As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain. The resulting sampling theorem extends not only the classical Whittaker-Shannon-Kotelnikov sampling ...

C06FKF Circular convolution or correlation of two real vectors, extra workspace for greater speed C06FPF Multiple one-dimensional real discrete Fourier transforms C06FQF Multiple one-dimensional Hermitian discrete Fourier transforms C06FRF Multiple one-dimensional complex discrete Fourier transforms C06FUF Two-dimensional complex discrete Fourier transform C06FXF Three-dimensional complex discr...

-Fractional Fourier Transform is a generalization of the classical Fourier Transform, which has found its most useful applications for the transient analysis of the signals. This paper studies the span of the Fractional Fourier Transform in relation with the amplitude and phase functions of the signal and provides a mathematical derivation for the generalized case. The derived expression is sho...

A new feature representation approach, the simultaneous usage of the real and imaginary Fourier components with taking into account the covariance between these components, was compared with the Cosine transform approach for Gaussian recognition. 2003 Elsevier B.V. All rights reserved.

We propose an algorithm that uses the discrete wavelet transform (DWT) as a tool to compute the discrete Fourier transform (DFT). The Cooley-Tukey FFT is shown to be a special case of the proposed algorithm when the wavelets in use are trivial. If no intermediate coeecients are dropped and no approximations are made, the proposed algorithm computes the exact result, and its computational comple...

We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to ...

We find a formula that relates the Fourier transform of a radial function on R with the Fourier transform of the same function defined on R. This formula enables one to explicitly calculate the Fourier transform of any radial function f(r) in any dimension, provided one knows the Fourier transform of the one-dimensional function t 7→ f(|t|) and the two-dimensional function (x1, x2) 7→ f(|(x1, x...

The fractional Fourier transform is a time–frequency distribution and an extension of the classical Fourier transform. There are several known applications of the fractional Fourier transform in the areas of signal processing, especially in signal restoration and noise removal. This paper provides an introduction to the fractional Fourier transform and its applications. These applications deman...

A 64-Point Fourier Transform Chip for High-Speed. Plications compared to the conventional radix-2 64-point FFT algorithm. Tbfft1V002.pdf. A 64-Point Fourier Transform Chip for Video. Motion Compensation Using Phase Correlation. Colin Chiu Wing Hui, Tiong Jiu Ding.A 64-point Fourier transform chip for high-speed wireless LAN application using OFDM. The core area of this chip is 6. 8 mm2.low-powe...