Weak Signal Detection Using Cumulative Method with MATLAB Implementation

Weak signal detection based on the cumulative method is an effective technique for extracting faint valid signals from strong noise backgrounds. This approach enhances target signals through multiple accumulations while suppressing random noise interference. Implementing this technique in MATLAB leverages its powerful matrix operations and signal processing toolbox capabilities.

The implementation methodology consists of three main steps: signal acquisition, cumulative processing, and result analysis. The process begins with simulating or acquiring noisy signals where target signal amplitude is typically much smaller than noise. Through repeated sampling, multiple signal segments are time-aligned and subjected to ensemble averaging. Since noise is random, it cancels out after multiple accumulations, while coherent target signals accumulate constructively due to phase consistency.

In MATLAB implementation, developers can use loop structures for sequential signal acquisition and stacking, or employ matrix operations for batch processing multiple datasets to improve computational efficiency. The critical implementation aspect involves ensuring strict synchronization between sampling intervals to prevent phase misalignment during accumulation. Post-processing analysis can evaluate detection performance through spectral analysis or time-domain waveform comparisons using functions like fft() and plot().

This method finds extensive applications in radar echo detection, biomedical signal processing, and other domains where signal-to-noise ratios are extremely low. The cumulative method significantly enhances detectability by allowing trade-offs between detection sensitivity and processing time through adjustments in accumulation cycles and sampling parameters using MATLAB's flexible programming environment.