Comment by waffletower

I was surprised to see such a long article on use and miuse of the Discrete Fourier Transform (DFT) with only brief and casual mention of "sidelobes" -- there wasn't formal discussion of the frequency response of the DFT window function and how it relates to transform output. The latter is typically represented evaluating the z-transform of the window function along the unit circle. While steeped in this mathematics the attendant visualizations can be helpful to impart an intuitive understanding of what the DFT is doing with its inputs. While I would recommend a text that covers the topic such as "A Digital Signal Processing Primer" by Ken Steiglitz, Gemini was able to show the response graph of a DFT window function with the following prompt: "what is the z transform of the hamming window in a discrete fourier transform context"