1. A recognition system comprising: feature extracting means for extracting a feature vector x from an input signal; and recognizing means for obtaining continuous density Hidden Markov Models (HMMs) of predetermined categories K represented by transition network models each having parameters of transition probabilities p(k,i,j) that a state Si transits to a next state Sj and output probabilities g(k,s) that the feature vector x is output in transition from the state Si to one of the states Si and Sj, and for recognizing the input signal on the basis of similarity between a feature vector sequence x of the feature vectors x each extracted by said feature extracting means and the continuous density HMMs; wherein said recognizing means includes memory means for storing a set of orthogonal vectors .phi..sub.m (k,s) provided for the continuous density HMMs, and processing means for obtaining each of the output probabilities g(k,s) for the continuous density HMMs in accordance with the orthogonal vectors .phi..sub.m (k,s) or a corresponding category k.