## 3 Resampling Filter-Based Wideband Flexible Monitoring
 \tag{19}\]  
The architecture of the resampling filter employing cubic interpolation is represented in Figure 2.  
For the baseband OFDM signal post-low-pass filtering, the aforementioned resampling filter based on cubic interpolation can be employed to achieve flexible and adjustable sampling rates, thereby facilitating the high-precision real-time monitoring of the broadband signal. Figure 2: Resampling filter structure based on cubic interpolation. Satellite Frequency Offset Dynamic Compensation Algorithm Based on Ephemeris and Coordinate System Transformation  
The LEO satellite exhibits characteristics of low altitude and high velocity, which inherently imbue the dynamic nature of the satellite's trajectory. This dynamism consequently results in Doppler frequency shifts in the received signal [34]. This section delineates a Doppler frequency offset compensation algorithm tailored for LEO satellites. In the literature [35], the dynamics of LEO satellite signals are analyzed through the simulation of satellite orbits and propagation environments. The methodology employed in this paper necessitates a significantly reduced amount of a priori ephemeris information for dynamic compensation. Initially, the \"two-line\" satellite orbit element format is derived from the satellite ephemeris. Utilizing these elements, the satellite's position and velocity in the Earth-Centered Inertial (ECI) coordinate system are computed. Subsequently, these coordinates are transformed into the Earth-Centered Fixed (ECF) coordinate system, facilitating the description of the satellite's relative position and velocity in terms of latitude and longitude. Finally, the Doppler frequency offset for the LEO satellite link is calculated. In the following, a detailed introduction will be provided. The calculation process is illustrated in Figure 3.  
As dictated by [PERSON]'s laws, the satellite's trajectory is an ellipse that pierces through the Earth's center plane. The satellite's orbital path can be accurately defined by a suite of Keplerian orbital parameters. These parameters facilitate the estimation of the satellite's relative position and velocity with respect to the Earth at any given moment within the ECI coordinate system. The Keplerian parameters that delineate the satellite's orbital trajectory include the right ascension of the ascending node (\(\Omega\)), the argument of perigee (\(\omega\)), the orbital inclination (\(i\)), the semi-major axis of the orbit (\(b\)), the eccentricity of the orbit (\(e\)), and the mean anomaly (\(M\)). In Equation (20), \(n\) represents the mean motion, which can be calculated from the semi-major axis \(b\) of the orbit. \(t_{p}\) denotes the epoch of perigee passage, and \(\mu\) is the gravitational constant of the Earth. Utilizing the mean motion \(n\) in place of the semi-major axis \(b\) as an orbital parameter is a common practice currently adopted by the National Aeronautics  
Figure 3: Coordinate system transformation process. and Space Administration (NASA) in the \"two-line\" satellite orbit element format. The corresponding six orbital parameters are \(\Omega\), \(i\), \(e\), \(\omega\), \(M\), and \(n\). \[ \begin{cases}n=2\pi/T=(\mu/a^{3})^{1/2},\\ M=n(t-t_{{}_{p}}).\end{cases}  \tag{20}\]  
The satellite ephemeris can be solved to determine the position and velocity of the satellite at any arbitrary time \(t\) within the ECI coordinate system as  
\[ \begin{cases}\mathbf{R}_{\mathrm{s}}=a(\cos\!E-e)\mathbf{P}+b\sqrt{1-e^{2}} \mathrm{sin}\mathbf{EQ}_{\mathrm{}}\\ \mathbf{V}_{\mathrm{s}}=\sqrt{\pi}\Big{[}\frac{-\mathrm{sin}E}{\sqrt{b}(1- \cos\!E)}\mathbf{P}+\frac{\sqrt{1-e^{2}}\mathrm{cos}E}{\sqrt{b}(1-\cos\!E)} \mathbf{Q}\Big{]}.\end{cases}  \tag{21}\]  
Within the equation, \(E\) denotes the eccentric anomaly, which can be determined given the mean anomaly \(M\) and the eccentricity \(e\) as follows:  
\[E-e\mathrm{sin}E=M. \tag{22}\]  
The vectors \(P\) and \(Q\) can be determined, respectively, by Equations (15) and (16). \[\mathbf{P}= \begin{bmatrix}P_{X}\\ P_{Y}\\ P_{Z}\end{bmatrix} =