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We propose a new least squares based estimation algorithm for carrier frequency offset and frequency dependent I/Q imbalance compensation with very low complexity for direct conversion receivers. Compared to conventional algorithms, our proposed estimation has considerably lesser computation due to a reduced order least squares step. Simulation results show that the proposed algorithm has about 1.5dB better accuracy in CFO estimation compared to conventional algorithms and it can completely eliminate I/Q imbalance based on BER performance results. We also showed that the proposed algorithm needs only a minimum 3rd order FIR filter to effectively remove an infinite impulse response modeled I/Q imbalance.