• Journal of IKEEE
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• v.19 no.3
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• pp.378-384
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• 2015

In conventional HEVC inverse core transform architectures, extra $n{\times}n$ inverse transform block is added to $2n{\times}2n$ inverse transform block, and it operates as one $2n{\times}2n$ inverse transform block or two $n{\times}n$ inverse transform blocks. Thus, same number of pixels are processed in the same time, but it suffers from increased hardware size due to extra $n{\times}n$ inverse transform block. To avoid this problem, a novel $8{\times}8$ HEVC inverse core transform architecture was proposed to eliminate extra $4{\times}4$ inverse transform block based on multiplier reuse. This paper extends this approach and proposes a novel HEVC $16{\times}16$ inverse core transform architecture. Its frame processing time is same in $4{\times}4$, $8{\times}8$, and $16{\times}16$ inverse core transforms, and reduces gate counts by 13%.

• Journal of electromagnetic engineering and science
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• v.6 no.4
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• pp.244-252
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• 2006

A block Jacket transform and. its block inverse Jacket transformn have recently been reported in the paper 'Fast block inverse Jacket transform'. But the multiplication of the block Jacket transform and the corresponding block inverse Jacket transform is not equal to the identity transform, which does not conform to the mathematical rule. In this paper, new binary block Jacket transforms and the corresponding binary block inverse Jacket transforms of orders $N=2^k,\;3^k\;and\;5^k$ for integer values k are proposed and the mathematical proofs are also presented. With the aid of the Kronecker product of the lower order Jacket matrix and the identity matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse, fast algorithm and prime based $P^k$ order of proposed binary block inverse Jacket transform, it can be applied in communications such as space time block code design, signal processing, LDPC coding and information theory. Application of circular permutation matrix(CPM) binary low density quasi block Jacket matrix is also introduced in this paper which is useful in coding theory.

• ETRI Journal
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• v.27 no.5
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• pp.511-524
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• 2005

In this paper, we propose a novel hardware architecture for an intra-prediction, integer transform, quantization, inverse integer transform, inverse quantization, and mode decision module for the macroblock engine of a new video coding standard, H.264. To reduce the cycle of intra prediction, transform/quantization, and inverse quantization/inverse transform of H.264, a reduction method for cycle overhead in the case of I16MB mode is proposed. This method can process one macroblock for 927 cycles for all cases of macroblock type by processing $4{\times}4$ Hadamard transform and quantization during $16{\times}16$ prediction. This module was designed using Verilog Hardware Description Language (HDL) and operates with a 54 MHz clock using the Hynix $0.35 {\mu}m$ TLM (triple layer metal) library.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.517-529
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• 2016

This study compares the inverse transform and the composition methods for generating data from the Lindley distribution. The expression for the inverse of the distribution function for the Lindley distribution does not exist in closed form. Hence, authors of many empirical studies on the Lindley distribution used methods for generating Lindley variates other than the inverse transform. We generated data from the Lindley distribution using the inverse transform approach by obtaining the Lindley variates numerically; we also generated data from this distribution using the composition approach. Following the generation of the Lindley variates using these two methods, we compare some statistical properties of the estimates of the Lindley model parameters based on the generated data. We conclude that the two methods produce similar results.

• JSTS:Journal of Semiconductor Technology and Science
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• v.12 no.2
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• pp.203-211
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• 2012

This paper proposes a $16{\times}16$ and $32{\times}32$ inverse transform architecture for HEVC (High Efficiency Video Coding). HEVC large transform of $16{\times}16$ and $32{\times}32$ suffers from huge computational complexity. To resolve this problem, we proposed a new large inverse transform architecture based on hardware reuse. The processing element is optimized by exploiting fully recursive and regular butterfly structure. To achieve low area, the processing element is implemented by shifters and adders without multiplier. Implementation of the proposed 2-D inverse transform architecture in 0.18 ${\mu}m$ technology shows about 300 MHz frequency and 287 Kgates area, which can process 4K ($3840{\times}2160$)@ 30 fps image.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.369-382
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• 2009

In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S($L_{a,b}^2$[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.4
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• pp.106-114
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• 2016

In this paper, we propose an efficient integer inverse transform structure for vp9 decoder. The proposed structure is a hardware structure which is easy to control and requires less hardware resources, and shares algorithms for realizing entire DCT(Discrete Cosine Transform), ADST(Asymmetric Discrete Sine Transform) and WHT(Walsh-Hadamard Transform) in vp9. The integer inverse transform for vp9 google model has a fast structure, named butterfly structure. The integer inverse transform for google C model, unlike universal fast structure, takes a constant rounding shift operator on each stage and includes an asymmetrical sine transform structure. Thus, the proposed structure approximates matrix coefficient values for all transform mode and is used to matrix operation method. With the proposed structure, shared operations for all inverse transform algorithm modes can be possible with reduced number of multipliers compared to the butterfly structure, which in turn manages the hardware resources more efficiently.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Journal of the Korean Mathematical Society
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• v.53 no.6
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• pp.1261-1273
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• 2016

In this paper, we analyze the necessary and sufficient condition introduced in [5]: that a functional F in $L^2(C_{a,b}[0,T])$ has an integral transform ${\mathcal{F}}_{{\gamma},{\beta}}F$, also belonging to $L^2(C_{a,b}[0,T])$. We then establish the inverse integral transforms of the functionals in $L^2(C_{a,b}[0,T])$ and then examine various properties with respect to the inverse integral transforms via the translation theorem. Several possible outcomes are presented as remarks. Our approach is a new method to solve some difficulties with respect to the inverse integral transform.

• Journal of Broadcast Engineering
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• v.28 no.1
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• pp.100-108
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• 2023

In hybrid block-based video coding, transform coding converts spatial domain residual signals into frequency domain data and concentrates energy in a low frequency band to achieve a high compression efficiency in entropy coding. The state-of-the-art video coding standard, VVC(Versatile Video Coding), uses DCT-2(Discrete Cosine Transform type 2), DST-7(Discrete Sine Transform type 7), and DCT-8(Discrete Cosine Transform type 8) for primary transform. In this paper, considering that DCT-2, DST-7, and DCT-8 are all linear transformations, we propose an inverse transform that reduces the number of multiplications in the inverse transform by using the linearity of the linear transform. The proposed inverse transform method reduced encoding time and decoding time by an average 26%, 15% in AI and 4%, 10% in RA without the increase of bitrate compared to VTM-8.2.