Signal identification in smart composite materials using the two-dimensional fast Fourier transform

Abstract This work is part of an effort to structurally integrate self-sensing functionality into smart composite materials using embedded microsensors and local network communication nodes. Here we address the issue of data management through the development of localized processing algorithms. We demonstrate that the two-dimensional fast Fourier transform (FFT) is a useful algorithm due to its hierarchical structure and ability to determine the relative magnitudes of different spatial wavelengths in a material. This may be applied, for example, to determine the global components of a strain field or temperature distribution. We develop two methods for implementing the distributed 2D FFT based on the radix-2 (row–column) and radix-2 × 2 (vector–radix) structures, and compare them in terms of computational requirements within a low power, low bandwidth network of microprocessors. Our results show that the vector–radix algorithm requires 50% fewer multiplications than the row–column algorithm when performed in a distributed manner. Since the most important information of the 2D FFT can often be found in the lowest frequency components, we develop pruning methods for the distributed row–column and vector–radix algorithms that reduce internode communication requirements by 50% in both cases. We conclude that the pruned version of the distributed vector–radix 2D FFT is the most efficient of the methods investigated for rapid signal identification in smart composite materials.