Happenings
| On the 20th July 2009, Dr Oscar Gustafsson, an assistant professor from Linköping University, Sweden, gave a talk on Multiplication without Multipliers: Algorithms, Applications and Extensions. This talk was co-organized by TL@NTU and CAS Singapore chapter. |
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General multipliers are often the most power and area consuming part of digital signal processing systems. During the years, much research have focused on either reducing the number of multipliers or replacing the multipliers with networks of shifts, adders, and subtracters. In this talk, we consider the second approach: when can we replace general multipliers with these networks and how do we do it efficiently? Such realizations are often referred to as multiplierless. The most common example in literature is transposed direct form FIR filters, where the input data is multiplied with several constant coefficients. By utilizing the redundancy between the constants, one can reduce the resource requirements such that often the multiplications are no longer the major part of the computation. This problem can be generalized to also include several inputs and shifts in other dimensions (typically time). This leads to that similar approaches can be used for e.g. DCTs, DFTs, and computations infinite fields. We discuss the major classes of algorithms, namely sub expression sharing and adder graph approaches, and their suitability for different problems and optimization criteria. Furthermore, we briefly discuss the area, time, and energy trade-offs. |
Below is an abstract of the talk.