Signal Processing: Fourier, Sampling, and Filters

Audio, images, sensors and instruments all rest on the same four ideas, and getting any of them wrong destroys data silently. This path builds the frequency domain and why sinusoids get the job, the sampling rule that cannot be broken and what aliasing does when it is, convolution and the filters built from it, and how to read a spectrum without mistaking the analysis for the signal. Every number is computed, so you can reproduce it.