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We present algorithms for automated macromodeling of nonlinear mixed-signal system blocks. A key feature of our methods is that they automate the generation of general-purpose macromodels that are suitable for a wide range of time- and frequency-domain analyses important in mixed-signal design flows. In our approach, a nonlinear circuit or system is approximated using piecewise-polynomial (PWP) representations. Each polynomial system is reduced to a smaller one via weakly nonlinear polynomial model-reduction methods. Our approach, dubbed PWP, generalizes recent trajectory-based piecewise-linear approaches and ties them with polynomial-based model-order reduction, which inherently captures stronger nonlinearities within each region. PWP-generated macromodels not only reproduce small-signal distortion and intermodulation properties well but also retain fidelity in large-signal transient analyses. The reduced models can be used as drop-in replacements for large subsystems to achieve fast system-level simulation using a variety of time- and frequency-domain analyses (such as dc, ac, transient, harmonic balance, etc.). For the polynomial reduction step within PWP, we also present a novel technique [dubbed multiple pseudoinput (MPI)] that combines concepts from proper orthogonal decomposition with Krylov-subspace projection. We illustrate the use of PWP and MPI with several examples (including op-amps and I/O buffers) and provide important implementation details. Our experiments indicate that it is easy to obtain speedups of about an order of magnitude with push-button nonlinear macromodel-generation algorithms.