A Noniterative Radix-8 CORDIC Algorithm with Low Latency and High Efficiency

An efficient, noniterative Radix-8 (NR-8) coordinate rotation digital computer (CORDIC) algorithm is proposed for low-latency and high-efficiency computation of the functions of sine, cosine, or the phase shift, with which the values of the functions are precisely computed by only using the angle in a narrow range of [0, π/12] rather than in a wide angle range of [0, π/2]. This algorithm is expressed by a formula that simplifies the traditional iterative processes by using a complex multiplier. The results obtained from the simulation and the experiment on an FPGA show that the NR-8 CORDIC algorithm operates well, with which the 16-bit precision output is extremely precise, with only 0.012% of the absolute error for computing the sine or cosine function with a step of 0.001°. Compared with the best conventional CORDIC algorithm, the clock latency of this algorithm significantly decreases down to less than 50%, only needs half of the logic resources and consumes half of the power. This algorithm also takes advantages over other newly improved CORDIC algorithms and requires less than half of the clock latency, even for a 23-bit precision output. Therefore, this algorithm could provide a potential application in real-time systems such as radar digital beamforming.

Design and Implementation of FFT IP using Pipelined Hybrid Adder and Distributed Arithmetic Based Complex Multiplier

In current inventive technology, latency, power and area are the crucial parameters to outline any kind of the algorithm on FPGA. The fundamental tool used for DSP applications is Fast Fourier Transform. FFT plays a vital role in acquiring the signal characteristics with least use of carrying out parameters. The adder plays an utmost importance. To make the best possible adder design regarding delay and area, various works have been proposed before. In proposed system, a combination different sub adders like Carry Look ahead adder (CLA), Ripple carry adder (RCA), and Carry save adder (CSA) is proposed. This reduces the delay and area but also increases the speed. The hybrid adders is proposed to represent FFT architecture inplace of conventional adders. Hybrid adder will act as a complex adder. Speed multipliers are fundamental parts of DSP systems. Multipliers are complex process and consumes more time. In order to lower the complexity multiplication, various multiplier less method are introduced. An efficient DA based complex multiplier is proposed, inplace of regular multiplier. The pipelining technique is applied only to hybrid adder. The design of Radix-2 FFT for 8 point of FFT, 1024 point of FFT is done, programmed using Verilog language. Using Xilinx 14.5i tool with Spartan 6 kit, Simulation is achieved.

High-Speed FIR Filter Design using Decision Tree Algorithm with FPGA Debugging

In recent years, the filter is one of the key elements in signal processing applications to remove unwanted information. However, traditional FIR filters have been consumed more resources due to complex multiplier design. Mostly the complexity of the FIR filter is dominated by multiplier design. The conventional multipliers can be realized by Single Constant Multiplication (SCM) and Multiple Constant Multiplication (MCM) algorithms using shift and add/subtract operations. In this paper, a hybrid state decision tree algorithm is introduced to reduce hardware utilization (area) and increase speed in filter tap cells of FIR. The proposed scheme generates a decision tree to perform shift & addition and accumulation based on the combined SCM/MCM approach. The proposed FIR filter was implemented in Xilinx Field Programmable Gate Array (FPGA) platform by using Verilog language. The experimental results of the DTG-FIR filter were averagely reduced the 48.259% of LUTs, 51.567 % of flip flops and 44.497 % of slices at 183.122 MHz of operating frequency on the Virtex-5 than existing VP-FIR.

Design and Analysis of Multipliers using Radix-8 Booth Encoding Technique for Low Power and Area Consumption

As innovation scaling is arriving at its points of confinement, new methodologies have been proposed for computational efficiency. Different techniques have been proposed with advancements in technology to model high-speed along with low power consumption and smaller area multipliers. For the radix-4 booth propagation algorithm for low-power and low complexity applications, an efficient approximate 8 bit redundant multiplier is used. To minimize the complication present in modified booth encoder, approximate Booth RB encoders have been introduced by modifying the truth table with incorrect bits, which resulted in a reduction of the power delay product. Approximate computing is a relevant technique for low power and high performance circuits as used in error-tolerant applications. Approximate or inexact computing is an attractive design methodology for low power design but accomplished by loosening up the necessity of precision. It becomes critical to maintain full accuracy to attain reduced power utilization. In this paper, the design of approximate redundant binary (RB) multipliers is studied and modified to build less complex multiplier with Radix-8 modified booth encoding technique to reduce area and complexities of architectures.

Complex Number Vedic Multiplier and its Implementation in a Filter

Complex numbers multiplication is a fundamental mathematical process in systems like digital signal processors (DSP). The main objective of complex number multiplication is to perform operations at lightning fast speed with less intake of power. In this paper, the best possible architecture is designed for a Real vedic multiplier based on the ancient Indian mathematical procedure known as URDHVA TIRYAKBHYAM SUTRA i.e. the structure of a MxM Vedic real multiplier architecture is developed. Then, a Vedic real multiplier solution of a complex multiplier is presented and its simulation results are obtained. The MxM Vedic real multiplier architecture, architecture of the Real Vedic multiplier solution for 32 x 32 bit complex numbers multiplication of complex multiplier and the architecture of a FIR filter has been code in Verilog and implementation is done through Modelsim 5.6 and Xilinx ISE 7.1 navigator.