Prony Series Digital Filter Implementation for Real Time Accelerometer Drift Compensation
Real-time Prony series filters model structural MEMS relaxation as discrete state poles to strip low-frequency drift before velocity integration.
Discrete Poles
Stability Identifier
Specific points in the complex z-plane where the transfer function of a digital system becomes infinite determine the frequency response and transient behavior. Engineers analyze discrete poles to predict how a sampled-data filter will react to changes in the input signal. The location of these points defines the damping ratio and the natural frequency of the digital control loop.
Mapping Location
Coordinate positions relative to the unit circle dictate whether a recursive filter remains stable over time. For any system using discrete poles, a position inside the circle indicates a decaying response, while a position outside leads to uncontrolled oscillation. Precision in the calculation of these values is necessary for predictable performance in real-time processing.
Numerical rounding in fixed-point arithmetic can shift these points and affect system behavior.
Frequency Influence
Proximity to the edge of the unit circle affects the sharpness of the filter transitions. When discrete poles are placed close to the circle, the system exhibits a narrow bandwidth and high selectivity. This configuration is useful for isolating a specific signal frequency from broadband noise.
It also increases the risk of ringing in the step response.
Transformation Synthesis
Mathematical techniques like the bilinear transform convert analog filter designs into their digital equivalents. This mapping determines the final arrangement of the discrete poles in the z-domain. The accuracy of the conversion ensures that the digital implementation matches the intended analog specification.