| Γ⁽ⁱ⁾ | ‖M⁽ⁱ⁾‖² | ||
| [r⁽ⁱ⁾]² = | —— | + | ———— . |
| α | (2α)² |
Both the center and radius of this hypersphere change as the machine adapts. The performance and optimality of hypersphere-type decision boundaries have been discussed in related work by Glaser[3] and Cooper.[4]
The threshold value, Γᵢ, is adapted so that it increases if the memory becomes a better replica of the signal with the result that γᵢ increases. On the other hand, if the memory is a poor replica of the signal (for example, if it contains noise alone), it is necessary that the threshold decay with time to the point where additional acceptances can modify the memory structure.
The experimental machine is entirely digital in operation and, as stated above, is capable of recovering waveforms of up to 10³ samples in duration. In a typical experiment, one might attempt to recover an unknown noise-perturbed, pseudo-random waveform of up to 10³ bits duration which occurs at random intervals. If no information is available as to the signal waveshape, the adaptive memory is blank at the start of the experiment.
In order to illustrate the operation of the machine most clearly, let us consider a repetitive binary waveform which is composed of 10³ bits of alternate “zeros” and “ones.” A portion of this waveform is shown in [Figure 2a]. The waveform actually observed is a noise-perturbed version of this waveform shown in [Figure 2b] at-6 db signal-to-noise ratio. The exact sign of each of the signal bits obviously could not be accurately determined by direct observation of [Figure 2b].
(a) Binary signal
(b) Binary signal plus noise
Figure 2—Binary signal with additive noise at-6 db SNR