seems to be missing some stuff. first, the notion that most real-valued functions can be decomposed to an infinite sum of orthogonal basis functions of which fourier bases are one. this is the key intuition that builds up the notion of linear decomposition and then from which the practical realities of computing finite dfts on sampled data arise. second, the talk of transients absent the use of stfts and spectrograms seems really weird to me. if you want to look at transients in nonstationary data, the stft and spectrogram visualization are critical. computing one big dft and looking at energy at dc to detect drift seems weird to me.

maybe this is the way mechanical engineers look at it, but leaving out stfts and spectrograms seems super weird to me.