The Impact of Finite Wordlength Implementation - Digital Signal Processing: An Introduction with MATLAB and Applications - page 208

Limit Cycles Due to Overflow This type of oscillation takes place when the
quantizer input exceeds the dynamic range. The magnitude of these limit cycles is
large and can not be mitigated by adding more bits of precision as with granular
limit cycles.
Recall that in the 2's-complement arithmetic system, if one adds two numbers
whose sum is greater than the allowable dynamic range, the carry will propagate
into the sign bit. Therefore, overflow tends to create very large errors due to the
switching of the result's sign. To avoid this type of oscillation, an alternative
addition characteristic, called 'saturation-overflow', is adopted. With this approach
steps are taken to ensure that the size of the error does not increase unexpectedly.
Saturation-overflow is achieved simply by clipping the result of accumulation if an
overflow is detected. This strategy limits the overflow error and prevents a change
of sign. This method is commonly used in signal processors and A/D converters
that use 2's-complement numbers.
References
1. Mitra, S.: Digital Signal Processing: A Computer Based Approach, 3rd edn. McGraw-Hill,
New York (2006)
2. Oppenheim, A.V., Schafer, R.W., Buck, J.R.: Discrete-Time Signal Processing, 2nd edn.
Prentice Hall Inc., NJ (1999)
3. Porat, B.: A Course in Digital Signal Processing. Wiley, New York (1997)
4. Vaidyanathan, P.P.: Multirtae Systems and Filter Banks, Prentice Hall Inc., NJ (1993)