Wavelets: a mathematical microscope
Artem Kirsanov・2 minutes read
Signal processing involves analyzing noisy signals in the real world using mathematical operations like Fourier transform and wavelet transform to extract structure and frequency components for better understanding and analysis. Wavelet transform provides a compromise between time and frequency resolution, offering a unique analysis tool for signals by adjusting the mother wavelet through time and frequency for a two-dimensional analysis space.
Insights
- Signal processing is crucial for objectively characterizing and quantifying the structure within noisy real-world signals, with Fourier transform offering insights into frequency components but sacrificing time information for frequency details.
- Wavelet transform, utilizing short-lived oscillations localized in time and satisfying constraints like zero mean and finite energy, provides a unique analysis tool that offers a compromise between time and frequency resolution, allowing for a more optimal analysis of signals in a two-dimensional space.
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Recent questions
What is signal processing?
The field dedicated to analyzing noisy signals.
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