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This paper generalizes time-domain lapped transforms (TDLTs) proposed by Tran et al. to oversampled systems, thus leading to time-domain oversampled lapped transforms (TDOLTs). These new transforms correspond to a subclass of oversampled linear-phase perfect reconstruction filterbanks (OLPPRFBs), which can be implemented by adding a prefilter before the discrete cosine transform (DCT) and a post-filter after the inverse discrete cosine transform (IDCT). Structures of the pre- and post-filters are developed, and the frame-theoretic properties of TDOLTs are analyzed. A new parameterization of lattice matrices through the Givens-QR factorization is proposed for unconstrained optimization. Comparisons with other parameterization methods are also included. Several design examples, along with some image coding results, are presented to demonstrate the validity of the theory and the potential of TDOLTs in image coding, especially in error-resilient coding.