Sub-Nyquist artefacts and sampling moiré effects

Sampling moiré effects are well known in signal processing. They occur when a continuous periodic signal g ( x ) is sampled using a sampling frequency f s that does not respect the Nyquist condition, and the signal-frequency f folds over and gives a new, false low frequency in the sampled signal. However, some visible beating artefacts may also occur in the sampled signal when g ( x ) is sampled using a sampling frequency f s which fully respects the Nyquist condition. We call these phenomena sub-Nyquist artefacts . Although these beating effects have already been reported in the literature, their detailed mathematical behaviour is not widely known. In this paper, we study the behaviour of these phenomena and compare it with analogous results from the moiré theory. We show that both sampling moirés and sub-Nyquist artefacts obey the same basic mathematical rules, in spite of the differences between them. This leads us to a unified approach that explains all of these phenomena and puts them under the same roof. In particular, it turns out that all of these phenomena occur when the signal-frequency f and the sampling frequency f s satisfy f ≈( m / n ) f s with integer m , n , where m / n is a reduced integer ratio; cases with n =1 correspond to true sampling moiré effects.

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Low-Frequency Signal Sampling Method Implemented in a PLC Controller Dedicated to Applications in the Monitoring of Selected Electrical Devices

Electronics ◽

10.3390/electronics10040442 ◽

2021 ◽

Vol 10 (4) ◽

pp. 442

Author(s):

Marcin Jaraczewski ◽

Ryszard Mielnik ◽

Tomasz Gębarowski ◽

Maciej Sułowicz

Keyword(s):

Power System ◽

Reactive Power ◽

Low Frequency ◽

Sampling Frequency ◽

Electrical Signal ◽

Distortion Factor ◽

Electrical Devices ◽

Frequency Sampling ◽

Sampled Signal ◽

Band Limited

High requirements for power systems, and hence for electrical devices used in industrial processes, make it necessary to ensure adequate power quality. The main parameters of the power system include the rms-values of the current, voltage, and active and reactive power consumed by the loads. In previous articles, the authors investigated the use of low-frequency sampling to measure these parameters of the power system, showing that the method can be easily implemented in simple microcontrollers and PLCs. This article discusses the methods of measuring electrical quantities by devices with low computational efficiency and low sampling frequency up to 1 kHz. It is not obvious that the signal of 50–500 Hz can be processed using the sampling frequency of fs = 47.619 Hz because it defies the Nyquist–Shannon sampling theorem. This theorem states that a reconstruction of a sampled signal is only guaranteed possible for a bandlimit fmax < fs, where fmax is the maximum frequency of a sampled signal. Therefore, theoretically, neither 50 nor 500 Hz can be identified by such a low-frequency sampling. Although, it turns out that if we have a longer period of a stable multi-harmonic signal, which is band-limited (from the bottom and top), it allows us to map this band to the lower frequencies, thus it is possible to use the lower sampling ratio and still get enough precise information of its harmonics and rms value. The use of aliasing for measurement purposes is not often used because it is considered a harmful phenomenon. In our work, it has been used for measurement purposes with good results. The main advantage of this new method is that it achieves a balance between PLC processing power (which is moderate or low) and accuracy in calculating the most important electrical signal indicators such as power, RMS value and sinusoidal-signal distortion factor (e.g., THD). It can be achieved despite an aliasing effect that causes different frequencies to become indistinguishable. The result of the research is a proposal of error reduction in the low-frequency measurement method implemented on compact PLCs. Laboratory tests carried out on a Mitsubishi FX5 compact PLC controller confirmed the correctness of the proposed method of reducing the measurement error.

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Experiment Investigation of Bistable Vibration Energy Harvesting with Random Wave Environment

Applied Sciences ◽

10.3390/app11093868 ◽

2021 ◽

Vol 11 (9) ◽

pp. 3868

Author(s):

Qiong Wu ◽

Hairui Zhang ◽

Jie Lian ◽

Wei Zhao ◽

Shijie Zhou ◽

...

Keyword(s):

Renewable Energy ◽

Energy Harvesting ◽

Cantilever Beam ◽

Large Scale ◽

Low Frequency ◽

Vibration Energy ◽

Random Wave ◽

Periodic Signal ◽

Vibration Energy Harvesting ◽

Motion Activity

The energy harvested from the renewable energy has been attracting a great potential as a source of electricity for many years; however, several challenges still exist limiting output performance, such as the package and low frequency of the wave. Here, this paper proposed a bistable vibration system for harvesting low-frequency renewable energy, the bistable vibration model consisting of an inverted cantilever beam with a mass block at the tip in a random wave environment and also develop a vibration energy harvesting system with a piezoelectric element attached to the surface of a cantilever beam. The experiment was carried out by simulating the random wave environment using the experimental equipment. The experiment result showed a mass block’s response vibration was indeed changed from a single stable vibration to a bistable oscillation when a random wave signal and a periodic signal were co-excited. It was shown that stochastic resonance phenomena can be activated reliably using the proposed bistable motion system, and, correspondingly, large-scale bistable responses can be generated to realize effective amplitude enlargement after input signals are received. Furthermore, as an important design factor, the influence of periodic excitation signals on the large-scale bistable motion activity was carefully discussed, and a solid foundation was laid for further practical energy harvesting applications.

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Complex Principal Component Analysis of Antarctic Ice Sheet Mass Balance

Remote Sensing ◽

10.3390/rs13030480 ◽

2021 ◽

Vol 13 (3) ◽

pp. 480

Author(s):

Jingang Zhan ◽

Hongling Shi ◽

Yong Wang ◽

Yixin Yao

Keyword(s):

Principal Component Analysis ◽

Ice Sheet ◽

Low Frequency ◽

Principal Component ◽

Equatorial Pacific ◽

Mass Change ◽

Frequency Variation ◽

Periodic Signal ◽

Time Frequency ◽

The Antarctic

Ice sheet changes of the Antarctic are the result of interactions among the ocean, atmosphere, and ice sheet. Studying the ice sheet mass variations helps us to understand the possible reasons for these changes. We used 164 months of Gravity Recovery and Climate Experiment (GRACE) satellite time-varying solutions to study the principal components (PCs) of the Antarctic ice sheet mass change and their time-frequency variation. This assessment was based on complex principal component analysis (CPCA) and the wavelet amplitude-period spectrum (WAPS) method to study the PCs and their time-frequency information. The CPCA results revealed the PCs that affect the ice sheet balance, and the wavelet analysis exposed the time-frequency variation of the quasi-periodic signal in each component. The results show that the first PC, which has a linear term and low-frequency signals with periods greater than five years, dominates the variation trend of ice sheet in the Antarctic. The ratio of its variance to the total variance shows that the first PC explains 83.73% of the mass change in the ice sheet. Similar low-frequency signals are also found in the meridional wind at 700 hPa in the South Pacific and the sea surface temperature anomaly (SSTA) in the equatorial Pacific, with the correlation between the low-frequency periodic signal of SSTA in the equatorial Pacific and the first PC of the ice sheet mass change in Antarctica found to be 0.73. The phase signals in the mass change of West Antarctica indicate the upstream propagation of mass loss information over time from the ocean–ice interface to the southward upslope, which mainly reflects ocean-driven factors such as enhanced ice–ocean interaction and the intrusion of warm saline water into the cavities under ice shelves associated with ice sheets which sit on retrograde slopes. Meanwhile, the phase signals in the mass change of East Antarctica indicate the downstream propagation of mass increase information from the South Pole toward Dronning Maud Land, which mainly reflects atmospheric factors such as precipitation accumulation.

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Speech Identification with Temporal and Spectral Modification in Subjects with Auditory Neuropathy

ISRN Otolaryngology ◽

10.5402/2012/671247 ◽

2012 ◽

Vol 2012 ◽

pp. 1-7

Author(s):

Vijaya Kumar Name ◽

C. S. Vanaja

Keyword(s):

Signal Processing ◽

Speech Processing ◽

Word Identification ◽

Low Frequency ◽

Auditory Neuropathy ◽

Study Word ◽

Spectral Modification ◽

The Individual ◽

High Pass ◽

Speech Identification

Background. The aim of this study was to investigate the individual effects of envelope enhancement and high-pass filtering (500 Hz) on word identification scores in quiet for individuals with Auditory Neuropathy. Method. Twelve individuals with Auditory Neuropathy (six males and six females) with ages ranging from 12 to 40 years participated in the study. Word identification was assessed using bi-syllabic words in each of three speech processing conditions: unprocessed, envelope-enhanced, and high-pass filtered. All signal processing was carried out using MATLAB-7. Results. Word identification scores showed a mean improvement of 18% with envelope enhanced versus unprocessed speech. No significant improvement was observed with high-pass filtered versus unprocessed speech. Conclusion. These results suggest that the compression/expansion signal processing strategy enhances speech identification scores—at least for mild and moderately impaired individuals with AN. In contrast, simple high-pass filtering (i.e., eliminating the low-frequency content of the signal) does not improve speech perception in quiet for individuals with Auditory Neuropathy.

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Study on the Performance of Chaotic Oscillator in Weak Signal Detection

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.263-266.516 ◽

2012 ◽

Vol 263-266 ◽

pp. 516-520

Author(s):

Yan Mang Su ◽

Zhen Bin Gao ◽

Xiao Zhe Liu ◽

Na Zheng

Keyword(s):

Initial Phase ◽

Signal To Noise Ratio ◽

Sampling Frequency ◽

Signal Frequency ◽

Chaotic Oscillator ◽

Reference Frequency ◽

Weak Signal Detection ◽

Accuracy Rate ◽

Frequency Detection ◽

Output Variance

For the frequency detection by using chaotic oscillator, in this paper, the results which are under the influence of the sampling frequency on the basis of theory that the output variance of the system will reach a maximum when the reference frequency equals to the signal frequency are analyzed. Experiments have indicated that the accuracy rate of the results will be improved and the signal to noise ratio (SNR) threshold will be reduced by increasing the sampling frequency to a certain degree. Besides, we have a further research on detecting the frequency of a signal with an initial phase based on the theory mentioned above, simulation experimental results have verified the output variance still has a drastic change when the reference frequency is equal to the signal frequency.

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Non-destructive ultrasonic tomography for concrete pavement evaluation: signal processing and image analysis of crucial parameters

Revista IBRACON de Estruturas e Materiais ◽

10.1590/s1983-41952017000600004 ◽

2017 ◽

Vol 10 (6) ◽

pp. 1182-1191

Author(s):

L. S. SALLES ◽

J. T. BALBO ◽

L. KHAZANOVICH

Keyword(s):

Signal Processing ◽

Concrete Slab ◽

Low Frequency ◽

Concrete Pavement ◽

Ultrasonic Tomography ◽

Transverse Cracks ◽

Pavement Maintenance ◽

Use Of Technology ◽

Pavement Evaluation ◽

Non Destructive

Abstract In recent years, due to the destructive and unproductive character of pavement specimen extraction, pavement maintenance technology intensified the use of non-destructive techniques for pavement evaluation which resulted in the development of several devices and evaluation methods. This paper describes the use of technology based on low frequency ultrasonic tomography for evaluation of concrete pavement parameters. The equipment was applied in three experimental sections with different concrete pavements built at the University of Sao Paulo campus. The ultrasonic signal processing is given. The results analysis enables the efficient and reliable identification of thickness and reinforcement position within the concrete slab. Construction problems were evidenced in one of experimental sections with thickness deficiencies and reinforcement in a position below projected. Furthermore, the use of a novel concrete quality indicator was correlated with the presence of transverse cracks and alkali-silica reaction within the sections.

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A High Efficient Baseband GNSS Signal Narrow Band Anti-Jamming Approach in Frequency Domain

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.926-930.1857 ◽

2014 ◽

Vol 926-930 ◽

pp. 1857-1860

Author(s):

Zhou Zheng ◽

Meng Yuan Li ◽

Wei Jiang Wang

Keyword(s):

Signal Processing ◽

Frequency Domain ◽

Narrow Band ◽

Low Frequency ◽

Frequency Resolution ◽

Interference Rejection ◽

High Efficient ◽

Digital Down Conversion ◽

Down Conversion ◽

Low Rate

In order to reduce the burden of the calculation and the low frequency resolution of the tradition GNSS signal intermediate narrow band anti-jamming method, it introduces a high efficient approach of narrow band interference rejection based on baseband GNSS signal processing. After digital down conversion to baseband and down sampling to a low rate, the interference is removed in frequency domain. According to the theoretical analysis and simulation, it claims that the method can reduce the calculation and increase the detection resolution in frequency domain which will realize a high efficient interference rejection.

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