33,496 research outputs found
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and
discrete sine transform (DST-IV), as well as for the modified discrete cosine
transform (MDCT) and its inverse, that achieve a lower count of real
multiplications and additions than previously published algorithms, without
sacrificing numerical accuracy. Asymptotically, the operation count is reduced
from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact
count is strictly lowered for all N > 4. These results are derived by
considering the DCT to be a special case of a DFT of length 8N, with certain
symmetries, and then pruning redundant operations from a recent improved fast
Fourier transform algorithm (based on a recursive rescaling of the
conjugate-pair split radix algorithm). The improved algorithms for DST-IV and
MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page
Generating optimized Fourier interpolation routines for density function theory using SPIRAL
© 2015 IEEE.Upsampling of a multi-dimensional data-set is an operation with wide application in image processing and quantum mechanical calculations using density functional theory. For small up sampling factors as seen in the quantum chemistry code ONETEP, a time-shift based implementation that shifts samples by a fraction of the original grid spacing to fill in the intermediate values using a frequency domain Fourier property can be a good choice. Readily available highly optimized multidimensional FFT implementations are leveraged at the expense of extra passes through the entire working set. In this paper we present an optimized variant of the time-shift based up sampling. Since ONETEP handles threading, we address the memory hierarchy and SIMD vectorization, and focus on problem dimensions relevant for ONETEP. We present a formalization of this operation within the SPIRAL framework and demonstrate auto-generated and auto-tuned interpolation libraries. We compare the performance of our generated code against the previous best implementations using highly optimized FFT libraries (FFTW and MKL). We demonstrate speed-ups in isolation averaging 3x and within ONETEP of up to 15%
A low multiplicative complexity fast recursive DCT-2 algorithm
A fast Discrete Cosine Transform (DCT) algorithm is introduced that can be of
particular interest in image processing. The main features of the algorithm are
regularity of the graph and very low arithmetic complexity. The 16-point
version of the algorithm requires only 32 multiplications and 81 additions. The
computational core of the algorithm consists of only 17 nontrivial
multiplications, the rest 15 are scaling factors that can be compensated in the
post-processing. The derivation of the algorithm is based on the algebraic
signal processing theory (ASP).Comment: 4 pages, 2 figure
Performance Analysis of Discrete Wavelet Multitone Transceiver for Narrowband PLC in Smart Grid
Smart Grid is an abstract idea, which involves the utilization of powerlines for sensing, measurement, control and communication for efficient utilization and distribution of energy, as well as automation of meter reading, load management and capillary control of Green Energy resources connected to the grid. Powerline Communication (PLC) has assumed a new role in the Smart Grid scenario, adopting the narrowband PLC (NB-PLC) for a low cost and low data rate communication for applications such as, automatic meter reading, dynamic management of load, etc. In this paper, we have proposed and simulated a discrete wavelet multitone (DWMT) transceiver in the presence of impulse noise for the NB-PLC channel applications in Smart Grid. The simulation results show that a DWMT transceiver outperforms a DFT-DMT with reference to the bit error rate (BER) performance
Reversible implementation of a disrete linear transformation
Discrete linear transformations form important steps in processing information. Many such transformations are injective and therefore are prime candidates for a physically reversible implementation into hardware. We present here the first steps towards a reversible digital implementation of two different integer transformations on four inputs: The Haar wavelet and the H.264 transform
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