Differential commuting operator and closed-form eigenfunctions for linear canonical transforms

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Differential commuting operator and closed-form eigenfunctions for linear canonical transforms.

The linear canonical transform (LCT) with a, b, c, d parameter plays an important role in quantum mechanics, optics, and signal processing. The eigenfunctions of the LCT are also important because they describe the self-imaging phenomenon in optical systems. However, the existing solutions for the eigenfunctions of the LCT are divided into many cases and they lack a systematic way to solve thes...

متن کامل

Eigenfunctions of linear canonical transform

The linear canonical transform (the LCT) is a useful tool for optical system analysis and signal processing. It is parameterized by a 2 2 matrix . Many operations, such as the Fourier transform (FT), fractional Fourier transform (FRFT), Fresnel transform, and scaling operations are all the special cases of the LCT. In this paper, we will discuss the eigenfunctions of the LCT. The eigenfunctions...

متن کامل

Fast linear canonical transforms.

The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization, sampling, and fast algorithms, and identify key results. We then propose a frequency-division fast linear canonical transform algorithm comparable to the Sande-Tukey fast Fourier tran...

متن کامل

Eigenfunctions of the offset Fourier, fractional Fourier, and linear canonical transforms.

The offset Fourier transform (offset FT), offset fractional Fourier transform (offset FRFT), and offset linear canonical transform (offset LCT) are the space-shifted and frequency-modulated versions of the original transforms. They are more general and flexible than the original ones. We derive the eigenfunctions and the eigenvalues of the offset FT, FRFT, and LCT. We can use their eigenfunctio...

متن کامل

Closed Form Solutions for Linear Differential and Difference Equations

Finding closed form solutions of differential equations has a long history in computer algebra. For example, the Risch algorithm (1969) decides if the equation y′ = f can be solved in terms of elementary functions. These are functions that can be written in terms of exp and log, where “in terms of” allows for field operations, composition, and algebraic extensions. More generally, functions are...

متن کامل

ذخیره 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: Journal of the Optical Society of America A

سال: 2013

ISSN: 1084-7529,1520-8532

DOI: 10.1364/josaa.30.002096