Study of CORDIC based processing element for digital signal processing algorithms

Abstract

There is a high demand for the efficient implementation of complex arithmetic operations in many Digital Signal Processing (DSP) algorithms. The COordinate Rotation DIgital Computer (CORDIC) algorithm is suitable to be implemented in DSP algorithms since its calculation for complex arithmetic is simple and elegant. Besides, since it avoids using multiplications, adopting the CORDIC algorithm can reduce the complexity. Here, in this project CORDIC based processing element for the construction of digital signal processing algorithms is implemented. This is a flexible device that can be used in the implementation of functions such as Singular Value Decomposition (SVD), Discrete Cosine Transform (DCT) as well as many other important functions. It uses a CORDIC module to perform arithmetic operations and the result is a flexible computational processing element (PE) for digital signal processing algorithms. To implement the CORDIC based architectures for functions like SVD and DCT, it is required to decompose their computations in terms of CORDIC operations. SVD is widely used in digital signal processing applications such as direction estimation, recursive least squares (RLS) filtering and system identification. Two different Jacobi-type methods for SVD parallel computation are usually considered, namely the Kogbetliantz (two-sided rotation) and the Hestenes (one- sided rotation) method. Kogbetliantz’s method has been considered, because it is suitable for mapping onto CORDIC array architecture and highly suitable for parallel computation. Here in its implementation, CORDIC algorithm provides the arithmetic units required in the processing elements as these enable the efficient implementation of plane rotation and phase computation. Many fundamental aspects of linear algebra rely on determining the rank of a matrix, making the SVD an important and widely used technique. DCT is one of the most widely used transform techniques in digital signal processing and it computation involves many multiplications and additions. The DCT based on CORDIC algorithm does not need multipliers. Moreover, it has regularity and simple architecture and it is used to compress a wide variety of images by transferring data into frequency domain. These digital signal-processing algorithms are used in many applications. The purpose of this thesis is to describe a solution in which a conventional CORDIC system is used to implement an SVD and DCT processing elements. The approach presented combines the low circuit complexity with high performance.