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Frequency Domain Spline Prioritization Optimization Adaptive Filters

The spline prioritization optimization adaptive filter (SPOAF) is a nonlinear filtering algorithm with a relatively simple architecture. It is composed of the FIR filter cascaded a nonlinear interpolation module. When the length of the FIR filter is long, the computational complexity will increase exponentially. To solve this problem, this paper proposes a frequency domain spline prioritization optimization adaptive filter (FDSPOAF). More specifically, the FIR filter is implemented in the frequency domain, using the fast Fourier transform and its inverse transform, which converts convolution in the time domain into multiplication in the frequency domain. This paper describes the detailed steps of the FDSPOAF method and analyzes the computational complexity. Finally, it is verified by numerical experiments that the algorithm can reduce the operation time. Compared with the traditional SPOAF algorithm, the proposed FDSPOAF algorithm can effectively reduce the operation time of the algorithm with comparable convergence performance.