A threshold activation-based simplified Lv’s transform algorithm for transient multi-component linear frequency modulation signals analysis

The high sampling rate in modern digital systems generates a large scale of data. To address the computational burden, this paper proposes a threshold activation-based simplified Lv's transform (SLVT) algorithm to analyze the transient multi-component linear frequency modulation signals. Only the signal arrival can trigger the signal analysis. This mechanism alleviates the computation pressure because of the sparsity of signals. The threshold activation mechanism enables transient signal detection and sampling rate adjustment, thereby enhancing the efficiency and effectiveness of the analytical process. The simplified Lv's transform (LVT) removes redundant computations on stretch weighting and the Discrete Fourier Transform (DFT) in Lv's transform. SLVT uses the efficient Bluestein chirp-z algorithm to implement the stretch keystone transform. The comparison results show that SLVT reduces the computational complexity of the original LVT by at least 30.8%. This algorithm exhibits superior performance compared to other advanced signal processing methods, such as discrete chirp Fourier transform, fractional Fourier transform, and Radon Wigner transform algorithms, in terms of parameter extraction accuracy, computational complexity, and execution time. Moreover, the implementation of a field programmable gate array accelerates SLVT computing by a factor of 116 in comparison to the CPU (Central Processing Unit) platform.