Smoothing Irregularly Sampled Signals by Convolutional RBF Networks I. S. Lim, N. W. John and K. A. Shore Convolutional Radial Basis Function (RBF) networks are introduced for smoothing out irregularly sampled signals. Our proposed technique involves training a RBF network and then convolving it with a Gaussian smoothing kernel in an analytical manner. Since the convolution results in an analytic form, the computation necessary for numerical convolution is avoided. Convolutional RBF networks need training only once, do not depend on any particular details of the training methods used, and different degrees of smoothing are immediately available. Introduction: Smoothing out signals is a common requirement in signal processing in order to reduce noise or unwanted detail. For irregularly sampled signals, however, the smoothing operation is difficult to apply because standard digital signal processing assumes a regular sampling. To smooth out irregular signals, we can use a neural network such as a RBF network [5] of the form f (x)= n  i=1 w i exp  − ‖x − x i ‖ 2 2σ 2 i  (1) satisfying interpolation conditions f (x i )= y i , where x i ∈ R d are data points, and y i ∈ R are function values. A RBF network is trained to minimize an error functional E[f ]= ∑ n i=1 (y i − f (x i )) 2 by solving a linear system Gw = y obtained by inserting the interpolation conditions in Equation 1. This interpo- lating RBF network is evaluated on a lattice for resampling, and then standard numerical convolution smoothes out these regularly resampled signals [2, 3]. However, this technique can be computation- 1