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Testing for a Random Walk Structure in the Frequency Evolution of a Tone in Noise
Scarlett Abramson1, William Moran1, Robin Evans1
1Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC 3010, Australia.
Sensors (Basel, Switzerland)
|August 26, 2022
Summary
This study introduces a new test to verify random walk structures in signal frequencies. The method enhances data analysis by confirming assumed models in noisy, complex-valued sinusoidal signals.
Area of Science:
- Signal Processing
- Statistical Inference
- Time Series Analysis
Background:
- Hypothesis testing relies on assumed data models.
- Verifying these models is crucial for accurate conclusions.
- Random walk behavior is often analyzed in time series data.
Purpose of the Study:
- Develop a model verification test for random walk-like structures.
- Assess variations in the frequency of complex-valued sinusoidal signals.
- Incorporate additive Gaussian noise considerations.
Main Methods:
- Jointly inferring random walk hypothesis tests from economics.
- Applying tests to frequency variations of sinusoidal signals.
- Including an additional test for frequency-domain random walk behavior.
Main Results:
- A novel model verification test is developed.
- The test is applicable to complex-valued sinusoidal signals with noise.
- It accounts for random walk behavior in frequency space.
Conclusions:
- The developed test accurately verifies random walk structures in signal frequencies.
- This enhances the reliability of data analyses involving such signals.
- The method provides a robust approach for noisy signal processing.
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