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This paper studies the theory and design of a class of perfect reconstruction (PR) uniform causal-stable infinite-impulse response (IIR) cosine modulated filter banks (CMFBs). The design approach is also applicable to the design of PR recombination nonuniform (RN) IIR CMFBs. The polyphase components of the prototype filters of these IIR CMFBs are assumed to have the same denominator so as to simplify the PR condition. In designing the proposed IIR CMFB, a PR FIR CMFB with similar specifications is first designed. The finite-impulse response prototype filter is then converted to a nearly PR (NPR) IIR CMFB using a modified model reduction technique. The NPR IIR CMFB so obtained has a reasonably low reconstruction error. Its denominator is designed to be a polynomial in zM, where M is the number of channels, to simplify the PR condition. Finally, it is employed as the initial guess to constrained nonlinear optimization software for the design of the PR IIR CMFB. Design results show that both NPR and PR IIR CMFBs with good frequency characteristics and different system delays can be obtained by the proposed method. By using these IIR CMFBs in the RN CMFBs, new RN NPR and PR IIR CMFBs can be obtained similarly.