A new FFT algorithm has been deduced, which is called the base-6 FFT algorithm. The amount for calculating the DFT of complex sequence of N =2 r by the base-6 FFT algorithm is M r( N )=14/3· N log 6 N -4 N +4 for...A new FFT algorithm has been deduced, which is called the base-6 FFT algorithm. The amount for calculating the DFT of complex sequence of N =2 r by the base-6 FFT algorithm is M r( N )=14/3· N log 6 N -4 N +4 for multiplication operation of real number and A r( N )=23/3· N log 6 N -2 N +2 for addition operation of real number. The amount for calculating the DFT of real sequence is a half of it with the complex sequence.展开更多
To solve the problem of the large Doppler frequency offset in the LEO communication system, this paper studies a rapid PN code acquisition method based on the PMF-FFT architecture, which searches the phase and frequen...To solve the problem of the large Doppler frequency offset in the LEO communication system, this paper studies a rapid PN code acquisition method based on the PMF-FFT architecture, which searches the phase and frequency offset and at the same time reduces the acquisition time. It presents an improved method equivalent to windowing function and uses windowing process to overcome the attenuation of related peak envelope caused by partial matched filters.展开更多
Starting from an index mapping for one to multi-dimensions, a general in-placeand in-order prime factor FFT algorithm is proposed in this paper. In comparing with existingprime factor FFT algorithms, this algorithm sa...Starting from an index mapping for one to multi-dimensions, a general in-placeand in-order prime factor FFT algorithm is proposed in this paper. In comparing with existingprime factor FFT algorithms, this algorithm saves about half of the required storage capacityand possesses a higher efficiency. In addition, this algorithm can easily implement the DFT andIDFT in a single subroutine,展开更多
A fast algorithm is proposed for recursively computing the DFTs of prime length. Only (N-1) / 2 real multiplications are required to compute all N frequency components in terms of permuting the input data. The multipl...A fast algorithm is proposed for recursively computing the DFTs of prime length. Only (N-1) / 2 real multiplications are required to compute all N frequency components in terms of permuting the input data. The multiplication in recursive computation is replaced by shifting. Complexity of the algorithm is studied. A factor η is introduced and presented. When the ratio of multiplier's period Tm to adder's period Ta is greater than the factor η (i.e.Tm / Ta >η), the new algorithm is faster than FFT. The necessary condition and error of the algorithm are studied. The signal-to-noise ratio for different length N is presented. A high accuracy scheme is proposed for improving the SNR about 20 -30dB.展开更多
DFT is widely applied in the field of signal process and others. Most present rapid ways of calculation are either based on paralleled computers connected by such particular systems like butterfly network, hypercube e...DFT is widely applied in the field of signal process and others. Most present rapid ways of calculation are either based on paralleled computers connected by such particular systems like butterfly network, hypercube etc; or based on the assumption of instant transportation, non-conflict communication, complete connection of paralleled processors and unlimited usable processors. However, the delay of communication in the system of information transmission cannot be ignored. This paper works on the following aspects： instant transmission, dispatching missions, and the path of information through the communication link in the computer cluster systems; layout of the dynamic FFT algorithm under the different structures of computer clusters.展开更多
In this paper, an intuitive comparison of the computational performance of orthogonal frequency division multiplexing (OFDM) system has been made in terms of complex calculations required using different Fourier trans...In this paper, an intuitive comparison of the computational performance of orthogonal frequency division multiplexing (OFDM) system has been made in terms of complex calculations required using different Fourier transform techniques. The different transform techniques are introduced such as discrete Fourier transform (DFT) and various types of fast Fourier transform (FFT) as 2-radix FFT, 4-radix FFT etc. and the very recent very fast Fourier transform (VFFT). With intuitive mathematical analysis, it has been shown that with the reduced complexity that VFFT can offer, OFDM performance can be greatly improved in terms of calculations needed.展开更多
基于快速傅里叶变换的快速迭代收缩阈值算法(fast iterative shrinkage threshold algorithm based on fast Fourier transform, FFT-FISTA)具有较高的计算效率,但其忽略点扩散函数的空间变化及卷绕误差,造成声源识别性能的损失,为此提...基于快速傅里叶变换的快速迭代收缩阈值算法(fast iterative shrinkage threshold algorithm based on fast Fourier transform, FFT-FISTA)具有较高的计算效率,但其忽略点扩散函数的空间变化及卷绕误差,造成声源识别性能的损失,为此提出基于函数波束形成的改进FFT-FISTA算法。改进算法以函数波束形成输出作为FFT-FISTA算法的迭代输入,建立函数波束形成、声源分布及升幂空间转移不变点扩散函数的线性方程组,基于周期边界条件下的快速傅里叶变换进行迭代求解,使被运算的非周期函数变为一个周期函数,解决补零边界带来的波数泄漏问题,可提高运算准确性,进一步提升成像性能;通过指数运算锐化点扩散函数主瓣,拓展点扩散函数空间转移不变性假设的适用性。仿真和试验结果表明,相较于常规FFT-FISTA算法,改进算法能提升成像空间分辨率及动态范围,扩大FFT-FISTA算法的有效成像区域,压缩气体泄漏试验结果验证了改进算法的有效性。展开更多
文摘A new FFT algorithm has been deduced, which is called the base-6 FFT algorithm. The amount for calculating the DFT of complex sequence of N =2 r by the base-6 FFT algorithm is M r( N )=14/3· N log 6 N -4 N +4 for multiplication operation of real number and A r( N )=23/3· N log 6 N -2 N +2 for addition operation of real number. The amount for calculating the DFT of real sequence is a half of it with the complex sequence.
文摘To solve the problem of the large Doppler frequency offset in the LEO communication system, this paper studies a rapid PN code acquisition method based on the PMF-FFT architecture, which searches the phase and frequency offset and at the same time reduces the acquisition time. It presents an improved method equivalent to windowing function and uses windowing process to overcome the attenuation of related peak envelope caused by partial matched filters.
基金Supported by the National Natural Science Foundation of China
文摘Starting from an index mapping for one to multi-dimensions, a general in-placeand in-order prime factor FFT algorithm is proposed in this paper. In comparing with existingprime factor FFT algorithms, this algorithm saves about half of the required storage capacityand possesses a higher efficiency. In addition, this algorithm can easily implement the DFT andIDFT in a single subroutine,
文摘A fast algorithm is proposed for recursively computing the DFTs of prime length. Only (N-1) / 2 real multiplications are required to compute all N frequency components in terms of permuting the input data. The multiplication in recursive computation is replaced by shifting. Complexity of the algorithm is studied. A factor η is introduced and presented. When the ratio of multiplier's period Tm to adder's period Ta is greater than the factor η (i.e.Tm / Ta >η), the new algorithm is faster than FFT. The necessary condition and error of the algorithm are studied. The signal-to-noise ratio for different length N is presented. A high accuracy scheme is proposed for improving the SNR about 20 -30dB.
文摘DFT is widely applied in the field of signal process and others. Most present rapid ways of calculation are either based on paralleled computers connected by such particular systems like butterfly network, hypercube etc; or based on the assumption of instant transportation, non-conflict communication, complete connection of paralleled processors and unlimited usable processors. However, the delay of communication in the system of information transmission cannot be ignored. This paper works on the following aspects： instant transmission, dispatching missions, and the path of information through the communication link in the computer cluster systems; layout of the dynamic FFT algorithm under the different structures of computer clusters.
文摘In this paper, an intuitive comparison of the computational performance of orthogonal frequency division multiplexing (OFDM) system has been made in terms of complex calculations required using different Fourier transform techniques. The different transform techniques are introduced such as discrete Fourier transform (DFT) and various types of fast Fourier transform (FFT) as 2-radix FFT, 4-radix FFT etc. and the very recent very fast Fourier transform (VFFT). With intuitive mathematical analysis, it has been shown that with the reduced complexity that VFFT can offer, OFDM performance can be greatly improved in terms of calculations needed.
文摘基于快速傅里叶变换的快速迭代收缩阈值算法(fast iterative shrinkage threshold algorithm based on fast Fourier transform, FFT-FISTA)具有较高的计算效率,但其忽略点扩散函数的空间变化及卷绕误差,造成声源识别性能的损失,为此提出基于函数波束形成的改进FFT-FISTA算法。改进算法以函数波束形成输出作为FFT-FISTA算法的迭代输入,建立函数波束形成、声源分布及升幂空间转移不变点扩散函数的线性方程组,基于周期边界条件下的快速傅里叶变换进行迭代求解,使被运算的非周期函数变为一个周期函数,解决补零边界带来的波数泄漏问题,可提高运算准确性,进一步提升成像性能;通过指数运算锐化点扩散函数主瓣,拓展点扩散函数空间转移不变性假设的适用性。仿真和试验结果表明,相较于常规FFT-FISTA算法,改进算法能提升成像空间分辨率及动态范围,扩大FFT-FISTA算法的有效成像区域,压缩气体泄漏试验结果验证了改进算法的有效性。
