为了克服卷积混合信号盲源分离双最小均方(Double least mean squeres,Double-LMS)算法在分离滤波器过长时计算量过大的问题,借助于傅里叶变换理论中的帕斯维尔定理,将其转化为频域积分算法。频域积分算法可以利用快速傅里叶变换实现,...为了克服卷积混合信号盲源分离双最小均方(Double least mean squeres,Double-LMS)算法在分离滤波器过长时计算量过大的问题,借助于傅里叶变换理论中的帕斯维尔定理,将其转化为频域积分算法。频域积分算法可以利用快速傅里叶变换实现,具有较高的计算效率,可以克服当分离滤波器过长时原算法效率低下的问题。仿真结果表明:新算法在保持了DoubleLMS算法良好分离性能的基础上,降低了原算法的复杂度,提高了计算效率。展开更多
In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain...In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will 展开更多
In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem ...In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.展开更多
文摘为了克服卷积混合信号盲源分离双最小均方(Double least mean squeres,Double-LMS)算法在分离滤波器过长时计算量过大的问题,借助于傅里叶变换理论中的帕斯维尔定理,将其转化为频域积分算法。频域积分算法可以利用快速傅里叶变换实现,具有较高的计算效率,可以克服当分离滤波器过长时原算法效率低下的问题。仿真结果表明:新算法在保持了DoubleLMS算法良好分离性能的基础上,降低了原算法的复杂度,提高了计算效率。
文摘In the history of mathematics different methods have been used to detect if a number is prime or not. In this paper a new one will be shown. It will be demonstrated that if the following equation is zero for a certain number p, this number p would be prime. And being m an integer number higher than (the lowest, the most efficient the operation). . If the result is an integer, this result will tell us how many permutations of two divisors, the input number has. As you can check, no recurrent division by odd or prime numbers is done, to check if the number is prime or has divisors. To get to this point, we will do the following. First, we will create a domain with all the composite numbers. This is easy, as you can just multiply one by one all the integers (greater or equal than 2) in that domain. So, you will get all the composite numbers (not getting any prime) in that domain. Then, we will use the Fourier transform to change from this original domain (called discrete time domain in this regards) to the frequency domain. There, we can check, using Parseval’s theorem, if a certain number is there or not. The use of Parseval’s theorem leads to the above integral. If the number p that we want to check is not in the domain, the result of the integral is zero and the number is a prime. If instead, the result is an integer, this integer will tell us how many permutations of two divisors the number p has. And, in consequence information how many factors, the number p has. So, for any number p lower than 2m?- 1, you can check if it is prime or not, just making the numerical definite integration. We will apply this integral in a computer program to check the efficiency of the operation. We will check, if no further developments are done, the numerical integration is inefficient computing-wise compared with brute-force checking. To be added, is the question regarding the level of accuracy needed (number of decimals and number of steps in the numerical integration) to have a reliable result for large numbers. This will
基金supported by the National Natural Science Foundation of China (Grant No. 10775097)the Research Foundation of the Education Department of Jiangxi Province of China (Grant No. GJJ10097)
文摘In a preceding letter （2007 Opt. Lett. 32 554） we propose complex continuous wavelet transforms and found Laguerre-Gaussian mother wavelets family. In this work we present the inversion formula and Parseval theorem for complex continuous wavelet transform by virtue of the entangled state representation, which makes the complex continuous wavelet transform theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.
