Matched Filter Implementation and Analysis

This document presents a matched filter implementation (developed as part of random signal coursework, which provides functional performance while leaving room for further optimization). The matched filter represents a fundamental signal processing technique widely used for signal correlation and detection. It operates by extracting components that correlate with a given reference signal, enabling precise identification and localization of specific signal patterns. The implementation employs cross-correlation algorithms where the filter's impulse response is typically designed as the time-reversed, complex-conjugated version of the target signal template. Key computational aspects include optimizing convolution operations through FFT-based fast correlation methods and setting appropriate detection thresholds. While this implementation covers basic functionality, numerous aspects warrant deeper investigation - including performance analysis under various noise conditions, computational efficiency improvements, and adaptive thresholding techniques for robust detection in practical scenarios.