Today we defined the Discrete Fourier Transform (DFT) and its inverse. The main mathematical property (stated as Result A in the text book) is that the DFT turns the convolution into a componentwise product. For n = 4, we derived this property stated in the book as corollary to Result A. At the end of the lecture, we gave a conceptual outline of filter design, which happens in the frequency domain. The inverse DFT is applied to get the transfer function of the filter in the time domain.