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Time interleaving can be used to significantly increase the sampling rate of an ADC system. However, the problem with time interleaving is that the ADCs are not exactly identical. This means that time, gain and offset mismatch errors are introduced in the ADC system, which cause nonharmonic distortion in the sampled signal. One way to decrease the impact of the mismatch errors is to spread the distortion over a wider frequency range by randomizing the order in which the ADCs are used in the interleaved structure. In this paper we analyze how the spectrum is affected by mismatch errors in a randomly interleaved ADC system. We also discuss how the mismatch errors can be estimated.