Maximum Ramanujan Spectrum Signal-to-Noise Ratio Deconvolution Method: Algorithm and Applications

In this article, a new deconvolution method, named maximum Ramanujan spectrum signal-to-noise ratio deconvolution (MRSD) method is proposed. MRSD updates the filter by maximizing the index of
v
-Ramanujan spectrum signal-to-noise ratio (
v
-RSSNR) to improve the noise reduction effect and the performance of feature enhancement. On the one hand, the concept of generalized envelope is introduced into the MRSD method, and flexible envelopes are used to enhance the weak state features, and the
v
-Ramanujan spectrum of the signal is analyzed by using the mixed Ramanujan Fourier transform, so as to provide an optimal plane for the evaluation of weak state features. On the other hand, the MRSD method designs the filter by maximizing the
v
-RSSNR index, and optimizes the objective function by gradient descent. The simulation and experimental analysis results show that MRSD method is an effective noise reduction method and can accurately extract weak state features.