Related papers: Type-IV DCT, DST, and MDCT algorithms with reduced…
In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…
A multiplierless pruned approximate 8-point discrete cosine transform (DCT) requiring only 10 additions is introduced. The proposed algorithm was assessed in image and video compression, showing competitive performance with state-of-the-art…
Video processing systems such as HEVC requiring low energy consumption needed for the multimedia market has lead to extensive development in fast algorithms for the efficient approximation of 2-D DCT transforms. The DCT is employed in a…
Discrete Cosine Transform (DCT) is very important in image compression. Classical 1-D DCT and 2-D DCT has time complexity O(NlogN) and O(N²logN) respectively. This paper presents a quantum DCT iteration, and constructs a quantum 1-D…
The $N$-point discrete Fourier transform (DFT) is a cornerstone for several signal processing applications. Many of these applications operate in real-time, making the computational complexity of the DFT a critical performance indicator to…
Two multiplierless algorithms are proposed for 4x4 approximate-DCT for transform coding in digital video. Computational architectures for 1-D/2-D realisations are implemented using Xilinx FPGA devices. CMOS synthesis at the 45 nm node…
Discrete trigonometric transforms (DTTs), such as the DCT-2 and the DST-7, are widely used in video codecs for their balance between coding performance and computational efficiency. In contrast, data-dependent transforms, such as the…
Two multiplierless pruned 8-point discrete cosine transform (DCT) approximation are presented. Both transforms present lower arithmetic complexity than state-of-the-art methods. The performance of such new methods was assessed in the image…
A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of…
Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…
In this paper, we propose a collection of approximations for the 8-point discrete cosine transform (DCT) based on integer functions. Approximations could be systematically obtained and several existing approximations were identified as…
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing…
Recent video codecs with multiple separable transforms can achieve significant coding gains using asymmetric trigonometric transforms (DCTs and DSTs), because they can exploit diverse statistics of residual block signals. However, they add…
Discrete Cosine Transform (DCT) can be used instead of conventional Discrete Fourier Transform (DFT) for the Orthogonal Frequency Division Multiplexing (OFDM) construction, which offers many advantages. In this paper, the…
The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In…
The design of the optimal inverse discrete cosine transform (IDCT) to compensate the quantization error is proposed for effective lossy image compression in this work. The forward and inverse DCTs are designed in pair in current image/video…
We study recursive algorithm for computing DCT of lengths $N=q 2^m$ ($m,q \in \mathbb{N}$, $q$ is odd) due to C.W.Kok. We show that this algorithm has the same multiplicative complexity as theoretically achievable by the prime factor…
In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm…