A Time-Domain Frequency Analyzer Based on Goertzel Algorithm
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Bibliographic record
Abstract
This article presents a novel time-domain implementation of the second-order Goertzel frequency analyzer, which can be extended for use in infinite impulse response (IIR)/finite impulse response (FIR) filters. A set of time-domain arithmetic circuits, including a one-step time register (TR), time amplifier (TA), time adder, and unit delay operator (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${z}^{-1}$ </tex-math></inline-formula>), are introduced to overcome the limitations of conventional time-domain filters. The working principles and nonidealities of each block are analyzed and compared with the existing methods. The proposed filter is implemented in a 180-nm CMOS process with a 0.9-V supply voltage. The designed frequency analyzer is tunable to extract the amplitude and phase angle of signals up to 400 Hz. Simulation results, targeting a 280-Hz signal at a 19.88-kHz sampling frequency, demonstrate that the filter can detect the amplitude and phase of a voltage signal in the time domain with an error below 5%. The filter achieves a resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$76.7~\text {dBV/s}$ </tex-math></inline-formula>, consumes less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$24~\mu \text {W}$ </tex-math></inline-formula> of power, and the estimated silicon area is almost <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.828~\mathrm {mm}^{2}$ </tex-math></inline-formula>.
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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 | 0.001 |
| 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