Biased logarithmic arithmetic in digital signal processing

Logarithmic arithmetic supports efficient multiplications but suffers from the drawback of cumbersome addition and subtraction operations, which require lookup tables. Recently, a biasing method has been proposed, providing savings in the table size. The original use of the method was in finite impulse response filters. In this work, the biasing approach is extended to recursive digital filters. The use of biased logarithmic addition in infinite impulse response filters is described, and the properties of the biased logarithmic number system are analysed.