Roundoff errors in block-floating-point systems

• Published in: IEEE transactions on signal processing Vol. 44; no. 4; pp. 783 - 790
• Main Authors: Kalliojarvi, K., Astola, J.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.1996; Institute of Electrical and Electronics Engineers
• Subjects: Analytical models; Applied sciences; Digital arithmetic; Digital filters; Dynamic range; Error analysis; Exact sciences and technology; Floating-point arithmetic; Information, signal and communications theory; Quantization; Roundoff errors; Sampling, quantization; Signal analysis; Signal and communications theory; Signal processing; Telecommunications and information theory; Digital filter; Quantization error; Computer arithmetic; Quantization; Signal processing; Digital processing; Floating point
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.492531

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.