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The high-speed and high-resolution ADC is a key enabler for many future wireless communications systems. The digital background calibration technique can be used to reduce the total power consumption by enhancing the linearity without using high-gain amplifiers. One of the main practical constraints in the wireless applications is a short time available for calibration. This paper proposes a novel fast calibration method of pipelined ADCs, suitable for wireless communications applications, where a sufficiently high resolution can be achieved without requiring any calibration period.