Fig. 1. (a) Schematic of the experimental setup. The inset depicts the detailed section for ODMR. (b) The magnetic field sensitivity measured by continuous wave ODMR method. The blue and red lines show the sensitivity obtained from the direct outputs of measurements with and without the differential method.

Fig. 2. (a) Schematic of the analysis of signals at different scales. (b) Block diagram of the compound filter system using wavelet denoising approach and the adaptive filter based on wavelet transform.

Fig. 3. Comparison of the filtered effect for the ODMR signals with and without the filter when an extra magnetic field is generated as a (a) square or (b) sinusoidal wave. There is a great deal of noise contained in the differential signal (green), followed by original wavelet filtered signal (blue) and the signal after the adaptive filtering (red).

Fig. 4. Evaluation of the SNR of the filtered signal with respect to the parameters of adaptive filter. (a) Variation with the step size μ parameter at a δ parameter of 0.012. (b) Variation with the δ parameter at a μ parameter of 0.69.

Fig. 5. (a) Comparison of the filtering effects for ODMR signals caused by a weak magnetic field in the form of a sinusoidal wave. (b) Time domain and (c) frequency domain characteristics of the signals with and without the filter system at a fixed frequency. The green lines represent the differential signal; the blue and red lines represent the original wavelet filtered signal and the final filtered signal, respectively.

Fig. 6. (a) Sensitivity comparison between the differential signal (green) and final signals filtered by various filters, where we produce a varying magnetic field of about 100 nT at a frequency of 10 Hz. Inset shows comparison of the fidelity of desired signals after being filtered: compound (Wavelet+NLMS) filter (97.77%), Butterworth filter (96.97%), Gaussian filter (94.74%), and Median filter (93.41%). (b) SNR enhancement effect for desired non-stationary magnetic signals with different amplitudes and different frequency using our filter system. More detailed analysis for frequency and magnetic field amplitudes is shown in (c) and (d), for final signals filtered by compound filter (blue), Butterworth filter (orange), Gaussian filter (yellow), and Median filter (purple).