A Note on the Diagonalization of the Discrete Fourier Transform
نویسندگان
چکیده
Following the approach developed by S. Gurevich and R. Hadani, an analytical formula of the canonical basis of the DFT is given for the case N = p where p is a prime number and p ≡ 1 (mod 4).
منابع مشابه
A general construction of Reed-Solomon codes based on generalized discrete Fourier transform
In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes enjoy nice algebraic properties just as the classic one.
متن کاملDetection of high impedance faults in distribution networks using Discrete Fourier Transform
In this paper, a new method for extracting dynamic properties for High Impedance Fault (HIF) detection using discrete Fourier transform (DFT) is proposed. Unlike conventional methods that use features extracted from data windows after fault to detect high impedance fault, in the proposed method, using the disturbance detection algorithm in the network, the normalized changes of the selected fea...
متن کاملApplication of the Weil representation: diagonalization of the discrete Fourier transform
We survey a new application of the Weil representation to construct a canonical basis Φ of eigenvectors for the discrete Fourier transform (DFT). The transition matrix Θ from the standard basis to Φ defines a novel transform which we call the discrete oscillator transform (DOT for short). In addition, we describe a fast algorithm for computing Θ in certain cases.
متن کاملVibration Suppression of Fuel Sloshing using Subband Adaptive Filtering (RESEARCH NOTE)
One of the main vibration problems of aerospace vehicles with liquid fuel propulsion system is fuel sloshing. This phenomenon is a low frequency vibrational challenge which can affect the motion of the vehicle and degrade the stability of the main control system. In this regards, the motion of the liquid will be very critical when the frequency of the sloshing is very close to the frequencies o...
متن کاملBenchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization
Signal processing techniques have been developed that use different strategies to bypass the Nyquist sampling theorem in order to recover more information than a traditional discrete Fourier transform. Here we examine three such methods: filter diagonalization, compressed sensing, and super-resolution. We apply them to a broad range of signal forms commonly found in science and engineering in o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/0902.1267 شماره
صفحات -
تاریخ انتشار 2009