Classical and Modern Spectral Estimation Methods: Two Major Categories of Spectral Estimation Techniques

Power spectrum estimation has wide-ranging applications and is extensively utilized across various scientific disciplines and application fields. In the "Modern Signal Processing" course, we studied two main categories of spectral estimation methods: classical spectral estimation and modern spectral estimation. Classical spectral estimation methods are based on Fourier transform approaches - while offering high computational efficiency through FFT algorithms, they suffer from limitations including low spectral resolution and significant side lobe leakage effects. These methods perform well for estimating long sequences where the periodogram or Welch's method can be effectively applied. To address the shortcomings of classical spectral estimation, researchers developed modern spectral estimation techniques that are based on parametric models of random processes. These include maximum likelihood estimation, maximum entropy method, AR (AutoRegressive) model approaches, and predictive filtering methods. Modern spectral estimation typically involves solving matrix equations (like the Yule-Walker equations for AR models) or using iterative algorithms (such as the Burg algorithm) for parameter estimation. Compared to classical methods, modern spectral estimation provides higher accuracy for short sequences, with both approaches serving complementary roles in different scenarios. After comprehensive study of modern spectral estimation techniques, I selected the AR model method as my simulation topic. The following section will present the theoretical foundations of AR models and demonstrate their practical implementation through simulation.