On the number representation in sub-expression sharing

The core of many DSP tasks is Multiplication of one data with several constants, i.e. in Digital filtering, image processing DCT and DFT. The Modern Portable equipments like Cellular phones and MP3 players which has DSP circuits, involve large number of multiplications of one variable with several constants (MCM) which leads to large area, delay and energy consumption in hardware. Multiplication operation can be realized using addition/subtraction and shifts without general multipliers. Different number representations are used in MCM algorithms and there are differnet views about different representations. Some of the authors termed the Canonic Signed Digit (CSD) representation as better for subexpression sharing. We have compared the results of CSD and Binary representations using our Generalized MCM Algorithm on Random Matrices and come to conclusion that binary representation is better compared to CSD when a system has multiple inputs and multiple outputs.