Mitigating End-Point Effects Using Mirror Extension Method

In signal processing, end-point effects represent a common challenge. The mirror extension method effectively addresses this issue by reflecting the signal at both ends to eliminate boundary distortions, thereby improving signal quality. This technique not only enables extrapolation of extremum information beyond the signal endpoints but also preserves the original signal characteristics without information loss. From an implementation perspective, the algorithm typically involves three key steps: 1) Identifying local maxima and minima within the signal, 2) Creating mirrored segments by reversing signal segments adjacent to the boundaries, and 3) Seamlessly concatenating the mirrored extensions with the original signal. Common applications include signal denoising and feature extraction where boundary continuity is critical. When implementing in code, developers often utilize array manipulation functions like numpy.flip() in Python or fliplr() in MATLAB to create mirrored segments, followed by concatenation operations to form the extended signal. Due to its computational efficiency and preservation of signal properties, the mirror extension method proves particularly valuable in Fourier analysis and wavelet transforms where boundary effects significantly impact results.