ROUNDOFF ERRORS IN BLOCK-FLOATING-POINT SYSTEMS

Block-floating-point representation is a special case of floating-poin t representation, where several numbers have a joint exponent term, In this paper, roundoff errors in signal processing systems utilizing bl ock-floating-point representation are studied, Special emphasis is on analysis of quantization errors when data is quantized to a block-boat ing-point format and on analysis of roundoff errors in digital filters utilizing block-floating-point arithmetic, Block-floating-point round off errors are found to depend on the signal level in the same way as floating-point roundoff errors, resulting in approximately constant si gnal-to-noise-ratios (SNRs) over relatively large dynamic range, Both the analysis and simulation results show that block-floating-point is an efficient number representation format. In data representation, a s uperior performance to fixed- or floating-point representations can be achieved with block-floating-point representation with same total num ber of bits per sample, In digital filters, block-floating-point arith metic can provide comparable performance to floating-point arithmetic with reduced complexity.