Optimized sparse fractional Fourier transform: Principle and performance analysis - Zhang, Hongchi; Shan, Tao; Liu, Shengheng; Tao, Ran (Signal processing, 2020)
•Neyman-Pearson detection is applied to estimate large coefficients of noise-corrupted signals in the fractional Fourier domain.•Distribution of phase error is obtained via Parzen-Rosenblatt window method.•Location error correction method is proposed.•Important properties of the proposed optimized sparse fractional Fourier transform are investigated via extensive simulations.•Real data collected from a continuous-wave radar is processed and the velocity of a free falling target is estimated. For the input signals that can be sparsely represented in the fractional Fourier domain, sparse discrete fractional Fourier transform (SDFrFT) has been proposed to accelerate the numerical computation of discrete fractional Fourier transform. While significantly alleviating the computational load, SDFrFT has narrow applicability since it is more suitable for large-scale input signals. In this regard, the objective of this work is to overcome the limitation and further optimize the numerical computation of SDFrFT by exploiting the underlying phase information. We first employ Neyman-Pearson approach to achieve a noise-robust detection. Then, we derive the probability distribution function of the phase error in the location stage and, accordingly, design a location error correction algorithm. The proposed algorithm, termed optimized sparse fractional Fourier transform (OSFrFT), can reduce the computational complexity while guarantee sufficient robustness and estimation accuracy. Simulation results are provided to validate the effectiveness of the proposed algorithm. A successful application of OSFrFT to continuous wave radar signal processing is also presented.