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- W2564671497 abstract "A function f : Z n → C can be represented as a linear combination f ( x ) = ∑ α ∈ Z n f ˆ ( α ) χ α , n ( x ) where f ˆ is the (discrete) Fourier transform of f . Clearly, the basis { χ α , n ( x ) : = exp ( 2 π i α x / n ) } depends on the value n . We show that if f has “large” Fourier coefficients, then the function f ˜ : Z m → C , given by f ˜ ( x ) = { f ( x ) when 0 ≤ x < min ( n , m ) , 0 otherwise , also has “large” coefficients. Moreover, they are all contained in a “small” interval around ⌊ m n α ⌉ for each α ∈ Z n such that f ˆ ( α ) is large. One can use this result to recover the large Fourier coefficients of a function f by redefining it on a convenient domain. One can also use this result to reprove a result by Morillo and Ràfols: single-bit functions, defined over any domain, are Fourier concentrated ." @default.
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- W2564671497 date "2018-07-01" @default.
- W2564671497 modified "2023-10-17" @default.
- W2564671497 title "On sets of large Fourier transform under changes in domain" @default.
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- W2564671497 doi "https://doi.org/10.1016/j.acha.2017.08.002" @default.
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