It seems likely that improvements in arithmetic speed will continue to outpace advances in communications bandwidth. Furthermore, as more and more problems are working on huge datasets, it is becoming increasingly likely that data will be distributed across many processors because one processor does not have sufficient storage capacity. For these reasons, we propose that an inexact DFT such as ...

Definitions Let F be the real vector space of real functions on 2 [n] (the set of subsets of [n] = {1,. .. , n}). Define an inner product on F by f, g = 1 2 n A⊆[n] f (A)g(A). For S ⊆ [n], let x S ∈ F be the function x S (A) = (−1) |A∩S|. Now we compute x S , x T = 1 2 n A⊆[n]

Quantum Fourier transform (QFT) is an important part of many quantum algorithms. However, there are few reports on fractional (QFRFT). The main reason that the definitions (FRFT) diverse, while some do not include unitarity, which leads to studies pointing out no QFRFT. In this paper, we first present a reformulation weighted (WFRFT) and prove its thereby proposing (QWFRFT). proposal QWFRFT pro...

Abstract Fast (sub-second) spectroscopy with high spectral resolution is of vital importance for revealing quantum chemistry kinetics complex chemical and biological reactions. Fourier transform (FT) spectrometers can achieve operate at hundreds ms time scales in rapid-scan mode. However, the linear translation a scanning mirror imposes stringent time-resolution limitations to these systems, wh...

This paper will look at an approach that uses symmetric properties of the basis function to remove redundancies in the calculation of discrete Fourier transform (DFT). We will develop an algorithm, called the quick Fourier transform (QFT), that will reduce 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 p...