29-08-2016, 03:53 PM
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Abstract
CORDIC is an acronym for Coordinate Rotation Digital Computer. It is a class of shift
and adds algorithms for rotating vectors in a plane, which is usually used for the
calculation of trigonometric functions, multiplication, division and conversion between
binary and mixed radix number systems of DSP applications, such as Fourier Transform.
A fast and energy-efficient CORDIC for the calculation of elementary function is always
needed in electronics systems i.e. DSP processors, image processing and arithmetic units
in microprocessors. On VLSI implementation level, the area also becomes quite
important as more area means more system cost. The three parameters i.e. power, speed
and area are always traded off. For DSP processors area and speed are the main ones. But
sometimes, increasing the speed also increases the power consumption, so there is an
upper bound of speed for a given power budget.
Since elementary functions calculation dominates the execution time of most DSP
algorithms, so there is need for high speed CORDIC algorithm. In this thesis, a very high
speed CORDIC algorithm is implemented for fast calculations and generation of trigonometric functions for generation of waveform VHDL is used to implement a technology-independent design.
Keyword: CORDIC
Introduction
CORDIC is an introduced by Jack E. Volder to describe the Coordinate Rotation
Digital Computer algorithm which he developed in 1959. It was used for the real time
navigation system at that time and was further extended by Walther in the year 1971.
It is used for the fast calculation of elementary functions like multiplication, division,
trigonometric functions, logarithmic function, and various conversions like conversion of
rectangular to polar coordinate and vice-versa. Although CORDIC may not be the fastest
technique to perform these operations, it is attractive due to the simplicity of its hardware
implementation, since the same iterative algorithm could be used for all these
applications using the basic shift-add operations. CORDIC algorithm can be applied in
two modes (ex. rotation and vectoring) and three types (ex. linear, circular and hyperbolic
mode). The algorithm is very attractive for hardware implementation because it uses only
elementary shift-and-add operations to perform the vector rotation. It only needs the use
of 2 shifter and 3 adder modules, so its power dissipation is very less and it is also very
compact. It is frequently used in an array of processing elements on VLSI chips.
CORDIC PRINCIPLE
It is based on vector rotation operation. Each rotation can be realized with shift and add arithmetic operations. Vector rotation from vector v to v’ through an angle give the x=cosine component and y=sine component. Rotation of any vector gives the equations
DIRECT DIGITAL SYNTHESYZER
In this section, we propose a new technique for generating arbitrary waveforms using the CORDIC processor. In the proposed design, the phase of hyperbolic DDS function generator is randomly modulated using a linear feedback shift register (LFSR). In the next subsection, we discuss the design of hyperbolic DDS based on the proposed CORDIC processor, following which the architecture of proposed AWG is described. The proposed DDS can be used to generate hyperbolic, exponential and other arbitrary waveforms. For generating sinusoidal waveforms, the output of circular CORDIC processor replaces the hyperbolic CORDIC processor in the proposed DDS.
Block diagram of waveform generation using CORDIC