## 3 Resampling Filter-Based Wideband Flexible Monitoring  
This section presents a broadband flexible monitoring approach based on resampling filters, which integrates resampling technology with low-pass filtering to enable the flexible adjustment of the sampling rate. The approach reduces the sampling rate to four times the symbol rate and subsequently applies low-pass filtering to achieve rate matching. Due to the receiver's lack of prior knowledge about the symbol rate during blind signal processing, a high sampling rate is often employed when sampling the signal. This leads to an excessively large observation bandwidth for the received signal, whereas the actual signal bandwidth is relatively narrow, which can adversely affect subsequent identification performance. In this paper, a digital resampling-based flexible low-pass filter is designed, which, in conjunction with the identified signal bandwidth, reduces the sampling rate to four times the symbol rate of the signal. In this paper, we leverage digital resampling techniques to interpolate the target rate sampling points directly from the known sampling points using interpolation filters. In accordance with the Nyquist Sampling Theorem, as long as the sampling frequency is greater than twice the signal bandwidth, the original signal (y(t)) can be recovered from the sampled values \(x(nT_{s})\). \[y(t)=\sum_{n=-\infty}^{+\infty}x(nT_{s})h(t-nT_{s}). \tag{12}\]  
In the expression, \(T_{s}\) represents the sampling period, \(h(t)=\frac{\sin(\pi t/T_{s})}{\pi t/T_{s}}\)  
Subsequently, the recovered signal is subject to resampling to obtain  
\[y(kT_{i})=\sum_{n=-\infty}^{+\infty}x(nT_{s})h(kT_{i}-nT_{s})=\sum_{n=-\infty }^{+\infty}x(nT_{s})h\left(T_{s}\left(\frac{kT_{i}}{T_{s}}-n\right)\right). \tag{13}\]  
Let \(m_{k}=\left\lfloor\frac{kT_{i}}{T_{s}}\right\rfloor\) (where \(\lfloor\cdot\rfloor\) denotes the floor function, which rounds down to the nearest integer), and \(\mu_{k}=\frac{kT_{i}}{T_{s}}-m_{k}\). Substituting these into Equation (13) yields. \[y(kT_{i})=\sum_{n=-\infty}^{+\infty}x(nT_{s})h((m_{k}+\mu_{k}-n)T_{s}). \tag{14}\]  
Upon defining \(m=m_{k}-n\), we obtain  
\[y(kT_{i})=\sum_{m=-\infty}^{+\infty}x((m_{k}-m)T_{s})h((\mu_{k}+m)T_{s}). \tag{15}\]  
Equation (15) demonstrates that our approach merely uses the reconstruction of the original signal as an intermediate step, whereas in practice, new sampling values can be directly obtained through the weighted summation of known sampled values. However, it is impossible to achieve a completely ideal resampling process because we cannot perform an infinite series of weighted summations. Instead, we resort to using a finite-length FIR(Finite Impulse Response) filter with performance close to the ideal, as a substitute. The truncated form of Equation (15) after applying the FIR filter can be expressed as  
\[y(kT_{i})=\sum_{m=-I_{1}}^{I_{2}}x((m_{k}-m)T_{s})h((\mu_{k}+m)T_{s})=\sum_{m=-I_ {1}}^{I_{2}}h_{I}(\mu_{k}+m)x(m_{k}-m). \tag{16}\]  
In this paper, we employ a cubic interpolation polynomial to approximate the filter for calculating the weighted coefficients, aiming to achieve performance as close as possible to that of an ideal filter. The impulse response expression for cubic interpolation is  
\[h_{c}(t)= \begin{cases}1-\frac{1}{2}|t|-|t|^{2}+\frac{1}{2}|t|^{3},&|t|<1,\\ 1-\frac{11}{6}|t|+|t|^{2}-\frac{1}{6}|t|^{3},&1\leq|t|<2,\\ 0,&|t|>2.\end{cases}  \tag{17}\]  
The frequency response is given by  
\[H_{c}(f)=\frac{e^{-j\pi\pi f_{S}}(2(\pi fT_{s})^{2}+3)(e^{j2\pi ft_{S}}-1)^{4} }{48(\pi fT_{s})^{4}}. \tag{18}\]  
Substitute Equation (17) into Equation (16), and by setting \(I_{1}=2\), \(I_{2}=1\), we obtain the expression for the cubic interpolation coefficient with respect to \(\mu\) as  
\[ \begin{split} C_{-2}&=\frac{1}{6}\mu^{3}-\frac{1}{6 }\mu,\qquad\qquad C_{-1}=-\frac{1}{2}\mu^{3}+\frac{1}{2}\mu^{2}+\mu,\\ C_{0}&=\frac{1}{2}\mu^{3}-\mu^{2}-\frac{1}{2}\mu+1, & C_{1}=-\frac{1}{6}\mu^{3}+\frac{1}{2}\mu^{2}-\frac{1}{3}\mu.\end{split}