CWPs

CWP stands for Continuous Wavelet Transform. It is a mathematical tool used in signal processing and data analysis to decompose a signal into different frequency components over time. Unlike the Short-Time Fourier Transform (STFT), which uses a fixed-size window for all frequencies, the CWP employs a variable-size window. This means it provides high time resolution for high-frequency components and high frequency resolution for low-frequency components.

The CWP works by correlating the signal with a "mother wavelet," which is a small wave-like function. This correlation is performed at various scales (related to frequency) and translations (related to time). The result is a time-frequency representation of the signal, often visualized as a scalogram. This representation allows for the analysis of non-stationary signals, where the frequency content changes over time.

Applications of the CWP are found in diverse fields. In geophysics, it's used to analyze seismic data. In medicine, it can be applied to electrocardiogram (ECG) or electroencephalogram (EEG) signals to detect anomalies. In finance, it aids in analyzing market trends. The CWP is particularly useful for detecting transient events, localizing features within a signal, and studying oscillatory patterns. Its ability to capture both time and frequency information makes it a powerful alternative to traditional Fourier-based methods for analyzing complex and dynamic data.