This section of the article, titled "Modal Analysis Theory and Testing," is authored by Ward Heylen, Stefan Lammens, and Paul Sas from the Division of Production Engineering, Machine Design, and Automation at the Katholieke Universiteit Leuven in Belgium. It is divided into several parts, each focusing on different aspects of modal analysis theory and testing. **PART A. THEORY** - **A.0. Introduction**: Provides an overview of the topics covered in the theory section. - **A.1. Analytical and Experimental Modal Analysis**: - **A.1.1. Single Degree of Freedom Systems**: Discusses system equations, transfer functions, poles, natural frequencies, damping ratios, residues, and frequency response functions. - **A.1.2. Multiple Degree of Freedom Systems**: Explores system equations, transfer functions, poles, natural frequencies, damping factors, modal vectors, modal participation factors, and frequency response function matrices. - **A.1.3. Examples**: Provides examples for both single and multiple degree of freedom systems. - **A.1.5. Conclusions**: Summarizes key points from the single and multiple degree of freedom systems. - **A.2. (Digital) Signal Processing: Basic Theory**: - **A.2.1. Fourier Transform for Different Signal Types**: Covers periodic signals, non-periodic functions, sampled time functions, and transforms. - **A.2.2. Analysis Parameters**: Discusses time scaling, time shift, frequency shift, energy relationships, integration, differentiation, and convolution. - **A.2.3. Errors and Windows**: Explores aliasing, leakage, and windows. - **A.2.4. Other Transforms**: Introduces Laplace and Z-transforms. - **A.2.5. Time and Frequency Functions and Applications**: Discusses autopower spectrum, autocorrelation function, crosspower spectrum, crosscorrelation function, averaging, frequency response functions, and coherence functions. - **A.2.7. Conclusions**: Summarizes the basic theory of signal processing. - **A.3. Modal Parameter Estimation**: - **A.3.1. Basic Modal Model Equations**: Provides an introduction to modal model equations. - **A.3.2. Basic Concepts**: Compares single and multiple degree of freedom methods, local and global parameter estimates, single and multiple input methods, modal and direct models, low order complete and high order incomplete models, real and complex mode shapes, time domain and frequency domain implementation, and classification. - **A.3.3. Single Degree of Freedom Methods**: Discusses peak picking, mode picking, and circle fitting. - **A.3.4. Multiple Degree of Freedom Time Domain Methods**: Introduces the Ibrahim time domain method, Polyreference least squares complexThis section of the article, titled "Modal Analysis Theory and Testing," is authored by Ward Heylen, Stefan Lammens, and Paul Sas from the Division of Production Engineering, Machine Design, and Automation at the Katholieke Universiteit Leuven in Belgium. It is divided into several parts, each focusing on different aspects of modal analysis theory and testing. **PART A. THEORY** - **A.0. Introduction**: Provides an overview of the topics covered in the theory section. - **A.1. Analytical and Experimental Modal Analysis**: - **A.1.1. Single Degree of Freedom Systems**: Discusses system equations, transfer functions, poles, natural frequencies, damping ratios, residues, and frequency response functions. - **A.1.2. Multiple Degree of Freedom Systems**: Explores system equations, transfer functions, poles, natural frequencies, damping factors, modal vectors, modal participation factors, and frequency response function matrices. - **A.1.3. Examples**: Provides examples for both single and multiple degree of freedom systems. - **A.1.5. Conclusions**: Summarizes key points from the single and multiple degree of freedom systems. - **A.2. (Digital) Signal Processing: Basic Theory**: - **A.2.1. Fourier Transform for Different Signal Types**: Covers periodic signals, non-periodic functions, sampled time functions, and transforms. - **A.2.2. Analysis Parameters**: Discusses time scaling, time shift, frequency shift, energy relationships, integration, differentiation, and convolution. - **A.2.3. Errors and Windows**: Explores aliasing, leakage, and windows. - **A.2.4. Other Transforms**: Introduces Laplace and Z-transforms. - **A.2.5. Time and Frequency Functions and Applications**: Discusses autopower spectrum, autocorrelation function, crosspower spectrum, crosscorrelation function, averaging, frequency response functions, and coherence functions. - **A.2.7. Conclusions**: Summarizes the basic theory of signal processing. - **A.3. Modal Parameter Estimation**: - **A.3.1. Basic Modal Model Equations**: Provides an introduction to modal model equations. - **A.3.2. Basic Concepts**: Compares single and multiple degree of freedom methods, local and global parameter estimates, single and multiple input methods, modal and direct models, low order complete and high order incomplete models, real and complex mode shapes, time domain and frequency domain implementation, and classification. - **A.3.3. Single Degree of Freedom Methods**: Discusses peak picking, mode picking, and circle fitting. - **A.3.4. Multiple Degree of Freedom Time Domain Methods**: Introduces the Ibrahim time domain method, Polyreference least squares complex