Chapter 3: Symplectic Fourier Transform and the DD Domain

Learning Objectives

• State the symplectic Fourier transform (SFT) in continuous and discrete forms
• Derive the SFT as the 2D transform that links the delay-Doppler and time-frequency planes
• Compute the ISFFT and SFFT used by the OTFS transmitter and receiver
• Place QAM data symbols on the DD grid and produce the corresponding TF-domain precoded OFDM frame
• Establish the discrete delay-Doppler grid with finite-dimensional Zak and SFT machinery