{"product_id":"flickermoth-the-pink-noise-moth-queen-mug","title":"Flickermoth, the Pink-Noise Moth Queen Mug","description":"\u003cp\u003eFlicker (1\/f) noise: spectral density S(f) ∝ 1\/f\u003csup\u003eα\u003c\/sup\u003e with α ≈ 1. When the fluctuating quantity is fractional frequency y (flicker FM, S\u003csub\u003ey\u003c\/sub\u003e(f) ∝ 1\/f), the Allan deviation stops falling and flattens into a floor, σ\u003csub\u003ey\u003c\/sub\u003e(τ) = const, so averaging longer stops helping; for white FM it falls as τ\u003csup\u003e−1\/2\u003c\/sup\u003e.\u003c\/p\u003e\n\u003cp\u003eThe joke: With white noise σ falls as 1\/√τ; with 1\/f it plateaus, so the extra 6 hours of averaging bought nothing. The slogan on the mug reads \u003cstrong\u003eAVERAGING LONGER. REGRETTING LONGER.\u003c\/strong\u003e\u003c\/p\u003e\n\u003cp\u003eSource: J. B. Johnson, Phys. Rev. 26, 71 (1925) (low-frequency 'flicker effect'); D. W. Allan, Proc. IEEE 54, 221 (1966).\u003c\/p\u003e","brand":"Printify","offers":[{"title":"11oz","offer_id":50976049692775,"sku":"21724511975243205581","price":21.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/16176038747523234160_2048.jpg?v=1793683500","url":"https:\/\/pixelatedphysics.com\/sv\/products\/flickermoth-the-pink-noise-moth-queen-mug","provider":"Pixelated Physics","version":"1.0","type":"link"}