Signal processing and pattern recognition algorithms make exten(cid:173) sive use of convolution. In many cases, computational accuracy is not as important as computational speed. This form of noise justifies some level of quantization in order to achieve faster feature extraction . Our approach consists of approximating regions of the signal with low degree polynomi(cid:173) als, and then differentiating the resulting signals in order to obtain impulse functions (or derivatives of impulse functions). With this representation, convolution becomes extremely simple and can be implemented quite effectively.

ABSTRACT: Most of mathematic forgetting curve models fit well with the forgetting data under the learning condition of one time rather than repeated. In the paper, a convolution model of forgetting curve is proposed to simulate the memory process during learning. In this model, the memory ability (i.e. the central procedure in the working memory model) and learning material (i.e. the input in the working memory model) is regarded as the system function and the input function, respectively. The status of forgetting (i.e. the output in the working memory model) is regarded as output function or the convolution result of the memory ability and learning material. The model is applied to simulate the forgetting curves in different situations. The results show that the model is able to simulate the forgetting curves not only in one time learning condition but also in multi-times condition. The model is further verified in the experiments of Mandarin tone learning for Japanese learners. And the predicted curve fits well on the test points. Keywords: Memory forgetting curves; Convolution; Mathematical modeling 1.Introduction Since Ebbinghaus proposed the eminent'forgetting curve' to quantitatively describe the procedure of memory [1], researchers have made great effort to find out the exactly form of the models for forgetting curve. The problem is still being considered as'central theoretical importance' [2].

Feature extraction is a typical example: The distance between a small pattern (i.e.

Feature extraction is a typical example: The distance between a small pattern (i.e.

Feature extraction is a typical example: The distance between a small pattern (i.e.