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Generalized multivariate analysis of variance (GMANOVA) and related reduced-rank regression are general statistical models that comprise versions of regression, canonical correlation, and profile analyses as well as analysis of variance (ANOVA) and covariance in univariate and multivariate settings. It is a powerful and, yet, not very well-known tool. We develop a unified framework for explaining, analyzing, and extending signal processing methods based on GMANOVA. We show the applicability of this framework to a number of detection and estimation problems in signal processing and communications and provide new and simple ways to derive numerous existing algorithms. Many of the methods were originally derived "from scratch", without knowledge of their close relationship with the GMANOVA model. We explicitly show this relationship and present new insights and guidelines for generalizing these methods. Our results could inspire applications of the general framework of GMANOVA to new problems in signal processing. We present such an application to flaw detection in nondestructive evaluation (NDE) of materials. A promising area for future growth is image processing.