We propose a sampling scheme for alias-free spectral analysis of signals. Unlike the existing approaches, the scheme is deterministic rather than random. The properties of the generated sampling sequences resemble those of the random sampling ones in the sense of suppressing/reducing aliasing. Nonetheless, the developed scheme is shown to be more efficient and is better suited to practical implementation. It is demonstrated that for signals with bounded variations, the error in the obtained Fourier transform from N number of samples is bounded and decays at the rate of log (N)/N.