Design and Implementation of Fractional Step Filters
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Bibliographic record
Abstract
This thesis investigates the design of fractional lowpass and highpass filters of order (n+a) with fractional step a through the stopband while maintaining a flat passband.Here n is an integer 1, 2, 3... and 0 < a < 1.The design of these filters uses an integer-order approximation of the fractional-order Laplacian operator s a .Simulations and physically realized integer order filters demonstrate the fractional step through the stopband for highpass and lowpass filters of order (1 + a) to (4 + a) in steps of 0.1, 0.5, and 0.9.Also proposed in this thesis is a modification to a second order approximation used for the fractional-order Laplacian operator, s a , where 0 < a < 1.This modification is used to create equal-ripple magnitude and phase responses, both having less cumulative and peak error than the original second order approximation.Fractional filters of order (1 + a) = 1.8 are realized using both the modified and original approximation to highlight the benefits of the modification.First order lowpass filters with fractional steps of 0.2, 0.5, and 0.8, are simulated using the approximation with experimental results verifying the operation of this approximation in the realization of fractional step filters.Fabricated integrated circuit fractional capacitors are used in the implementation of a fractional Tow-Thomas biquad.This demonstrates a fractional step low-pass filter without the use of the approximated fractional Laplacian operator.Experimental results verify the operation of the fractional step filter and fractional behaviour of the capacitors.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it