Principles of Wavelet Time-Frequency (Scale) Plot Generation with Implementation

This section details the step-by-step methodology for generating wavelet time-frequency plots, demonstrated using a synthetic signal composed of two sinusoidal components at 100Hz and 200Hz. Code implementation insights are provided where applicable.

1. Signal Time-Domain Sampling: First, the signal undergoes time-domain sampling for temporal analysis. This involves defining a time window and sampling within it (e.g., using MATLAB's window functions). Adjusting window size trades off time-frequency resolution—shorter windows enhance temporal precision, while longer windows improve frequency resolution. Implementation typically involves defining sampling parameters like Fs (sampling frequency) and t (time vector).

2. Wavelet Decomposition: The sampled signal is decomposed using wavelet transforms (e.g., Continuous Wavelet Transform with MATLAB's cwt function). This step breaks the signal into scale-dependent components, mapping time-domain data to a joint time-frequency representation. Key parameters include wavelet type (e.g., Morlet) and scale ranges, which correlate with frequency bands.

3. Time-Frequency Plot Generation: After decomposition, wavelet coefficients are visualized as a time-frequency plot (scaleogram). The plot’s intensity reflects signal energy distribution across time and frequency. In code, this is achieved by plotting coefficient magnitudes against time and scales (converted to frequencies using scal2frq). Color mapping (e.g., pcolor or imagesc) highlights energy variations.

4. Post-Processing and Analysis: The resulting plot can be further processed for feature extraction—e.g., identifying signal components via ridge detection or analyzing non-stationary traits using thresholding algorithms. Tools like MATLAB’s wavedec enable multi-level decomposition for granular insights.

While wavelet time-frequency plotting requires expertise in signal processing, understanding these core steps and their code equivalents facilitates effective analysis of non-stationary signals’ temporal and spectral characteristics.