کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1707743 1519468 2015 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The AFD methods to compute Hilbert transform
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مکانیک محاسباتی
پیش نمایش صفحه اول مقاله
The AFD methods to compute Hilbert transform
چکیده انگلیسی

In the literature adaptive Fourier decomposition is abbreviated as AFD that addresses adaptive rational approximation, or alternatively adaptive Takenaka–Malmquist system approximation. The AFD type approximations may be characterized as adaptive approximations by linear combinations of parameterized Szegö and higher order Szegö kernels. This note proposes two kinds of such analytic approximations of which one is called maximal-energy AFDs, including core AFD, Unwending AFD and Cyclic AFD; and the other is again linear combinations of Szegö kernels but generated through SVM methods. The proposed methods are based on the fact that the imaginary part of an analytic signal is the Hilbert transform of its real part. As consequence, when a sequence of rational analytic functions approximates an analytic signal, then the real parts and imaginary parts of the functions in the sequence approximate, respectively, the original real-valued signals and its Hilbert transform. The two approximations have the same errors in the energy sense due to the fact that Hilbert transformation is a unitary operator in the L2L2 space. This paper for the first time promotes the complex analytic method for computing Hilbert transforms. Experiments show that such computational methods are as effective as the commonly used one based on FFT.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics Letters - Volume 45, July 2015, Pages 18–24
نویسندگان
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