A Novel Theorem with Potential Application to Automatic Equalization

When the signs of the alternate terms of a symmetric discrete time series are reversed and the resultant series is convolved with the original, the newly created time series will have alternate values equal to zero. This theory is shown here to have a potential application in the design of a single-shot zero-forcing equalizer (of the adjust and freeze type). The system can be easily generalized to handle partial response signals.