Decimating a uniformly sampled signal a factor D involves low-pass antialias filtering with normalized cutoff frequency 1/D followed by picking out every Dth sample. Alternatively, decimation can be done in the frequency domain using the fast Fourier transform (FFT) algorithm, after zero-padding the signal and truncating the FFT. We outline three approaches to decimate non-uniformly sampled signals, which are all based on interpolation. The interpolation is done in different domains, and the inter-sample behavior does not need to be known. The first one interpolates the signal to a uniformly sampling, after which standard decimation can be applied. The second one interpolates a continuous-time convolution integral, that implements the antialias filter, after which every Dth sample can be picked out. The third frequency domain approach computes an approximate Fourier transform, after which truncation and IFFT give the desired result. Simulations indicate that the second approach is particularly useful. A thorough analysis is therefore performed for this case, using the assumption that the non-uniformly distributed sampling instants are generated by a stochastic process.

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Non-Uniform Sampling in Statistical Signal Processing

Alias-free DSP (DASP) is a methodology of processing signals digitally inside bandwidths that are wider than the famous Nyquist limit of half of the sampling frequency. DASP is facilitated by suitable combination of nonuniform sampling and appropriate processing algorithms. In this paper we propose a new method of constructing sampling schemes for the needs of DASP. Unlike traditional approaches that rely on randomly selected sampling instants we use deterministic schemes. A method of optimizing such sequences aimed at minimization of aliasing is proposed. The approach is tested numerically in an experiment where an undersampled signal is processed using DASP; first to estimate the signal's spectrum support function and then the spectrum itself. We demonstrate advantages of the proposed approach over those that use random sampling.

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Optimal periodic sampling sequences for nearly-alias-free digital signal processing

A prototype for DSP-based power quality monitoring device has been proposed, developed and investigated. Solution is based on 16-bit more than 100 ks/s analog-front-end, modern programmable DSP, and various data saving and communication interfaces. A special software-PLL has been developed, for synchronous measurements with 50 or 60 Hz line frequency. Prototype measures RMS values of voltages and currents in 3-phase power system, and also harmonics, active and reactive powers, and transients, and other features, required by according standards.

DSP-based Power-Quality Monitoring Device

Most conventional control algorithms cause numerical problems where data is collected at sampling rates that are substantially higher than the dynamics of the equivalent continuous-time operation that is being implemented. This is of relevant interest in applications of digital control, in which high sample rates are routinely dictated by the system stability requirements rather than the signal processing needs. Digital control systems exhibit bandwidth limitations enforced by their closed-loop frequency requirements that demand very high sample rates. Considerable recent progress in reducing sample frequency requirements has been made through the use of non-uniform sampling schemes, so called alias - free signal processing. The approach prompts the simplification of complex systems and consequently enhances the numerical conditioning of the implementation algorithms that otherwise would require very high uniform sample rates. However, the control communities have not yet investigated the use of intentional non-uniform sampling. The purpose of this article is to address some algorithmic issues when using such regimes for digital control.

Non-uniform sampling strategies for digital control

In nonuniform sampling (NUS), signal amplitudes and time stamps are delivered in pairs. Several methods to compute an approximate Fourier transform (AFT) have appeared in literature, and their posterior properties in terms of alias suppression and leakage have been addressed. In this paper, the sampling times are assumed to be generated by a stochastic process. The main result gives the prior distribution of several AFTs expressed in terms of the true Fourier transform and variants of the characteristic function of the sampling time distribution. The result extends leakage and alias suppression with bias and variance terms due to NUS. Specific sampling processes as described in literature are analyzed in detail. The results are illustrated on simulated signals, with particular focus to the implications for spectral estimation.

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Frequency Domain Analysis of Signals With Stochastic Sampling Times

In some applications the observed samples are inherently nonuniform. In contrast to that in this paper we take advantage of deliberate nonuniform sampling and perform DSP where the classical approaches leave off. For instance think about mobile communication or digital radio. Deliberate nonuniform sampling promises increased equivalent sampling rates with reduced overall hardware costs. The equivalent sampling rate is the sampling rate that a uniform sampling device would require in order to achieve the same processing bandwidth. While the equivalent bandwidth of a realizable system may well extend into the GHz range its mean sampling rate is usually in the MHz range. Current existing prototype systems achieve 40 times the bandwidth of a classic DSP system that would operate uniformly (cf. [Y. Artyukh, et al., Evaluation of Pseudorandom Sampling Process, 1997] and [Y. Artyukh, et al., virtual Oscilloscope of the DASP-Lab System 1997]). Throughout the literature on nonuniform sampling (e. g. [I. Bilinskis and A. Mikelsons, 1992], [F. Marvasti, 2001] and [J.J. Wojtiuk, 2000]) many sampling schemes have been investigated. In this paper the authors discuss a nonuniform sampling scheme that is especially suited to be implemented in digital devices, thus, fully exploiting state-of-the-art ADCs without violating their specifications. An analysis of the statistical properties of the algorithm is given to demonstrate common pitfalls and to prove its correctness.

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Optimal sampling functions in nonuniform sampling driver designs to overcome the Nyquist limit

Deliberate nonuniform sampling promises increased equivalent sampling rates with reduced overall hardware costs of the DSP system. The equivalent sampling rate is the sampling rate that a uniform sampling device would require in order to achieve the same processing bandwidth. Equivalent bandwidths of realizable systems may well extend into the GHz range while the mean sampling rate stays in the MHz range. Current prototype systems (IECS) have an equivalent bandwidth of 1.6 GHz at a mean sampling rate of 80 MHz, achieving 40 times the bandwidth of a classic DSP system that would operate uniformly at 80 MHz. Throughout the literature on nonuniform sampling, different sampling schemes have been investigated. This paper focuses on nonuniform sampling schemes optimized for fast and efficient hardware implementation. To our knowledge, this is the first proposal of an efficient nonuniform sampling driver (SD) design in the open literature.

Nonuniform sampling driver design for optimal ADC utilization

General principles of high-precision event timing based on DSP approach are discussed with emphasis made on the particular fast method for such event timing. The latest specific implementation of this method and its main features (basic error components, achievable final precision and operation speed) are considered in more details. By this example it is shown that the method can provide picosecond precision at measurement rate up to tens of MHz. Ill. 4, bibl. 6 (in English; summaries in English, Russian and Lithuanian)..

/pdf/potential-of-the-dsp-based-method-for-fast-precise-event-14zu0jtu6f.pdf

Potential of the DSP-based Method for Fast Precise Event Timing

Considered demodulator uses periodic rectangular functions instead of conventional sinusoidal ones for calculation of Fourier coefficients defining complex amplitude. This allows considerable simplifying the demodulator design and increasing its operation speed. Specifically, the demodulator provides periodic measurement of phase and peak amplitude of narrowband signal in KHz frequency band of its complex modulation with effective amplitude resolution about 16-17 bits. The demodulator is mainly oriented to applications related to bio-impedance analysis under natural bio-modulation. Ill. 5, bibl. 2 (in English; summaries in English, Russian and Lithuanian).

/pdf/digital-synchronous-demodulator-for-measurement-of-complex-l2rd2j1fdp.pdf

Digital Synchronous Demodulator for Measurement of Complex Amplitude Deviation

Effective non-linearity correction is one of the most important problem for development of high-performance event timers based on Digital Signal Processing (DSP) methods. Suggested approach to resolving this problem is based on determination of a correction function using constant period test pulse sequences with seemingly random modular values. It is shown that such an approach allows achieving non-linearity correction with picosecond precision at test pulse sequence lengths quite acceptable for practical applications. Precision of DSP-based event timers can be improved in this way up to a few picoseconds.

E. Boole

Papers

Optimal sampling functions in nonuniform sampling driver designs to overcome the Nyquist limit

Nonuniform sampling driver design for optimal ADC utilization

Potential of the DSP-based Method for Fast Precise Event Timing

Digital Synchronous Demodulator for Measurement of Complex Amplitude Deviation

Determination of correction function for reducing integral non-linearity of DSP-based event timer