Phase Compensation Architectures for Asynchronous Decimation Delays in Multirate Feedback Loops
Dynamic Farrow filters and state observers restore feedback phase margin by compensating time-varying asynchronous decimation group delays in real time.
Lagrange Polynomial Interpolation
Fractional Estimation
Signal reconstruction algorithms use a mathematical curve-fitting technique to estimate value points between discrete sensor samples without increasing the physical sampling rate. This method is called lagrange polynomial interpolation, which constructs a unique polynomial of the lowest possible degree that passes through a set of given data points. It is widely applied in software-defined radio receiver chains to adjust fractional clock offsets.
Mathematical Formulation
The algorithm calculates coefficients by evaluating the product of fractional differences over the distance between sample times. Through lagrange polynomial interpolation, a sensor signal chain can approximate the continuously variable timing offsets required for sample rate conversion. This formulation remains computationally demanding for higher degrees due to the need for nested multiplications.
Metrological Verification
Precision testing of these interpolators relies on calculating the residual error between the interpolated waveform and a pure analog reference sine wave. These test protocols are defined by engineering bodies to guarantee that spurious-free dynamic range is not degraded. Calibration instruments sweep the phase offset to verify that the interpolation error remains below the system noise floor.
Numerical Constraint
High-degree polynomials produce severe oscillations near the interval boundaries when the sample points are spaced equally. This phenomenon limits the practical order of the interpolation to low values.