Topic
Discrete sine transform
About: Discrete sine transform is a research topic. Over the lifetime, 3269 publications have been published within this topic receiving 73181 citations.
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TL;DR: The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT and is used to filter a two-dimensional picture, and the results are presented with a comparison to the standard FFT.
Abstract: A transform analogous to the discrete Fourier transform is defined on the Galois field GF(p), where p is a prime of the form k X 2n + 1, where k and n are integers. Such transforms offer a substantial variety of possible transform lengths and dynamic ranges. The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT. A transform of this type is used to filter a two-dimensional picture (e.g., 256 X 256 samples), and the results are presented with a comparison to the standard FFT. An absence of roundoff errors is an important feature of this technique.
44 citations
TL;DR: In an algorithm proposed here, DFT coefficients are computed via the Walsh transform (WT), which is superior to the fast Fourier transform (FFT) approach in applications where L is relatively small compared with N.
Abstract: This paper presents a new computational algorithm for the discrete Fourier transform (DFT). In an algorithm proposed here, DFT coefficients are computed via the Walsh transform (WT). The number of multiplications required by the new algorithm is approximately NL/6, where N is the number of data points and L is the number of Fourier coefficients desired. As such, it is superior to the fast Fourier transform (FFT) approach in applications where L is relatively small compared with N. It is also useful in cases where the Walsh and Fourier coefficients are both desired.
44 citations
01 Jan 2006
TL;DR: The definition of LCT and some special cases are given at first, followed by its properties as listed, and the discrete linear canonical transform is introduced.
Abstract: As an emerging tool for signal processing,the linear canonical transform(LCT) proves itself to be more general and flexible than the Fourier transform as well as the fractional Fourier transform.So it can slove problems that can't be dealt with well by the latter.In this paper,the definition of LCT and some special cases are given at first,followed by its properties as listed.Besides,the discrete linear canonical transform is introduced.The implication of LCT is illustrated finally,displaying(LCT's) potentials and capabilities in the field of signal processing.
44 citations
TL;DR: Using the NUFFT scheme, nonuniform fast cosine transform and fast Hankel transform algorithms are developed and provide an efficient tool for numerical differentiation and integration, the key in the solutions to differential equations and volume integral equations.
Abstract: We review our efforts to apply the nonuniform fast Fourier transform (NUFFT) and related fast transform algorithms to numerical solutions of Maxwell's equations in the time and frequency domains. The NUFFT is a fast algorithm to perform the discrete Fourier transform of data sampled nonuniformly (NUDFT). Through oversampling and fast interpolation, the forward and inverse NUFFTs can be achieved with O(N log/sub 2/ N) arithmetic operations, asymptotically the same as the regular fast Fourier transform (FFT) algorithms. Using the NUFFT scheme, we develop nonuniform fast cosine transform (NUFCT) and fast Hankel transform (NUFHT) algorithms. These algorithms provide an efficient tool for numerical differentiation and integration, the key in the solutions to differential equations and volume integral equations. We present sample applications of these nonuniform fast transform algorithms in the numerical solution to Maxwell's equations.
44 citations
TL;DR: The dilating Gabor transformation is introduced by using a changeable window of Gaussian function in a conventional Gabor transform to analyze the optical fringes of 3-D shape measurement, providing more accurate results than Fourier transform and Gabortransform.
Abstract: In order to overcome the limitations of conventional Fourier transform and Gabor transform analyzing nonstationary signals, dilating Gabor transform is applied to analyze the optical fringes of 3-D shape measurement. The dilating Gabor transformation is introduced by using a changeable window of Gaussian function in a conventional Gabor transform. This phase analysis method provides more accurate results than Fourier transform and Gabor transform. Simulation and experimental results are presented that demonstrate the validity of the principle.
44 citations