• ETRI Journal
• /
• 제45권6호
• /
• pp.1035-1045
• /
• 2023

We propose a novel graphics processing unit (GPU) algorithm that can handle a large-scale 3D fast Fourier transform (i.e., 3D-FFT) problem whose data size is larger than the GPU's memory. A 1D FFT-based 3D-FFT computational approach is used to solve the limited device memory issue. Moreover, to reduce the communication overhead between the CPU and GPU, we propose a 3D data-transposition method that converts the target 1D vector into a contiguous memory layout and improves data transfer efficiency. The transposed data are communicated between the host and device memories efficiently through the pinned buffer and multiple streams. We apply our method to various large-scale benchmarks and compare its performance with the state-of-the-art multicore CPU FFT library (i.e., fastest Fourier transform in the West [FFTW]) and a prior GPU-based 3D-FFT algorithm. Our method achieves a higher performance (up to 2.89 times) than FFTW; it yields more performance gaps as the data size increases. The performance of the prior GPU algorithm decreases considerably in massive-scale problems, whereas our method's performance is stable.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2003년도 신호처리소사이어티 추계학술대회 논문집
• /
• pp.473-476
• /
• 2003

We suggest 2 dimensional Fast Fourier Transform using Polynomial Transform and integer Fast Fourier Transform. Unlike conventional 2D-FFT using the direct quantization of twiddle factor, the suggested 2D-FFT adopts implemented by the lifting so that the suggested 2D-FFT is power adaptable and reversible. Since the suggested FFT performg integer-to-integer mapping, the transform can be implemented by only bit shifts and auditions without multiplications. In addition. polynomial transform severely reduces the multiplications of 2D-FFT. While preserving the reversibility, complexity of this algorithm is shown to be much lower than that of any other algorithms in terms of the numbers of additions and shifts.

• 전기전자학회논문지
• /
• 제25권4호
• /
• pp.697-702
• /
• 2021

고속 푸리에 변환(Fast Fourier Transform, FFT)은 다양한 응용처에서 널리 사용되는 주요 신호처리 블록이다. 일반적으로 1024 포인트 이상의 긴 FFT 처리의 경우 높은 SQNR(Signal-to-Quantization Ratio)를 유지하면서도 낮은 하드웨어 복잡도의 구현이 매우 중요하다. 본 논문에서는 낮은 복잡도의 FFT 알고리즘과 간단한 동적스케일링 기법을 제시한다. 이를 통해 2048 포인트 FFT연산에 대해서 널리 알려진 radix-2 알고리즘에 비해 곱셉기의 수를 절반으로 줄일 수 있으며, 또한 twiddle factor를 저장하기 위해 필요한 테이블의 크기를 radix-2 및 radix-2² 알고리즘에 비해 각각 35% 및 53%로 축소할 수 있다. 그리고 내부 데이터의 폭을 점진적으로 늘리지 않고서도 55dB 이상의 높은 SQNR을 달성하는 것을 확인하였다.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제12권7호
• /
• pp.3438-3454
• /
• 2018

In this paper, we propose a robust blind watermarking scheme for high-definition video. In the embedding process, luminance component of each frame is transformed by 2-dimensional fast Fourier transform (2D FFT). A secret key is used to generate a matrix of random numbers for the security of watermark information. The matrix is transformed by inverse steerable pyramid transform (SPT). We embed the watermark into the low and mid-frequency of 2D FFT coefficients with the transformed matrix. In the extraction process, the 2D FFT coefficients of each frame and the transformed matrix are transformed by SPT respectively, to produce two oriented sub-bands. We extract the watermark from each frame by cross-correlating two oriented sub-bands. If a video is degraded by some attacks, the watermarks of frames contain some errors. Thus, we use an ensemble position-based error correcting algorithm to estimate the errors and correct them. The experimental results show that the proposed watermarking algorithm is imperceptible and moreover is robust against various attacks. After embedding 64 bits of watermark into each frame, the average peak signal-to-noise ratio between original frames and embedded frames is 45.7 dB.

• 한국방송∙미디어공학회:학술대회논문집
• /
• 한국방송공학회 2009년도 IWAIT
• /
• pp.498-503
• /
• 2009

As for Hadamard Transform, because the calculation time of this transform is slower than Discrete Cosine Transform (DCT) and Fast Fourier Transform (FFT), the effectiveness and the practicality are insufficient. Then, the computational complexity can be decreased by using the butterfly operation as well as FFT. We composed calculation time of FFT with that of Fast Complex Hadamard Transform by constructing the algorithm of Fast Complex Hadamard Transform. They are indirect conversions using program of complex number calculation, and immediate calculations. We compared calculation time of them with that of FFT. As a result, the reducing the calculation time of the Complex Hadamard Transform is achieved. As for the computational complexity and calculation time, the result that quadrinomial Fast Complex Hadamard Transform that don't use program of complex number calculation decrease more than FFT was obtained.

• 대한기계학회논문집A
• /
• 제25권8호
• /
• pp.1253-1260
• /
• 2001

Transient thermal analysis of a three-dimensional axisymmetric automotive disk brake is presented in this paper. Temperature fields are obtained using a hybrid FFT-FEM scheme that combines Fourier transform techniques and finite element method. The use of a fast Fourier transform algorithm can avoid singularity problems and lead to inexpensive computing time. The transformed problem is solved with finite element scheme for each frequency domain. Inverse transforms are then performed for time domain solution. Numerical examples are presented for validation tests. Comparisons with analytical results show very good agreement. Also, a 3-D simulation, based upon an automotive brake disk model is performed.

• 정보처리학회논문지D
• /
• 제14D권2호
• /
• pp.169-180
• /
• 2007

본 논문은 함수 변환(Function Transform)과 FFT(Fast Fourier Transform)를 사용하는 새로운 XML 문서 클리스터링 기법에 대하여 논한다. 본 문서 클러스터링 기법은 조정자 없이 점진적으로 수행된다. XML 문서는 엘리먼트의 계층적인 구조에 기반하여 이산 함수로 변환된다. 이산 함수는 FFT를 사용하여 벡터로 변환된다. 문서를 나타내는 벡터는 가중치 유클리디안 거리 메트릭을 사용하여 비교된다. 비교 결과가 미리 정의된 값보다 작을 때에는 비교되는 두 개의 문서는 구조적으로 비슷한 것으로 간주되어 동일한 그룹으로 분류된다. XML 문서 클리스터링은 XML 문서의 저장과 검색에 유용하게 사용될 수 있다. 800개의 합서 문서와 520개의 실제 문서를 사용하여 실험하였다. 실험 결과는 함수변환과 FFT는 XML 문서를 엘리먼트의 구조를 기반으로 하여 점진적으로 조정자 없이 효과적으로 분류하는 것을 보여주었다.

• 한국방사선학회논문지
• /
• 제12권4호
• /
• pp.491-496
• /
• 2018

1.5Tesla와 3.0Tesla의 MRI 검사의 DWI (diffusion-weighted imaging) 펄스시퀀스에서 노이즈 스펙트럼을 분석하여 MRI검사의 기초자료를 제공하여 임상에서 적용하는데 목적이 있다. MRI 검사에서 ACR (American College of Radiology) 팬텀과 노이즈 스펙트럼은 Wavepad sound editor version 8.13 (NCH software, Green wood Village, CO, USA)로 FFT (fast Fourier transform), TFFT (time based fast Fourier transform)를 분석하였다. MR 1.5Tesla와 3.0Tesla의 DWI 펄스 시퀀스에서 검사실에 따른 노이즈 스펙트럼 및 FFT와 TFFT를 분석하였다. 1.5Tesla에 비해 3.0Tesla에서 FFT 및 TFFT에서 주파수 진폭의 노이즈 임계값은 1.5Tesla에서 -6 dB 사이였고, 3.0Tesla에서는 0 dB 사이로 분석되어 환자의 소음감소를 위한 DWI 펄스시퀀스를 환자에게 적절하게 임상에서 적용할 필요가 있다.

• Journal of electromagnetic engineering and science
• /
• 제19권1호
• /
• pp.6-12
• /
• 2019

An IE-FFT algorithm is implemented and applied to the electromagnetic (EM) solution of perfect electric conducting (PEC) scattering problems. The solution of the method of moments (MoM), based on the magnetic field integral equation (MFIE), is obtained for PEC objects with closed surfaces. The IE-FFT algorithm uses a uniform Cartesian grid to apply a global fast Fourier transform (FFT), which leads to significantly reduce memory requirement and speed up CPU with an iterative solver. The IE-FFT algorithm utilizes two discretizations, one for the unknown induced surface current on the planar triangular patches of 3D arbitrary geometries and the other on a uniform Cartesian grid for interpolating the free-space Green's function. The uniform interpolation of the Green's functions allows for a global FFT for far-field interaction terms, and the near-field interaction terms should be adequately corrected. A 3D block-Toeplitz structure for the Lagrangian interpolation of the Green's function is proposed. The MFIE formulation with the IE-FFT algorithm, without the help of a preconditioner, is converged in certain iterations with a generalized minimal residual (GMRES) method. The complexity of the IE-FFT is found to be approximately $O(N^{1.5})$and $O(N^{1.5}logN)$ for memory requirements and CPU time, respectively.

• 전력전자학회논문지
• /
• 제13권3호
• /
• pp.206-212
• /
• 2008

본 논문에서는 계통 연계형 태양광 발전 시스템의 새로운 FFT에 의한 위상추종 알고리즘을 제안한다. 신재생 에너지 분야에 적용되는 계통연계형 인버터에서는 계통과 동기를 위해서 반드시 계통의 위상 정보가 필요하다. 일반적으로 사용하는 3상 D-Q 변환에 의한 위상 추종과 달리 새롭게 제안하는 FFT를 사용하는 알고리즘은 게인튜닝 부분이 필요 없어 직접제어가 가능하며, FFT의 특성상 기본주파수 이외의 성분을 제외한 강력한 노이즈 제거효과로 인해 노이즈에 강한 특징을 가지고 있다. 시뮬레이션과 실험을 통하여 제안한 알고리즘의 성능이 만족함을 보였다.