Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

one of the most common signals used for achieving high range resolution in radar is stepped-frequency signals. when a target is stationary in these radars, dft (discrete fourier transform) based processing is used to attain high range resolution profile (hrrp). however, in the case of moving target, due to spreading of the echo signal spectrum, dft based processing is not optimal and decreases ...

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) in [3]. It also has been generalized into the 2-D unseparable fractional Fourier transform wit...

The discrete fractional Fourier transform (DFRFT) is the generalization of discrete Fourier transform. Many types of DFRFT have been derived and are useful for signal processing applications. In this paper, we will introduce a new type of DFRFT, which are unitary, reversible, and flexible; in addition, the closed-form analytic expression can be obtained. It works in performance similar to the c...

Generalized Discrete Fourier Transform (GDFT) with nonlinear phase is a complex valued, constant modulus orthogonal function set. GDFT can be effectively used discrete multi-tone (DMT), orthogonal frequency division multiplexing (OFDM) and code division multiple access (CDMA) communication systems. The constant modulus transforms like discrete Fourier transform (DFT), Walsh transform, and Gold ...

Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributiona...

Two standard tools for signal analysis are the short{time Fourier transform and the continuous wavelet transform. These tools arise as matrix coeecients of square integrable representations of the Heisenberg and aane groups respectively, and discrete frame decompositions of L 2 arise from approximations of corresponding reproducing formulae. Here we study two groups, the so-called aane Weyl-Hei...