Have fun: E.g., there is Enders A. Robinson, 'Multichannel Time Series Analysis with Digital Computer Programs', Holden-Day, San Francisco. So, the main appl

Have fun: E.g., there is Enders A. Robinson, 'Multichannel Time Series Analysis with Digital Computer Programs', Holden-Day, San Francisco. So, the main application here is finding oil! So, go "boom" and send a sound wave into the earth. At each different layer, get back a reflection of part of the energy. So, to get back just the layers, just use the FFT. Also have fun with X-ray diffraction, holography, etc. For signal processing, the core foundational point is that a 'time-invariant linear system' can be fully described by Fourier theory. Basically the output is a convolution of the input, and the fast way to do a convolution is with the FFT. The impact of the FFT on signal processing was enormous. Have fun!