Floating-point signal processing-arithmetic, roundoff-noise, and limit cycles

The number of representation and the range of floating-point numbers is treated for floating-point signal processing. The addition and multiplication operations which are most important for digital signal processing are explained in detail including the necessary normalization operations. Quantization errors in terms of the probability densities of the relative errors are analyzed in detail for roundoff-quantization, two´s-complement-truncation, and magnitude-truncation. The roundoff-noise is determined for a single quantizer and for complex signal processing flowgraphs. The problem of limit cycles is discussed briefly