A time-interleaved digital-to-analog converter system, comprising a digital pre-distorter configured to receive an input digital signal and an error signal and output a distorted digital signal based on the input digital signal and the error signal; a time-interleaved digital-to-analog converter having a first sample rate, the time-interleaved digital-to-analog converter configured to convert the distorted digital signal to an analog signal; and a calibration system. The calibration system includes an analog-to-digital converter having a second sample rate equal to or lower than the first sample rate, the analog-to-digital converter configured to receive the analog signal and covert the analog signal to a down-sampled digital signal, a discrete-time linear model configured to receive the input digital signal and the error signal and output a model signal, and a combiner to subtract the down-sampled digital signal from the model signal to generate the error signal.