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This thesis develops and evaluates a number of new concepts and tools for the analysis of signals using variable overlapped windows and orthonormal bases. Windowing, often employed as a spectral estimation technique, can result in irreparable distortions in the transformed signal. By placing conditions on the window and incorporating it into the orthonormal representation, any signal distortion resulting from the transformation can be eliminated or cancelled in reconstruction. This concept is critical to the theory underpinning this thesis. As part of this evaluation, a tensor product based general N-point fast Fourier transform algorithm was implemented in the DOD standard language, Ada. The most prevalent criticism of Ada is slow execution time. This code is shown to be comparable in execution time performance to the corresponding FORTRAN code. Also, as part of this thesis, a new paradigm is presented for solving the finite length data problem associated with filter banks and lapped transforms. This result could have significant importance in many Air Force applications, such as processing images in which the objects of interest are near the borders. Additionally, a limited number of experiments were performed with the coding of speech. The results indicate the lapped transform evaluated in this thesis has potential as a low bit rate speech coder.