Generation of a Random Signal and Two Sinusoidal Signals with Closely-Spaced Frequencies

This article focuses on generating a random signal along with two sinusoidal signals having closely-spaced frequencies, followed by comprehensive signal analysis. The key implementation tasks include:

1. Calculating autocorrelation coefficients and correlation functions for the random signal, and generating corresponding graphical plots using MATLAB's xcorr function and plotting commands.

2. Computing power spectra of both random signals using various parametric modeling approaches, including periodogram and Welch methods implemented via pwelch and periodogram functions.

3. Estimating parameters for AR, MA, and ARMA models using common parameter estimation techniques such as maximum likelihood estimation and recursive least squares algorithms. Users can select appropriate model orders and compare results with MATLAB toolbox functions like ar, arma, and related system identification tools.

4. Performing spectral estimation using notch filtering techniques and MUSIC (Multiple Signal Classification) algorithms, implemented through functions like peig and root-MUSIC methods for high-resolution frequency detection.

5. Applying noise reduction to the noisy sinusoidal signals using Wiener filtering and LMS (Least Mean Squares) adaptive filtering approaches, with practical implementation using wiener2 and adaptfilt.lms objects.

6. Assuming the signal represents linear displacement in a specific direction of an aircraft, we can implement Kalman filtering for signal enhancement using kalman filter functions for state estimation and noise reduction.

7. Conducting spectral estimation using higher-order spectrum theory and estimating corresponding AR, MA, and ARMA models through bispectral analysis techniques and higher-order statistical methods.

8. Performing wavelet-based denoising using discrete wavelet transform (DWT) implementations like wdenoise, and comparing the results with previous denoising methods to evaluate performance differences.

By completing these tasks, we gain deeper insights into signal characteristics and acquire practical experience with essential signal processing techniques commonly used in engineering applications.