Hilbert-Huang Transform (HHT) is a novel data analysis technique for nonlinear and non-stationary data. We present a time-frequency analysis of both simulated light curves and an X-ray burst from the X-ray burster 4U 1702-429 with both the HHT and the Windowed Fast Fourier Transform (WFFT) methods. Our results show that the HHT method has failed in all cases for light curves with Poissonian flu...

Fractional Fourier Transform is a generalization of the classical Fourier Transform. The Fractional Fourier span in general depends on the amplitude and phase functions of the signal and varies with the transform order. However, with the development of the Fractional Fourier filter banks, it is advantageous in some cases to have different transform orders for different filter banks to achieve b...

The Ridgelet Packets library provides a large family of orthonormal bases for functions f(x, y) in L(dxdy) which includes orthonormal ridgelets as well as bases deriving from tilings reminiscent from the theory of wavelets and the study of oscillatory Fourier integrals. An intuitively appealing feature: many of these bases have elements whose envelope is strongly aligned along specified ‘ridges...

This paper describes a diagnostic system for processing high-bandwidth vibration data from distributed sensors for monitoring and diagnosis of electromechanical machines. The system employs time-frequency and principal component analysis techniques to extract and compress features and a Bayesian decision analysis to combine and classify data from multiple sources. Experimental multi-sensor diag...

In this paper, a concept of integer fast Fourier transform (IntFFT) for approximating the discrete Fourier transform is introduced. Unlike the fixed-point fast Fourier transform (FxpFFT), the new transform has the properties that it is an integer-to-integer mapping, is power adaptable and is reversible. The lifting scheme is used to approximate complex multiplications appearing in the FFT latti...

This paper describes a novel structure for a hardwired fast Fourier transform (FFT) signal processor that promises to permit digital spectrum analysis to achieve throughput rates consistent with extremely wide-band radars. The technique is based on the use of serial storage for data and intermediate results and multiple arithmetic units each of which carries out a sparse Fourier transform. Deta...

• Forward and Inverse 32-, 64-, 128-, 256-, 512-, 1,024-, and 2,048-Point Complex FFT • Decimation–In-Time (DIT) Radix-2 Implementation Optimized for Actel FPGAs • Selection of Unconditional or Conditional Block Floating-Point Scaling • Embedded RAM-Block-Based Twiddle Factor Generator • 8to 16-Bit Configurable Input/Output Data and Twiddle Coefficients Precision • Naturally Ordered Input and O...

Fast Quaternionic Fourier Transform 1 Acknowledgements I am grateful to all those who contributed to this project, to my professors, especially Gerald Sommer, and other professionals who have taken the time to answer questions and forced me to ask new ones. I particularly appreciate the professional wisdom and assistance of Thomas B ulow, the support in technical details by Udo Mahlmeister and ...

In the next two lectures, we will continue to expand our toolbox for computing in frequency domain, by adding two important computational tools. The first, the Fast Fourier Transform (FFT) is a family of algorithms for efficiently computing the Discrete Fourier Transform. These algorithms are of great practical importance, as theymake it possible to perform frequency domain analysis of very lar...