Prony Series Deconvolution of Viscoelastic Die Attach Relaxation in Accelerometers
Real-time digital inverse Prony filtering decouples time-dependent polymer stress relaxation from true acceleration signals in high-precision micro-sensors.
Infinite Impulse Response
Signal Recursion
Recursive digital filtering structures provide a feedback path where output samples influence subsequent values. An infinite impulse response design creates a memory mechanism that continues to oscillate after the cessation of input excitation. Stability depends on the location of poles within the unit circle of the Z plane.
Realization occurs through direct forms or lattice structures where coefficients define the transfer function.
Filter Stability
Quantization errors appear when coefficients lack sufficient bit depth to maintain precise pole placement. Fixed point arithmetic introduces rounding noise that accumulates within the feedback loop. Sensitivity to coefficient accuracy necessitates higher word lengths compared to non-recursive equivalents.
Proper scaling prevents overflow conditions during intermediate calculations while preserving the signal dynamic range.
Phase Linearity
Frequency dependent delays distort the signal timing across the spectrum. Phase response characteristics remain nonlinear in basic implementations because the energy distribution shifts unevenly across the passband. Designers apply compensation methods or all pass equalizers to correct the group delay when temporal alignment remains a priority.
Periodic signals undergo varying shifts that alter the shape of transient events.
Computational Economy
Low order implementations achieve steep roll off characteristics that exceed the performance of non-recursive designs with identical sample counts. Processing efficiency increases because fewer multiplications generate complex magnitude curves. High order applications require cascading stages to minimize sensitivity to numeric precision.
Recursive topologies offer substantial memory savings in embedded hardware where processing cycles remain constrained.