mistake #1 when trying to understand or explain the Fourier Transform is to discuss the breakdown of f(t) into sine/cosine components. it's much easier to unde

mistake #1 when trying to understand or explain the Fourier Transform is to discuss the breakdown of f(t) into sine/cosine components. it's much easier to understand in terms of the original e^(i * w * t) waveforms, and the effects of integrating [-inf,inf]integ[f(t) * e^(-i * W * t)] for any given W. there's a nice visualization of this that involves considering the "helical" e^(i * w * t) waveforms and the twist that e^(-i * W * t) applies to these. bla bla bla.