Fractional Fourier transform as a signal processing tool: An overview of recent developments <s> Pattern recognition <s> Abstract Pattern recognition, based on matched filtering, can be generalized by replacing the standard Fourier operations by fractional Fourier operations. One important consequence of this is that the system is no longer space invariant. We study the impact of space variance, and point out that space variance may be desirable under certain circumstances. We illustrate our theoretical conclusions by simulated experiments. <s> BIB001 </s> Fractional Fourier transform as a signal processing tool: An overview of recent developments <s> Pattern recognition <s> This study investigates fractional Fourier transform pre-processing of input signals to neural networks. The fractional Fourier transform is a generalization of the ordinary Fourier transform with an order parameter a. Judicious choice of this parameter can lead to overall improvement of the neural network performance. As an illustrative example, we consider recognition and position estimation of different types of objects based on their sonar returns. Raw amplitude and time-of-flight patterns acquired from a real sonar system are processed, demonstrating reduced error in both recognition and position estimation of objects. <s> BIB002
Given that the FRFT provides an extra parameter (e.g., the rotation angle) in comparison with the ordinary Fourier transform, the FRFT also provides additional degrees of freedom in pattern recognition systems. For example, the FRFT was used as a pre-processor for a neural network BIB002 . The use of fractional based pre-processing resulted in an improved performance comparing to both no preprocessing and ordinary Fourier transform pre-processing. Also, the fractional based pre-processing resulted in a substantial reduction of classification and localization error. While use of the fractional Fourier transform increases the cost of the training procedure, the improvements achieved with its use come at no additional routine operating cost. Furthermore, it has been also shown that pattern recognition methods based on matched filtering can be generalized by replacing the standard Fourier operations by fractional Fourier operations BIB001 . However, these systems become time (or space) varying systems.