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Abstract:
Signal processing and pattern recognition algorithms make
extensive use of convolution. In many cases, computational accuracy
is not as important as computational speed. In feature extraction,
for instance, the features of interest in a signal are usually
quite distorted. 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 polynomials, 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. The true
convolution can be recovered by integrating the result of the
convolution. This method yields substantial speed up in feature
extraction and is applicable to convolutional neural
networks
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