Statistical Analysis of Frequency Response Functions (FRF) - MATLAB Library

Overview This upload contains the source code and the official technical reference manual for the FRF Statistics Library. Performing statistical analysis directly on complex numbers in the frequency domain is often mathematically cumbersome and non-intuitive. This MATLAB library bridges that gap by transforming complex frequency-domain data into time-domain Pseudo Impulse Responses (PIRs). By applying robust non-parametric bootstrapping techniques to these PIRs, the toolset allows researchers to evaluate their data without assuming a strict normal distribution. Note: This repository is the official, actively maintained continuation of the FRF Statistics Library originally developed at Uniklinik Freiburg. Key Capabilities: Time-Domain Transformation: Converts complex FRF components into time-domain PIR signals. MIMO Support: Concatenates Multi-Input Multi-Output arrays into analytical "Supervectors" for system-wide evaluation. Band Generation: Computes highly accurate Bootstrap Confidence Bands (for system averages) and Prediction Bands (for future individual measurements). Group Comparisons: Executes unpaired statistical tests to identify significant differences between independent groups of FRFs. PERMANOVA Testing: Performs Permutational Multivariate Analysis of Variance on complex, multidimensional FRF datasets. Individual Sample Evaluation: Calculates exact empirical probabilities (PDF/CDF) and minimal encompassing prediction bands to evaluate a single test sample against a historical baseline. Contents: FRF_Manual.pdf: A didactic, step-by-step reference manual explaining the mathematical concepts and practical usage of each function. MATLAB Source Code: The complete suite of .m functions and utility scripts. Example Scripts & Data: Three comprehensive pipelines (SCRIPT_Example.m, SCRIPT_Example_MIMO.m, SCRIPT_MinBandExample.m) with accompanying .mat datasets demonstrating SISO, MIMO, and individual sample testing.