Small-Size Algorithms for Type-IV Discrete Cosine Transform with Reduced Multiplicative Complexity
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l-Size Algorithms for Type-IV Discrete Cosine Transform with Reduced Multiplicative Complexity 1
Aleksandr Cariow1* and Ùukasz Lesiecki1**
West Pomeranian University of Technology, Szczecin, Poland *ORCID: 0000-0002-4513-4593, e-mail: [email protected] **ORCID:0000-0002-4305-0687, e-mail: [email protected] Received January 16, 2020 Revised May 20, 2020 Accepted July 29, 2020
Abstract—Discrete cosine transforms are widely used in smart radioelectronic systems for processing and analysis of incoming information. The popularity of using these transform is explained by the presence of fast algorithms that minimize the computational and hardware complexity of their implementation. Type-IV discrete cosine transform occupies a special place in the list of the specified transformations. This article proposes several algorithmic solutions for implementing the type-IV discrete cosine transform. The effectiveness of the proposed solutions is explained by the possibility of factorization of the DCT-IV matrix, which leads to a decrease in computational and implementation complexity. A set of completely parallel type-IV DCT algorithms for small lengths of signal sequences (N = 2, 3, 4, 5, 6, 7, 8, 9) is presented. DOI: 10.3103/S0735272720090022
1. INTRODUCTION Discrete cosine transform (DCT) [1]–[7] is widely used in many radioelectronic and telecommunication systems for data processing and transmission including digital signal and image processing [8]–[10], radar imaging [11], digital watermarking [12], [13], hyperspectral data analysis and compressed sensing [14], [15], and others [16]–[18]. With the development of engineering and technology for the production of smart sensors, data processing methods based on DCT began to be used in intelligent sensor networks and systems [19]. In fact, there are eight different types of DCT [7]. The discrete cosine transform of type-IV (DCT-IV) is one of the most important transforms in the arsenal of DCTs. It is DCT-IV that plays a significant role in the effective implementation of orthogonal overlapping transforms and the modified discrete cosine transform (MDCT) [20]–[25]. Since DCT-IV is a time-consuming transform, many effective algorithms have been developed for the fast implementation of type IV DCT [26]–[34]. A number of publications are devoted to hardware accelerators of this transform implemented on VLSI platforms: ASIC and FPGA [35], [36]. This gave a new impetus to the development and application of new hardware-oriented resource-efficient DCT algorithms. Thus, numerous fast algorithms for efficient DCT-IV implementation have been developed to minimize the computational complexity and implementation costs. With rare exceptions, most of the publications known to the authors mainly consider fast DCT-IV algorithms for sequences having the length equal to a power of two. Moreover, as a rule, an example for N = 8 is considered as an illustration [4], [33], [34]. However, as in the case of other discrete orthogonal transforms [37]–[41], DCT-IV algorithms for other small length
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