Fourier Transform and Convolution Product in Signal Processing

This lecture covers the Fourier transform, its properties, and the convolution product, which is essential in signal processing. The convolution product is defined for two functions and has properties similar to regular multiplication. It is crucial in various contexts, especially in the study of linear time-invariant filters. These filters transform input signals into output signals, with the output signal obtained by convolving the input signal with a specific function. The lecture also explores practical applications of the convolution product in designing filters, such as low-pass and band-pass filters, and discusses the importance of the transfer function in signal processing.