This paper is concerned with a synthesis study of the fast Fourier transform (FFT), the short time Fourier transform (STFT and the Wigner distribution (WD) in analysing the phonocardiogram signal (PCG) or heart cardiac sounds.     The FFT (Fast Fourier Transform) can provide a basic understanding of the frequency contents of the heart sounds. The STFT is obtained by calculating the Fourier tran...

We show that every scalar valued continuous function f(g) on a compact group G may be written as f(g) = 〈Φ(g)ξ, η〉 for all g ∈ G, where ξ, η are vectors in a separable Hilbert space H, and Φ(g) is a strongly continuous unitary valued function on G which is a product of unitary representations and antirepresentations of G on H. This product is countable, but always converges uniformly on G. More...

The 2D fractional Brownian motion (fBm) model provides a useful tool to model textured surfaces whose roughness is scale-invariant. To represent textures whose roughness is scaledependent, we generalize the fBm model to the extended selfsimilar (ESS) model in this research. We present an estimation algorithm to extract the model parameters from real texture data. Furthermore, a new incremental ...

We revisit the issue of ripples in the primordial power spectra caused by trans-Planckian physics, and the potential for their detection by future cosmological probes. We find that for reasonably large values of the first slow-roll parameter ǫ ( > ∼ 0.001), a positive detection of trans-Planckian ripples can be made even if the amplitude is as low as 10. Data from the Large Synoptic Survey Tele...

This paper gives an example of an auto-regressive (AR) spectral analysis on transient musical sounds. The attack part of many musical sounds is mostly too short to be analysed by a short-time Fourier analysis, whereas this short period of time is long enough for several AR-methods. The AR-spectra obtained from short segments of signals with attack transients have a sufficiently high frequency r...

This application note describes the basics of the Fast Fourier Transform and how to use a Digital Signal Processing Library. The library and design example use Microchip’s dsPIC30F Series Digital Signal Controller, specifically the dsPIC30F3013. The Transform Analysis discusses the differences between the Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT), and how the FFT is ...

Spread options are a fundamental class of derivative contracts written on multiple assets and are widely traded in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient, and flexible enough to apply in general asset models. The present paper introduces a new formula for ge...

A novel approach for scalable length Fast Fourier Transform (FFT) in single Processing Element (single PE) architecture has been developed. Scalable length FFT design meets the different lengths requirement of FFT operation in OFDM system [1]. An efficient mechanism that named Interleaved Rotated Data Allocation (IRDA) to replace multiple-port memory with single-port memory has also been propos...

Application of the cyclotomic Fast Fourier Transform algorithm to the syndrome evaluation problem in classical Reed-Solomon decoders is described. A number of complexity reduction tricks is suggested. Application of the algorithm leads to significant reductions in the complexity of syndrome evaluation. Moreover, automatic generation of the program code implementing the described algorithm is po...

Algorithms for the rapid computation of the forward and inverse discrete Fourier transform for points which are nonequispaced or whose number is unrestricted are presented. The computational procedure is based on approximation using a local Taylor series expansion and the fast Fourier transform (FFT). The forward transform for nonequispaced points is computed as the solution of a linear system ...