Exploração do algoritmo CORDIC para redução de potência em arquiteturas de transformada rápida de Fourier (FFT)

Abstract

This work explores the use of CORDIC (COordinate Rotation Digital Computer) algorithm in dedicated Fast Fourier Transform (FFT) architectures. Fully sequential architectures of different sizes (different numbers of points) for specific FFT algorithm projects are implemented and compared. The CORDIC algorithm has been widely used in FFT architectures to generate the twiddle factors, since this algorithm eliminates the need to use multiplier circuits, besides reducing the ROM memory requirements. Since the twiddle factors are composed of factors of cosines and sines, the work explores the relationship between the number of bits and the number of iterations in the CORDIC algorithm. The main scope is to verify the impact on energy consumption in ASIC architectures for sine and cosine functions. By the obtained results it has been verified that there is a direct relationship between the number of bits and iterations used by CORDIC and the impact of this on hardware. The best fit regarding accuracy is dependent on the application. In other words, the number of bits at the circuit input and the number of iterations that CORDIC must perform are individually related to the accuracy required by the final application. From the design space enabled by the implementations of the CORDIC algorithm, is explored its use in sequential FFT architectures. The main goal is to establish a low power design methodology for FFT architectures based on the use of the CORDIC algorithm. For this purpose, FFTs of 32, 64, 128 and 256 sizes were implemented with CORDIC. The main results showed that the use of CORDIC is advantageous when compared to the explicit classical twiddle factor storage solution in all scenarios. However, based on the results obtained, it was observed that there were still opportunities for improvement. Three additional CORDIC versions (v.2, v.3 and v.4) were then developed, the best of which was used in a re-reading of the initially implemented FFT. The results demonstrate a significant improvement when using the most recent versions of CORDIC and FFT. The results also demonstrate that CORDIC is an advantageous alternative when considering its area-power cost at lower operating frequencies.