At each sample instant, two measurements are made on the input vector, an energy measurement ‖Y⁽ⁱ⁾‖² and a polarity coincidence cross-correlation with the present estimate of the signal vector stored in memory. If the weighted sum of the energy and cross-correlation measurements exceeds the present threshold value Γᵢ, the input vector is accepted as containing the signal (properly shifted in time), and the input vector is added to the memory. The adaptive memory has 2^{Q} levels, 2^{Q-1} positive levels, 1 zero level and 2^{Q-1}-1 negative levels. New contributions are made to the memory by normal vector addition except that saturation occurs when a component value is at the maximum or minimum level. The acceptance or rejection of a given input vector is based on a hypersphere decision boundary. The input vector is accepted if the weighted sum γᵢ exceeds the threshold Γᵢ γᵢ = Y⁽ⁱ⁾∙M⁽ⁱ⁾ + α‖Y⁽ⁱ⁾‖² ⩾ Γᵢ. [Illustration: Figure 1—Block diagram of the adaptive binary waveform detector] Geometrically, we see that the input vector is accepted if it falls on or outside of a hypersphere centered at ⮕C⁽ⁱ⁾ = -⮕M⁽ⁱ⁾/2α having radius squared 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] [3] F. M. Glaser, “Signal Detection by Adaptive Filters,” _IRE Trans. Information Theory_, pp. 87-90; April 1961. [4] P. W. Cooper, “The Hypersphere in Pattern Recognition,” _Information and Control_, pp. 324-346; December 1962. 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.