We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are...We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ＂Y＂ type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.展开更多
In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead ...In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead of complex exponential basis in this case to improve the system performance. However, in multicarrier transmission, the high peak to average power ratio (PAPR) of the transmitted signal is one of the difficult problems that face both the chirp and the exponential basis. In this paper, an evaluation for the PAPR performance of a multicarrier system based on the fractional cosine transform (FrCT) is introduced and then compared with DFrFT and FFT. Moreover, applying the SLAM technique over these systems is provided to understand the behaviour of these systems when applying SLAM. Simulations verify that this system obtains a better PAPR performance. Moreover, further PAPR reduction can be gained using the well-known PAPR reduction methods. Moreover, applying SLAM technique improves the performance of (dB) by 4 dB to 5 dB and all systems become as competitive to each other when SLAM is applied. Finally, BER performance comparison among OFDM, Discrete Cosine Transform MCM (DCT- MCM), Discrete Hartley Transform MCM (DHT-MCM), DFrFT-OCDM and DFrCT- OCDM MCM systems was done by means of simulation over 100,000 multicarrier blocks for each one and showed that our proposed scenario gave the best performance.展开更多
We consider complex-valued functions f ∈ L^1 （R^2＋）, where R＋ ：= [0,∞）, and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to o...We consider complex-valued functions f ∈ L^1 （R^2＋）, where R＋ ：= [0,∞）, and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to one of the two-dimensional Lipschitz classes Lip（a,β） for some 0 〈 α,β ≤ 1; or to one of the Zygmund classes Zyg（α,β） for some 0 〈 α,β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L^1 （R^2＋）.展开更多
Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + ...Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.展开更多
The Fourier transform is very important to numerous applications in science and engineering. However, its usefulness is hampered by its computational expense. In this paper, in an attempt to develop a faster method fo...The Fourier transform is very important to numerous applications in science and engineering. However, its usefulness is hampered by its computational expense. In this paper, in an attempt to develop a faster method for computing Fourier transforms, the authors present parallel implementations of two new algorithms developed for the type IV Discrete Cosine Transform （DCT-IV） which support the new interleaved fast Fourier transform method. The authors discuss the realizations of their implementations using two paradigms. The first involved commodity equipment and the Message-Passing Interface （MPI） library. The second utilized the RapidMind development platform and the Cell Broadband Engine （BE） processor. These experiments indicate that the authors＇ rotation-based algorithm is preferable to their lifting-based algorithm on the platforms tested, with increased efficiency demonstrated by their MPI implementation for large data sets. Finally, the authors outline future work by discussing an architecture-oriented method for computing DCT-IVs which promises further optimization. The results indicate a promising fresh direction in the search for efficient ways to compute Fourier transforms.展开更多
This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a ...This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.展开更多
A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform...A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π, and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.展开更多
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ...Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.展开更多
基金supported by the Scientific Research Starting Foundation of HoHai University,China(2084/40801136)the Fundamental Research Funds for the Central Universities(No.2009B12514)
文摘We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ＂Y＂ type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.
文摘In doubly selective fading channels, the orthogonal frequency division multiplexing (OFDM) multicarrier system may fail. Chirp like basis (fractional Fourier transform-fractional cosine transform) may be used instead of complex exponential basis in this case to improve the system performance. However, in multicarrier transmission, the high peak to average power ratio (PAPR) of the transmitted signal is one of the difficult problems that face both the chirp and the exponential basis. In this paper, an evaluation for the PAPR performance of a multicarrier system based on the fractional cosine transform (FrCT) is introduced and then compared with DFrFT and FFT. Moreover, applying the SLAM technique over these systems is provided to understand the behaviour of these systems when applying SLAM. Simulations verify that this system obtains a better PAPR performance. Moreover, further PAPR reduction can be gained using the well-known PAPR reduction methods. Moreover, applying SLAM technique improves the performance of (dB) by 4 dB to 5 dB and all systems become as competitive to each other when SLAM is applied. Finally, BER performance comparison among OFDM, Discrete Cosine Transform MCM (DCT- MCM), Discrete Hartley Transform MCM (DHT-MCM), DFrFT-OCDM and DFrCT- OCDM MCM systems was done by means of simulation over 100,000 multicarrier blocks for each one and showed that our proposed scenario gave the best performance.
基金Supported partially by the Program TMOP-4.2.2/08/1/2008-0008 of the Hungarian National Development Agency
文摘We consider complex-valued functions f ∈ L^1 （R^2＋）, where R＋ ：= [0,∞）, and prove sufficient conditions under which the double sine Fourier transform fss and the double cosine Fourier transform fcc belong to one of the two-dimensional Lipschitz classes Lip（a,β） for some 0 〈 α,β ≤ 1; or to one of the Zygmund classes Zyg（α,β） for some 0 〈 α,β ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L^1 （R^2＋）.
文摘Let stand for the polar coordinates in R2, ?be a given constant while satisfies the Laplace equation in the wedge-shaped domain or . Here αj(j = 1,2,...,n + 1) denote certain angles such that αj αj(j = 1,2,...,n + 1). It is known that if r = a satisfies homogeneous boundary conditions on all boundary lines ?in addition to non-homogeneous ones on the circular boundary , then an explicit expression of in terms of eigen-functions can be found through the classical method of separation of variables. But when the boundary?condition given on the circular boundary r = a is homogeneous, it is not possible to define a discrete set of eigen-functions. In this paper one shows that if the homogeneous condition in question is of the Dirichlet (or Neumann) type, then the logarithmic sine transform (or logarithmic cosine transform) defined by (or ) may be effective in solving the problem. The inverses of these transformations are expressed through the same kernels on or . Some properties of these transforms are also given in four theorems. An illustrative example, connected with the heat transfer in a two-part wedge domain, shows their effectiveness in getting exact solution. In the example in question the lateral boundaries are assumed to be non-conducting, which are expressed through Neumann type boundary conditions. The application of the method gives also the necessary condition for the solvability of the problem (the already known existence condition!). This kind of problems arise in various domain of applications such as electrostatics, magneto-statics, hydrostatics, heat transfer, mass transfer, acoustics, elasticity, etc.
文摘The Fourier transform is very important to numerous applications in science and engineering. However, its usefulness is hampered by its computational expense. In this paper, in an attempt to develop a faster method for computing Fourier transforms, the authors present parallel implementations of two new algorithms developed for the type IV Discrete Cosine Transform （DCT-IV） which support the new interleaved fast Fourier transform method. The authors discuss the realizations of their implementations using two paradigms. The first involved commodity equipment and the Message-Passing Interface （MPI） library. The second utilized the RapidMind development platform and the Cell Broadband Engine （BE） processor. These experiments indicate that the authors＇ rotation-based algorithm is preferable to their lifting-based algorithm on the platforms tested, with increased efficiency demonstrated by their MPI implementation for large data sets. Finally, the authors outline future work by discussing an architecture-oriented method for computing DCT-IVs which promises further optimization. The results indicate a promising fresh direction in the search for efficient ways to compute Fourier transforms.
文摘This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals.
基金This work was supported by the Guangdong Natural Science Foundation of China (No. 021089).
文摘A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π, and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.
基金国家自然科学基金，NKBRD of China，Doctor Foundation of Education Commission of China
文摘Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions.
