Angle recoding cordic-based systolic arrays for DFT and DHT of prime length

For senior/graduate-level courses in Discrete-Time Signal Processing. THE definitive, authoritative text on DSP -- ideal for those with an introductory-level knowledge of signals and systems. Written by prominent, DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field --without limiting itself to specific technologies with relatively short life spans.

Discrete-Time Signal Processing

The COordinate Rotation DIgital Computer(CORDIC) is a special-purpose digital computer for real-time airborne computation. In this computer, a unique computing technique is employed which is especially suitable for solving the trigonometric relationships involved in plane coordinate rotation and conversion from rectangular to polar coordinates. CORDIC is an entire-transfer computer; it contains a special serial arithmetic unit consisting of three shift registers, three adder-subtractors, and special interconnections. By use of a prescribed sequence of conditional additions or subtractions, the CORDIC arithmetic unit can be controlled to solve either set of the following equations: Y' = K(Y cos? + X sin?) X' = K(X cos? - Y sin?), or R = K?X2 + Y2 ? = tan-1 Y/X, where K is an invariable constant. This special arithmetic unit is also suitable for other computations such as multiplication, division, and the conversion between binary and mixed radix number systems. However, only the trigonometric algorithms used in this computer and the instrumentation of these algorithms are discussed in this paper.

The CORDIC Trigonometric Computing Technique

High speed signal processing depends critically on parallel processor technology. In most applications, general-purpose parallel computers cannot offer satisfactory real-time processing speed due to severe system overhead. Therefore, for real-time digital signal processing (DSP) systems, special-purpose array processors have become the only appealing alternative. In designing or using such array Processors, most signal processing algorithms share the critical attributes of regularity, recursiveness, and local communication. These properties are effectively exploited in innovative systolic and wavefront array processors. These arrays maximize the strength of very large scale integration (VLSI) in terms of intensive and pipelined computing, and yet circumvent its main limitation on communication. The application domain of such array processors covers a very broad range, including digital filtering, spectrum estimation, adaptive array processing, image/vision processing, and seismic and tomographic signal processing, This article provides a general overview of VLSI array processors and a unified treatment from algorithm, architecture, and application perspectives.

Angle recoding cordic-based systolic arrays for DFT and DHT of prime length

References

Discrete-Time Signal Processing

The CORDIC Trigonometric Computing Technique

VLSI Array processors

VLSI array processors

Computer arithmetic: Principles, architecture, and design

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