Reconstruction of a signal from multirate observations: A recursive approach

In this paper, we develop a recursive formulation for the reconstruction of a signal from multirate ob-servations. We model the observations as the outputs of a decimated analysis bank and convert the re-construction problem into a matrix synthesis filter design problem. We use the mean-square criterion to minimize the reconstruction error and obtain a synthesis bank solution for a given filter length and de-lay in reconstruction. We then derive a recursive method with arbitrary step size for computing the same beginning from any smaller length solution. We also derive a recursive formulation for the mean-square error (MSE) with similar flexibility. This method is computationally efficient when compared to the direct computation of a solution. Additionally, it aids in studying the properties of the solutions as a function of filter length. Finally, we present experimental results that demonstrate the advantages of the recursive method developed. (c) 2023 Elsevier B.V. All rights reserved.