System Impulse Response Transfer Function Estimation Using Hankel Matrix Method

Estimating system impulse response transfer functions using the Hankel matrix method is an effective approach based on pulse sequence data. This technique extracts impulse response characteristics from pulse sequences to analyze system stability and performance metrics. The implementation involves constructing a Hankel matrix from the impulse response data, where the matrix structure organizes time-series data in a systematic pattern for system identification. Key algorithmic steps include performing singular value decomposition (SVD) on the Hankel matrix to extract system modes and determine the system order, followed by solving a least-squares problem to obtain the transfer function coefficients. Special attention must be given to signal-to-noise ratio considerations to ensure the resulting transfer function maintains high accuracy and reliability. Proper noise handling techniques, such as truncating smaller singular values, help mitigate the effects of measurement noise. Therefore, the Hankel matrix method serves as a crucial tool for system identification, enabling comprehensive analysis and investigation of system properties through numerical linear algebra operations.