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The current trend in building low-cost yet flexible radio transceivers is to use the so-called direct-conversion principle, which is based on complex (I/Q) up- and down conversions. Such transceivers are, however, sensitive to mismatches between the I and Q branches. These mismatches are unavoidable in any practical implementation, and result in finite attenuation of the mirror frequencies. In addition to the mirror-frequency interference problem, I/Q mismatches can severely compromise the performance of power amplifier linearization techniques based on pre-distortion. The effects of these impairments are becoming more pronounced as higher order modulated waveforms and/or more wideband multichannel signals are used. This brief focuses on digital-signal-processor-based I/Q mismatch calibration in wideband direct-conversion transmitters, assuming the challenging case of frequency-dependent I/Q mismatch. First, a novel widely linear (WL) calibration structure is introduced, suitable for frequency-dependent calibration. Then, two alternative principles for calibration parameter estimation are proposed. The first estimation approach stems from second-order statistics of complex communication signals, while the second technique is based on WL least-squares model fitting. Both estimators are shown by simulations to yield very good calibration performance. The obtainable performance is further assessed using laboratory RF signal measurements.