fourier.pdf
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A Scale Invariant Frequency Domain Kernel Tianshu Huang and Nimit Kalra 1 Signal Space 1.1 Background Definition 1. The Fourier transform of f is denoted fˆ or F (f ), with both notations used interchangeably. Theorem 1 (Plancherel Theorem). For complex valued functions f, g ∈ L2 , Z Z f (x)g(x)dx = fˆ(ξ)ĝ(ξ)dξ ⇐⇒ hf, gi = hfˆ, ĝi R R As a corollary (Parseval’s Theorem), using f = g ⇒ f g = |f |2 , Z Z…
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