The Fourier and Hilbert transforms Under the Bargmann transform
نویسندگان
چکیده
منابع مشابه
Fourier Transforms and the Fast Fourier Transform ( FFT ) Algorithm
and the inverse Fourier transform is f (x) = 1 2π ∫ ∞ −∞ F(ω)e dω Recall that i = √−1 and eiθ = cos θ+ i sin θ. Think of it as a transformation into a different set of basis functions. The Fourier transform uses complex exponentials (sinusoids) of various frequencies as its basis functions. (Other transforms, such as Z, Laplace, Cosine, Wavelet, and Hartley, use different basis functions). A Fo...
متن کاملPathologies cardiac discrimination using the Fast Fourir Transform (FFT) The short time Fourier transforms (STFT) and the Wigner distribution (WD)
This paper is concerned with a synthesis study of the fast Fourier transform (FFT), the short time Fourier transform (STFT and the Wigner distribution (WD) in analysing the phonocardiogram signal (PCG) or heart cardiac sounds. The FFT (Fast Fourier Transform) can provide a basic understanding of the frequency contents of the heart sounds. The STFT is obtained by calculating the Fourier tran...
متن کاملGeneralizations of the Bargmann Transform
We present a new way of obtaining the Bargmann transform between L 2 (R n) and the Fock space F = F(C n) via a simple restriction principle applied to holo-morphic functions. This same principle also recovers the transform between functions on a compact Lie group and holomorphic functions on its complexii-cation studied by Gross, Hall, Hijab et al., see 1] and 2], and it gives in a similar way ...
متن کاملA generalized Mobius transform, arithmetic Fourier transforms, and primitive roots
A general approach to arithmetic Fourier transforms is developed. The implementation is based on sine and cosine killer procedures pertaining to a generalized Möbius transform involving reduced periodic multiplicative arithmetical functions. It is shown that cosine killer procedures exist whenever one half of Euler’s totient function of the order of the transform is odd. Primitive roots and ind...
متن کاملA generalized Mobius transform and arithmetic Fourier transforms
A general approach to arithmetic Fourier transforms is developed. The implementation is based on the concept of killer polynomials and the solution of an arithmetic deconvolution problem pertaining to a generalized Mobius transform. This results in an extension of the Bruns procedure, valid for all prime numbers, and in an AFT that extracts directly the sine coefficients from the Fourier series.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Complex Variables and Elliptic Equations
سال: 2017
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476933.2017.1324430