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In many signal processing applications such as in underwater acoustic array beamforming, the need arises to implement digital phase shifters. Conventional methods of implementation make use of digital interpolation and decimation to derive FIR (Finite-duration Impulse Response) realizations. Such filters, however, are capable of providing delays that are only rational fractions of the unit delay. To obtain delays that are arbitrary factors of the unt delay, two novel methods are presented: the first method makes use of a windowing technique and the second method makes use of a frequency-sampling approach. In both methods the constraint of exactly linear phase is relaxed and the departures from linear phase are kept very small. To ensure that the new phase shifters attain a high level of performance, comprehensive error measures have been developed and applied; these performance measures consists of a normalized rms error, the phase delay error and the group delay error. Moreover, these error measures are applicable to any method of designing digital phase shifters. In addition, for the frequency-sampling designs, the concept of an effective filter length is introduced; this concept takes into account the wraparound error that arises in fast-convolution signal processing operations. Aside from the presentation of the design procedures and error measures, examples are included to illustrate the salient features of the two new methods. Keywords include: Digital Phase Shifters, Windowing, Frequency-Sampling, Time Delay Realization, and Beamforming Time Delay.