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FS InvFS DFT InvDFT

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Properties for CTFT Linearity Symmetry Duality Convolution Time-scale Multiplication Modulation Delay

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Properties for DTFT Periodic Convolution Multiplication Delay Modulation Upsampling

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Important signals Delta Complex exponentials, sinusoids Rectangular pulse, sinc Exponentials

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