An Interesting Fourier Transform – 1/F Noise
Power-law signals have a neat Fourier trick: their transforms are power laws too, but with important caveats. Steve Smith walks through the t^α ↔ ω^{-(α+1)} relation, shows how the unit step, the Gamma scaling and a nontrivial phase change the picture, and highlights the special α = -0.5 case that links to 1/f noise. The post frames why phase and physical interpretation keep 1/f noise mysterious.
Summary
Steve Smith explains the relationship between power-law signals and their Fourier transforms, emphasizing how certain parameters can alter the outcome. He focuses on the unique case of α = -0.5, connecting it to the enigmatic 1/f noise and discussing the significance of phase in understanding its complexities.
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