Lattices Part II — Dual Lattices , Fourier Transform , Smoothing Parameter , Public Key
نویسنده
چکیده
Fourier transform Consider the interval [0, λ] and suppose that we identify the point λ with 0 (i.e., think of it as a Torus and work modulo λ). Another way to think about this is as the basic cell of the lattice λZ, whose dual is the lattice (1/λ)Z. A periodic function on this torus has to period length of the form λ/n for an integer n. Thus, the Fourier transform of a function on this torus involves representing it as a sum of functions of the form x 7→ e−2πinx/λ. More generally, the Fourier transform of a function f on P(L) represents f as the sum of functions of the form x 7→ e2πi〈x,y〉 where y is an element in L∗. That is, we have the following theorem:
منابع مشابه
Lattices Part II — Dual Lattices , Fourier Transform , Smoothing Parameter , Public Key Encryption
Fourier transform Consider the interval [0, λ] and suppose that we identify the point λ with 0 (i.e., think of it as a Torus and work modulo λ). Another way to think about this is as the basic cell of the lattice λZ, whose dual is the lattice (1/λ)Z. A periodic function on this torus has to period length of the form λ/n for an integer n. Thus, the Fourier transform of a function on this torus i...
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