Research Article Logarithm of the Discrete Fourier Transform
نویسندگان
چکیده
Our choice of normalization factor ensures that F is unitary: F† ◦F = I , where I is the identity transformation, and F† is the Hermitian conjugate of F, that is, (F†) jk = Fk j . Also recall that the exponential of a matrix M is given by the infinite series (M) . = ∑∞ p=0(1/p!)M (provided it converges). Thus a complex-linear map f : Cn→Cn is a logarithm for F if F = exp ( f ), and we write f = log(F). For more information on the exponential and logarithm maps see, [1, Chapter 4].
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