Chapter 2: The Zak Transform

Learning Objectives

• State the definition of the Zak transform and derive its quasi-periodicity property
• Compute the Zak transform of rectangular, Gaussian, and chirp pulses
• Connect the Zak transform to the short-time Fourier transform (STFT) and the Gabor frame
• Explain how the Zak transform maps a time-domain pulse to the delay-Doppler plane
• Derive the discrete Zak transform and its role as the 'prototype' building block of OTFS