Fourier Transformation and Dirac Pulse Train

This lecture covers the Fourier transformation, including the sampling property, generalized Fourier transformation, and its relation with the sign function. It also delves into the Dirac pulse train, its definition, Fourier transformation, and formal calculations. The development in series of Fourier, convergence of the Fourier series, and partial sums are discussed. Additionally, the lecture explores the interpretation of Fourier series, convolutional shift, periodization, frequency sampling, and the Fourier series of a periodic signal. The synthesis of periodic signals, simple generators, and the efficiency of periodization and frequency sampling are also addressed.