New phase-shifting techniques have recently been proposed to suppress the complex-conjugate ambiguity in frequency-domain optical-coherence tomography. A phase shift is introduced, in an elegant fashion, by incorporating a small beam offset at the scanning mirror. The tomogram is then computed by using a combination of Hilbert and Fourier transforms. This is a marked deviation from the conventional approaches, wherein each A-scan is reconstructed independently of the others. In this paper, we formulate the problem in a signal processing framework and provide theoretical proofs for maximal and partial suppression of complex-conjugate ambiguity. To supplement the theoretical derivations, we provide experimental results on in vivo measurements of a human finger nail.