MATLAB Simulation for Time Delay Estimation Using Correlation Method

This MATLAB simulation implements correlation-based time delay estimation, designed to work with any WAV audio file format. The system employs cross-correlation algorithms to calculate time differences between signals, utilizing MATLAB's built-in functions like xcorr for efficient computation. The implementation includes comprehensive error analysis modules that calculate statistical metrics such as mean squared error (MSE) and standard deviation to evaluate estimation accuracy.

The simulation performs detailed analysis of wave file properties including frequency spectrum analysis using FFT algorithms, amplitude characteristics through envelope detection, and phase shift measurements via Hilbert transform implementation. These analyses help identify potential issues in signal quality that might affect delay estimation precision. The code incorporates parameter optimization features allowing users to adjust sampling rate settings using MATLAB's audioread function and modify bit depth parameters to enhance processing performance.

The core algorithm calculates time delays by finding peak positions in the cross-correlation function, implemented with peak detection algorithms and interpolation techniques for sub-sample accuracy. Additional features include signal preprocessing routines for noise reduction and normalization, ensuring robust performance across various audio conditions. This MATLAB simulation serves as a comprehensive tool for accurate time delay estimation and wave file performance optimization through systematic parameter tuning and analytical validation.