Roundoff errors in block-floating-point systems

Block-floating-point representation is a special case of floating-point representation, where several numbers have a joint exponent term. In this paper, roundoff errors in signal processing systems utilizing block-floating-point representation are studied. Special emphasis is on analysis of quantization errors when data is quantized to a block-floating-point format and on analysis of roundoff errors in digital filters utilizing block-floating-point arithmetic, block-floating-point roundoff errors are found to depend on the signal level in the same way as floating-point roundoff errors, resulting in approximately constant signal-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 superior performance to fixed- or floating-point representations can be achieved with block-floating-point representation with same total number of bits per sample. In digital filters, block-floating-point arithmetic can provide comparable performance to floating-point arithmetic with reduced complexity