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Direct conversion orthogonal frequency division multiplexing (OFDM) systems suffer from transmit and receive analog processing impairments such as in-phase/quadrature (I/Q) imbalance causing inter-carrier interference (ICI) among sub-carriers. Another source of performance-limiting ICI in OFDM systems is Doppler spread due to mobility. However, the nature of ICI due to each of them is quite different. Unlike previous work which considered these two impairments separately, we develop a unified mathematical framework to characterize, estimate, and jointly mitigate ICI due to I/Q imbalance and high mobility. Based on our general model, we derive a closed-form expression for the degradation in signal-to-interference-plus-noise ratio (SINR) due to the impairments. Moreover, we exploit the special ICI structure to design efficient OFDM channel estimation and digital baseband compensation schemes for joint transmit/receive frequency-independent (FI) and frequency-dependent (FD) I/Q imbalances under high-mobility conditions.