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.