Frequency Estimation of Sinusoidal Signals in Noise using Pisarenko Harmonic Decomposition, MUSIC Algorithm, and ESPRIT Algorithm

Frequency estimation of sinusoidal signals contaminated by noise can be achieved through advanced spectral estimation techniques including Pisarenko Harmonic Decomposition, MUSIC algorithm, and ESPRIT algorithm. The signal model consists of sinusoidal components with specified frequencies, amplitudes, and phases, combined with additive white Gaussian noise having controlled variance. The implementation uses 128 data samples for frequency estimation. The experimental procedure involves two main phases: 1. Each algorithm is executed independently for 20 trials to obtain frequency estimates. For each method, we record all estimated values and compute statistical measures including mean and variance to evaluate estimation consistency and precision. Code implementation typically involves covariance matrix computation, eigenvalue decomposition for Pisarenko and MUSIC, and rotational invariance techniques for ESPRIT. 2. We systematically increase the noise power to observe and analyze the performance degradation of each method. This sensitivity analysis helps compare algorithmic robustness under different signal-to-noise ratio conditions. The implementation would include noise variance scaling and monitoring estimation error metrics. Through this comprehensive evaluation, we gain deeper insights into frequency estimation methodologies for sinusoidal signals in noisy environments, enabling comparative analysis of algorithm performance across varying noise power conditions. Key implementation aspects include proper parameter selection, matrix dimension handling, and statistical averaging techniques for reliable performance assessment.