The performance of today's communication systems is highly dependent on the employed analog-to-digital converters (ADCs), and in order to provide more flexibility and precision for the emerging communication technologies, high-performance ADCs are required. In this regard, the time-interleaved operation of an array of ADCs (TI-ADC) can be a reasonable solution. A TI-ADC can increase its throughput by using M channel ADCs or subconverters in parallel and sampling the input signal in a time-interleaved manner. However, the performance of a TI-ADC badly suffers from the mismatches among the channel ADCs. The mismatches among channel ADCs distort the TI-ADC output spectrum by introducing spurious tones besides the actual signal components. This thesis deals with the adaptive background calibration of frequency-response mismatches in a TI-ADC. By modeling each channel ADC as a linear time-invariant system, we develop the continuous-time, discrete-time, and time-varying system models of a TI-ADC. These models help us to characterize the behavior of a TI-ADC in the presence of frequency response mismatches. First we model the channel frequency responses with gain and timing mismatches only which are approximated using a first-order Taylor's series expansion. Consequently, we present a blind calibration structure that uses the filtered-X least-mean square~(FxLMS) algorithm to calibrate the gain and timing mismatches. Besides its simplicity and ease of scalability, this calibration technique works well with different types of input signals and significantly improves the performance of a TI-ADC. Next a digital background blind calibration structure for frequency response mismatches in a two-channel TI-ADC is presented. Contrary to the other calibration techniques in the literature, our calibration technique is not dependent on the type of the input signal and the channel mismatch models. We represent the frequency response mismatches by a polynomial series of fixed order that allows us to characterize the mismatch by the coefficients of this series. Later these coefficients are estimated by using the FxLMS algorithm that helps in the reconstruction of the input signal. Finally, a flexible digital background non-blind calibration structure is presented that uses an extra low-resolution ADC as reference and an M-periodic time-varying filter to adaptively calibrate the frequency response mismatches in a TI-ADC. This structure may be used to calibrate any linear frequency response mismatches including gain and timing mismatches. All these digital calibration techniques make it possible to overcome the performance artifacts of frequency response mismatches in a TI-ADC.