Upper and Lower Envelope Obtained via Secondary Endpoint Mirror Extension Method

This article employs the secondary endpoint mirror extension method to extract upper and lower envelopes. A critical implementation note is that the input parameters consist of extreme points obtained through the MaMin function. The algorithm's advantage lies in its ability to deliver more accurate results, particularly when processing signals containing multiple frequency components. From a computational perspective, this method incorporates boundary handling techniques that prevent noise interference in the signal, thereby enhancing the stability of the envelope extraction process.

It is worth noting that alternative methods exist for envelope extraction, such as least squares approximation and Hilbert transform. While these approaches may yield superior results under specific conditions, the secondary endpoint mirror extension method remains a straightforward and effective solution. The implementation typically involves three key steps: 1) Identifying extreme points using the MaMin function, 2) Applying mirror extension at secondary endpoints to handle boundary effects, and 3) Connecting extreme points with cubic spline interpolation to form smooth envelopes. This methodology warrants further research and practical application in signal processing workflows.