Frequency domain alignment of discrete-time signals

Alignment of discrete-time signals using time shifts obtained through cross correlation techniques in the time domain without interpolation can only be done to within an integer multiple of the sampling period. In this paper, we discuss an alignment procedure for discrete-time signals which overcomes this difficulty by determining the time shifts through a parameter optimization problem in the discrete frequency domain. This approach essentially avoids fitting parabolae to the cross correlation peaks and does not require unwrapping the phase spectra of the signals to be aligned.