Mathematics Colloquia and Seminars

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A blind calibration method is presented for timing mismatches in a multichannel time-interleaved analog to digital converter (ADC) formed by $N$ parallel ADCs. The proposed method requires that the input signal should be slightly oversampled and that the input should contain energy, at least intermittently, in $N/2$ frequency bands. The oversampling condition ensures that there exists a frequency band around the zero frequency where the Fourier transforms of the $N$ ADC subchannels contain only $N-1$ alias components. Then the matrix power spectral density (PSD) of the ADC subchannels is rank deficient over this frequency band. Accordingly, when the timing offsets are known, it is possible to construct a filter bank that nulls the vector signal produced by the ADC outputs. A parametric form of this filter bank is used to develop an adaptive null steering algorithm for estimating the ADC timing offsets. The filter bank employs $2N-1$ fixed FIR filters and $N-1$ unknown timing offset parameters which are estimated by using an adaptive stochastic gradient technique. A convergence analysis is presented for the blind calibration method. Numerical simulations demonstrate the effectiveness of the proposed technique for white noise input and for inputs containing several sinusoidal components.