Design and FPGA Implementation of CORDIC-based 8-point 1D DCT Processor

CORDIC or CO-ordinate Rotation DIgital Computer is a fast, simple, efficient and powerful algorithm used for diverse Digital Signal Processing applications. Primarily developed for real-time airborne computations, it uses a unique computing technique which is especially suitable for solving the trigonometric relationships involved in plane co-ordinate rotation and conversion from rectangular to polar form. It comprises a special serial arithmetic unit having three shift registers, three adders/subtractors, Look-Up table and special interconnections. Using a prescribed sequence of conditional additions or subtractions the CORDIC arithmetic unit can be controlled to solve either of the following equations: Y’=K (Ycos λ+ Xsin λ) X’=K (Xcos λ - Ysin λ); where K is a constant In this project: • A CORDIC-based processor for sine/cosine calculation was designed using VHDL programming in Xilinx ISE 10.1. The CORDIC module was tested for its functionality and correctness by test-bench analysis. Subsequently, FPGA implementation of the CORDIC core followed by ChipScopePro analysis of the output logic waveforms was performed. • Using this CORDIC core a DCT processor was designed to calculate the 8-point 1D DCT. The functionality and operational correctness of this processor was tested, first on the test-bench and then via ChipScopePro analysis, post FPGA implementation. The output obtained in both the cases was compared with the actual values to test for consistency and the percentage of accuracy was established. Power consumption and FPGA resource utilization were observed. The results obtained were discussed

AREA AND POWER-EFFICIENT RECONFIGURABLE DIGITAL DOWN CONVERTER ON FPGA

This paper presents a field-programmable gate array (FPGA)-based digital down converter (DDC) that can reduce the bandwidth from about 70 MHz to 182.292 kHz. The proposed DDC consists of a polyphase COordinate Rotation DIgital Computer (CORDIC) processor and a multirate filter. The advantage of polyphase CORDIC processor is to process with high sample rate input data and produces computational efficient noiseless baseband spectrum. The pipeline multirate filter works at a high clock speed. Moreover, the multirate filter generates a fractional sample rate factor using a cubic B-spline Farrow filter. The proposed DDC is coded with optimal hardware description language (HDL) and tested on Kintex-7 Xilinx FPGA as the target device. Experimental results indicate that the proposed design saves chip area, power consumption and operates at high speed without loss of any functionality. Additionally, the proposed design offers sufficient spurious-free dynamic range (SFDR) and produces less than 1 Hz frequency resolution at the output

CORDICのハードウェア構成及び応用に関する研究

電気通信大学201

Error Analysis of CORDIC Processor with FPGA Implementation

The coordinate rotation digital computer (CORDIC) is a shift-add based fast computing algorithm which has been found in many digital signal processing (DSP) applications. In this paper, a detailed error analysis based on mean square error criteria and its implementation on FPGA is presented. Two considered error sources are an angle approximation error and a quantization error due to finite word length in fixed-point number system. The error bound and variance are discussed in theory. The CORDIC algorithm is implemented on FPGA using the Xilinx Zynq-7000 development board called ZedBoard. Those results of theoretical error analysis are practically investigated by implementing it on actual FPGA board. In addition, Matlab is used to provide theoretical value as a baseline model by being set up in double-precision floating-point to compare it with the practical value of errors on FPGA implementation.Comment: 5 pages, 7 Figure

A CORDIC based QR Decomposition Technique for MIMO Detection

CORDIC based improved real and complex QR Decomposition (QRD) for channel pre-processing operations in (Multiple-Input Multiple-Output) MIMO detectors are presented in this paper. The proposed design utilizes pipelining and parallel processing techniques and reduces the latency and hardware complexity of the module respectively. Computational complexity analysis report shows the superiority of our module by 16% compared to literature. The implementation results reveal that the proposed QRD takes shorter latency compared to literature. The power consumption of 2x2 real channel matrix and 2x2 complex channel matrix was found to be 12mW and 44mW respectively on the state-of-the-art Xilinx Virtex 5 FPGA

FPGA-Based Co-processor for Singular Value Array Reconciliation Tomography

This thesis describes a co-processor system that has been designed to accelerate computations associated with Singular Value Array Reconciliation Tomography (SART), a method for locating a wide-band RF source which may be positioned within an indoor environment, where RF propagation characteristics make source localization very challenging. The co-processor system is based on field programmable gate array (FPGA) technology, which offers a low-cost alternative to customized integrated circuits, while still providing the high performance, low power, and small size associated with a custom integrated solution. The system has been developed in VHDL, and implemented on a Virtex-4 SX55 FPGA development platform. The system is easy to use, and may be accessed through a C program or MATLAB script. Compared to a Pentium 4 CPU running at 3 GHz, use of the co-processor system provides a speed-up of about 6 times for the current signal matrix size of 128-by-16. Greater speed-ups may be obtained by using multiple devices in parallel. The system is capable of computing the SART metric to an accuracy of about -145 dB with respect to its true value. This level of accuracy, which is shown to be better than that obtained using single precision floating point arithmetic, allows even relatively weak signals to make a meaningful contribution to the final SART solution

Efficient arithmetic for high speed DSP implementation on FPGAs

The author was sponsored by EnTegra Ltd, a company who develop hardware and software products and services for the real time implementation of DSP and RF systems. The field programmable gate array (FPGA) is being used increasingly in the field of DSP. This is due to the fact that the parallel computing power of such devices is ideal for today’s truly demanding DSP algorithms. Algorithms such as the QR-RLS update are computationally intensive and must be carried out at extremely high speeds (MHz). This means that the DSP processor is simply not an option. ASICs can be used but the expense of developing custom logic is prohibitive. The increased use of the FPGA in DSP means that there is a significant requirement for efficient arithmetic cores that utilises the resources on such devices. This thesis presents the research and development effort that was carried out to produce fixed point division and square root cores for use in a new Electronic Design Automation (EDA) tool for EnTegra, which is targeted at FPGA implementation of DSP systems. Further to this, a new technique for predicting the accuracy of CORDIC systems computing vector magnitudes and cosines/sines is presented. This work allows the most efficient CORDIC design for a specified level of accuracy to be found quickly and easily without the need to run lengthy simulations, as was the case before. The CORDIC algorithm is a technique using mainly shifts and additions to compute many arithmetic functions and is thus ideal for FPGA implementation

An Exploration of MPEG-7 Shape Descriptors

The Multimedia Content Description Interface (ISO/IEC 15938), commonly known to as MPEG-7, became a standard as of September of 2001. Unlike its predecessors, MPEG- 7 standardizes multimedia metadata description. By providing robust descriptors and an effective system for storing them, MPEG-7 is designed to provide a means of navigation through audio-visual content. In particular, MPEG-7 provides two two-dimensional shape descriptors, the Angular Radial Transform (ART) and Curvature Scaled Space (CSS), for use in image and video annotation and retrieval. Field Programmable Gate Arrays (FPGAs) have a very general structure and are made up of programmable switches that allow the end-user, rather than the manufacturer, to configure these switches for whatever design is needed by their application. This flexibly has led to the use of FPGAs for prototyping and implementing circuit designs as well as their use being suggesting as part of reconfigurable computing. For this work, an FPGA based ART extractor was designed and simulated for a Xilinx Virtex-E XCV300e in order to provide a speedup over software based extraction. The design created is capable of processing over 69,4400 pixels a minute. This design utilizes 99% of the FPGA\u27s logical resources and operates at a clock rate of 25 MHz. Along with the proposed design, the MPEG-7 shape descriptors were explored as to how well they retrieved similar objects and how these objects matched up to what a human would expect. Results showed that the majority of the retrievals made using the MPEG-7 shape descriptors returned visually acceptable results. It should be noted that even the human results had a high amount of variance. Finally, this thesis briefly explored the potential of utilizing the ART descriptor for optical character recognition (OCR) in the context of image retrieval from databases. It was demonstrated that the ART has potential for use in OCR, however there is still research to be performed in this area