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 ...

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational compl...

This paper looks at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of the discrete Fourier transform (DFT). We develop an algorithm, called the quick Fourier transform (QFT), that reduces the number of oating point operations necessary to compute the DFT by a factor of two or four over direct methods or Goertzel's method for prime leng...

Shape is an essential visual feature of an image and it is widely used to describe image content in image classification and retrieval. In this paper, two new Fourier-based approaches for contour-based shape description are presented. These approaches present Fourier descriptors in multiple scales, which improves the shape classification and retrieval accuracy. The proposed methods outperform o...