Mirror Extension of Signal Endpoints

In signal processing, preprocessing techniques are frequently employed to enhance analysis outcomes. One widely used preprocessing method is mirror extension, which effectively eliminates edge effects that arise during signal processing operations. Particularly in Hilbert transform applications, mirroring signal segments at both ends can substantially mitigate boundary distortions, thereby yielding more accurate analytical results. The implementation typically involves creating symmetric reflections of the signal's initial and final segments - for instance, extending the left end by mirroring the first N samples in reverse order, and similarly extending the right end using the last M samples. This approach maintains signal continuity while avoiding artificial discontinuities that cause spectral leakage. Therefore, employing preprocessing techniques like mirror extension is essential in signal processing workflows to ensure optimal transformation results.