In this paper, we propose a spectral interpolation method using a distortion geodesic line, which is defined as the curve with minimal accumulated distortion. We apply the distortion geodesic line to interpolation of two given spectra (vectors). The first part of this paper describes the definition of the distortion geodesic line. It is shown that a geodesic line is characterized by the Riemannian metric which is introduced as a bilinear form of the second partial derivatives of a given distortion measure. The second part describes an inequality for the WLR measure on several interpolating curves. This inequality guarantees that the accumulated WLR distortion value for any two given spectra, ƒ⁽⁰⁾ and ƒ⁽¹⁾, on the correlation interpolation curve, is always smaller than the direct WLR value d_WLR(ƒ⁽⁰⁾, ƒ⁽¹⁾). This property is easily extended to a category of several distortion measures. The third part describes an application of the distortion geodesic line to spectral interpolation, and numerically shows that the interpolation line on the correlation parameter is the best of several kinds of LPC based parameters.

We propose a new type of the digital neuron model by using multi-input multilevel-quanitized digital phase-locked loop (MM-DPLL), where the input is represented by the phase modulated signal. It is shown that this model has the characteristics of the neuron; spatial summation, temporal summation and thresholding. We applied our model to the pattern recognition and to the Hopfield type associative memory, in order to verify that the network by this model can operate properly. In the pattern recognition, we used the perceptron convergence procedure (delta rule), and confirm the possibility of learning by modifying the connection weights. In the associative memory, we confirm that the network can learn five digit patterns of the fundamental memories, and also can recall the correct pattern for the noisy input pattern.