Fourier Transform: Concepts and Applications

This lecture introduces the Fourier transform as a tool to analyze signals beyond periodicity. The instructor explains the formula, conventions, and physical interpretation of the Fourier transform. They discuss the differences between Fourier series and transform, emphasizing the continuous spectrum of frequencies in the transform. Applications in signal processing and differential equations are highlighted, with a focus on the invertibility of the transform. Important properties such as linearity, modulation, and energy conservation are covered. The lecture concludes with the key concept that derivatives in the time domain correspond to multiplications in the frequency domain, showcasing the utility of the Fourier transform in solving differential equations.