Complete Identification of Permissible Sampling Rates for First-Order Sampling of Multi-Band Bandpass Signals

The first-order sampling of multi-band bandpass signals with arbitrary band positions is considered in this paper. Gaps between the spectral sub-bands are utilized to achieve lower sampling rates than the Nyquist. The lowest possible sampling rate along with other permissible sampling rates is identified via a unique partition of the frequency axis. With the complete identification of all the permissible sampling rates, a necessary and sufficient sampling theorem for multi-band bandpass signals is presented in terms of a series of csinc-interpolators

Optimal and Permissible Sampling Rates for First-Order Sampling of Two-Band Signals

Sampling theory plays an essential role in the advancement of digital signal processing (DSP). All known DSP processors only work with digital samples of an analog signal (continuous-time signal). Therefore, reliable sampling of a signal is crucial for the successive phases of DSP. A well-known industry standard for sufficient sampling of an analog signal is that the sampling rate is at least twice the highest frequency of the signal. Obviously, the greater the highest frequency of the signal, the higher the sampling rate required, hence, more wear and tear on the sampling device. This research focuses on developing sampling methods for passband signals, which arises for broad-band signal processing, and it has drawn great interests in the DSP community. A first-order sampling method with optimal and total identification of all permissible sampling rates for two-band passband signals is studied in this work. A rigorous proof for all the sampling rates is presented. It is shown that the new sampling rates are much lower than the industrial standard. Therefore, the new sampling mechanism has sound theoretical and commercial values. Quantitative analysis is performed on the proposed sampling method, including a fast algorithm for computing all feasible sampling rates for two-band passband signals

A Universal Interpolative Filter for Low-Pass And Bandpass Signals-CSINC Interpolator

A FIR csinc interpolative filter design for bandpass signals is presented in this paper. The filter coefficients are calculated from the covariance of basis functions for the bandpass function space. They are invariant with respect to the samples of the input signals. The csinc model also works for low-pass signals as one of the design parameters approaches zero. The performance of the csinc filter is analyzed from the perspectives of accuracy, stability, and adaptation to noise in the samples. Comparisons are made between the csinc model and the existing interpolation models in the literature