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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
1.The Four Fourier transforms The signal spaces The transform definitions 2.Relationships 3.Important properties
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
Properties 1 Sinusoids
Example FS & FT of periodic signals
Properties 2 Time change
Properties 3 Symmetry
Properties 4 More symmetry
Properties 5 Duality
Properties 6 Convolution
Discrete-time Fourier Transform (DTFT)
Fourier series 012 1
Discrete Fourier Transform (DFT) 07 1
Fourier series and DTFT
SummaryDefinitions CTFT InvCTFT DTFT InvDTFT
FS InvFS DFT InvDFT
Properties for CTFT Linearity Symmetry Duality Convolution Time-scale Multiplication Modulation Delay
Properties for DTFT Periodic Convolution Multiplication Delay Modulation Upsampling
Important signals Delta Complex exponentials, sinusoids Rectangular pulse, sinc Exponentials
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