| Mathematical operations on complex numbers are commonly required in numerous computer applications. The use of complex number computations in the design algorithms for various digital signal processing (DSP) has received considerable attention in recent years. Algorithms in complex orthogonal transformations, correlations, and filtrations are a part of arithmetic computations such as geometric analysis in graphics or signal processing. The digital signal processing algorithms and modern digital communication systems such as equalization, modulation and demodulation are all deal with data streams represented by complex numbers. These applications require efficient representation and manipulation, in addition to treatment of complex numbers. These algorithms usually include arithmetic operations. The digital signal processing demands always increase and higher performance in the implementation of algorithms are investigated. Therefore, the implementations of the arithmetic operations of the complex numbers for high-performance especially for complex number multiplier are of significant interest.; A novel method for complex numbers representation and the arithmetic operations on them was introduced for computer vision which is a relatively new area. The proposed Redundant Complex Binary Number System (RCBNS) was developed by combining a Redundant Binary Number and a complex number in the base (−1+j).; A Redundant Complex Binary Number System consists of both the real and the imaginary parts presented by a radix number system that forms a single redundant integer digit set. This system is formed by using complex radix of (−1+j) and a digit set of α = 3, where α assumes a value of −3, −2, −1, 0, 1, 2, 3. The arithmetic operations on these complex numbers treat the real and the imaginary parts as one unit. Carry-free addition is the advantage in the arithmetic operations that uses operands in the Redundant Complex Binary Number System.; Conversion of decimal complex numbers in the standard binary form to the RCBNS form is accomplished by converting the decimal complex number to the complex binary form and then the real part and the imaginary part to be treated in one unit. Two methods for the conversion to the RCBNS form are presented. These complex numbers in the RCBNS form are used to perform arithmetic operations, addition, subtraction, multiplication and division. The results of arithmetic operations on complex number are available in the RCBNS form. These results in the RCBNS form should be reconverted back to the Standard Binary Number form.{09}Two methods are presented for the reconversion. Both methods are based on separating the real part and the imaginary part of each row of four digit positions of the RCBNS number and forward them to two dedicated registers. The comparisons of the proposed multiplier with other existing multipliers were done. Finally, methodology and processes of the proposed work were modeled (functional and behavioral) using a hardware description language, VHDL. In this research, the RCBNS form for complex number reduces the number of steps required to perform complex number arithmetic operations, thus enhancing the speed. |
