scholarly journals Wavelet Analysis of Red Noise and Its Application in Climate Diagnosis

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhihua Zhang
Keyword(s):  
Wavelet Analysis ◽  
Power Spectrum ◽  
General Formula ◽  
Spectral Peak ◽  
Wavelet Power Spectrum ◽  
Statistical Framework ◽  
Analytic Wavelet ◽  
Real Analytic

Signals are often destroyed by various kinds of noises. A common way to statistically assess the significance of a broad spectral peak in signals and the synchronization between signals is to compare with simple noise processes. At present, wavelet analysis of red noise is studied limitedly and there is no general formula on the distribution of the wavelet power spectrum of red noise. Moreover, the distribution of the wavelet phase of red noise is also unknown. In this paper, for any given real/analytic wavelet, we will use a rigorous statistical framework to obtain the distribution of the wavelet power spectrum and wavelet phase of red noise and apply these formulas in climate diagnosis.

scholarly journals Comment on "Significance tests for the wavelet power and the wavelet power spectrum" by Ge (2007)

2012 ◽  
Vol 30 (12) ◽  
pp. 1743-1750 ◽  
Author(s):  
Z. Zhang ◽  
J. C. Moore
Keyword(s):  
Power Spectrum ◽  
White Noise ◽  
Continuous Time ◽  
Gaussian White Noise ◽  
Morlet Wavelet ◽  
Wavelet Power Spectrum ◽  
Significance Tests ◽  
Statistical Framework ◽  
Correct Formula

Abstract. As the main result in Ge's paper, Ge announced that he proved a formula on the distribution of Morlet wavelet power spectrum of continuous-time Gaussian white noise in a rigorous statistical framework. In this paper, we will show that Ge's formula is wrong and each step of Ge's proof is wrong. Moreover, we give and prove a correct formula in a rigorous statistical framework.

scholarly journals Artificial Detection of Lower-Frequency Periodicity in Climatic Studies by Wavelet Analysis Demonstrated on Synthetic Time Series

2019 ◽  
Vol 58 (9) ◽  
pp. 2077-2086 ◽  
Author(s):  
Assaf Hochman ◽  
Hadas Saaroni ◽  
Felix Abramovich ◽  
Pinhas Alpert
Keyword(s):  
Time Series ◽  
Wavelet Analysis ◽  
Power Spectrum ◽  
Low Frequency ◽  
Real Data ◽  
Careful Analysis ◽  
Wavelet Power Spectrum ◽  
Natural Oscillations ◽  
Local Singularity ◽  
Climatic Time Series

AbstractThe continuous wavelet transform (CWT) is a frequently used tool to study periodicity in climate and other time series. Periodicity plays a significant role in climate reconstruction and prediction. In numerous studies, the use of CWT revealed dominant periodicity (DP) in climatic time series. Several studies suggested that these “natural oscillations” would even reverse global warming. It is shown here that the results of wavelet analysis for detecting DPs can be misinterpreted in the presence of local singularities that are manifested in lower frequencies. This may lead to false DP detection. CWT analysis of synthetic and real-data climatic time series, with local singularities, indicates a low-frequency DP even if there is no true periodicity in the time series. Therefore, it is argued that this is an inherent general property of CWT. Hence, applying CWT to climatic time series should be reevaluated, and more careful analysis of the entire wavelet power spectrum is required, with a focus on high frequencies as well. A conelike shape in the wavelet power spectrum most likely indicates the presence of a local singularity in the time series rather than a DP, even if the local singularity has an observational or a physical basis. It is shown that analyzing the derivatives of the time series may be helpful in interpreting the wavelet power spectrum. Nevertheless, these tests are only a partial remedy that does not completely neutralize the effects caused by the presence of local singularities.

scholarly journals Significance tests for the wavelet power and the wavelet power spectrum

2007 ◽  
Vol 25 (11) ◽  
pp. 2259-2269 ◽  
Author(s):  
Z. Ge
Keyword(s):  
Wavelet Analysis ◽  
Power Spectrum ◽  
Lake Michigan ◽  
Random Noise ◽  
Gaussian White Noise ◽  
Covariance Structure ◽  
Sampling Period ◽  
Wavelet Power Spectrum ◽  
Significance Tests ◽  
Significance Levels

Abstract. Significance tests usually address the issue how to distinguish statistically significant results from those due to pure randomness when only one sample of the population is studied. This issue is also important when the results obtained using the wavelet analysis are to be interpreted. Torrence and Compo (1998) is one of the earliest works that has systematically discussed this problem. Their results, however, were based on Monte Carlo simulations, and hence, failed to unveil many interesting and important properties of the wavelet analysis. In the present work, the sampling distributions of the wavelet power and power spectrum of a Gaussian White Noise (GWN) were derived in a rigorous statistical framework, through which the significance tests for these two fundamental quantities in the wavelet analysis were established. It was found that the results given by Torrence and Compo (1998) are numerically accurate when adjusted by a factor of the sampling period, while some of their statements require reassessment. More importantly, the sampling distribution of the wavelet power spectrum of a GWN was found to be highly dependent on the local covariance structure of the wavelets, a fact that makes the significance levels intimately related to the specific wavelet family. In addition to simulated signals, the significance tests developed in this work were demonstrated on an actual wave elevation time series observed from a buoy on Lake Michigan. In this simple application in geophysics, we showed how proper significance tests helped to sort out physically meaningful peaks from those created by random noise. The derivations in the present work can be readily extended to other wavelet-based quantities or analyses using other wavelet families.

scholarly journals Wavelet analysis applied on temporal data sets in order to reveal possible pre-seismic radio anomalies and comparison with the trend of the raw data 

2021 ◽  
Author(s):  
Giovanni Nico ◽  
Pier Francesco Biagi ◽  
Anita Ermini ◽  
Mohammed Yahia Boudjada ◽  
Hans Ulrich Eichelberger ◽  
...  
Keyword(s):  
Time Series ◽  
Wavelet Analysis ◽  
Power Spectrum ◽  
Power Spectra ◽  
Wavelet Spectrum ◽  
Time Signal ◽  
Time Behavior ◽  
Sudden Increase ◽  
Night Time ◽  
Raw Data

<p>Since 2009, several radio receivers have been installed throughout Europe in order to realize the INFREP European radio network for studying the VLF (10-50 kHz) and LF (150-300 kHz) radio precursors of earthquakes. Precursors can be related to “anomalies” in the night-time behavior of  VLF signals. A suitable method of analysis is the use of the Wavelet spectra.  Using the “Morlet function”, the Wavelet transform of a time signal is a complex series that can be usefully represented by its square amplitude, i.e. considering the so-called Wavelet power spectrum.</p><p>The power spectrum is a 2D diagram that, once properly normalized with respect to the power of the white noise, gives information on the strength and precise time of occurrence of the various Fourier components, which are present in the original time series. The main difference between the Wavelet power spectra and the Fourier power spectra for the time series is that the former identifies the frequency content along the operational time, which cannot be done with the latter. Anomalies are identified as regions of the Wavelet spectrogram characterized by a sudden increase in the power strength.</p><p>On January 30, 2020 an earthquake with Mw= 6.0 occurred in Dodecanese Islands. The results of the Wavelet analysis carried out on data collected some INFREP receivers is compared with the trends of the raw data. The time series from January 24, 2020 till January 31, 2000 was analyzed. The Wavelet spectrogram shows a peak corresponding to a period of 1 day on the days before January 30. This anomaly was found for signals transmitted at the frequencies 19,58 kHz, 20, 27 kHz, 23,40 kHz with an energy in the peak increasing from 19,58 kHz to 23,40 kHz. In particular, the signal at the frequency 19,58 kHz, shows a peak on January 29, while the frequencies 20,27 kHz and 23,40 kHz are characterized by a peak starting on January 28 and continuing to January 29. The results presented in this work shows the perspective use of the Wavelet spectrum analysis as an operational tool for the detection of anomalies in VLF and LF signal potentially related to EQ precursors.</p>

Wavelet power spectrum-based autofocusing algorithm for time delayed and integration charge coupled device space camera

2012 ◽  
Vol 51 (21) ◽  
pp. 5216 ◽  
Author(s):  
Shuping Tao ◽  
Guang Jin ◽  
Xuyan Zhang ◽  
Hongsong Qu ◽  
Yuan An
Keyword(s):  
Power Spectrum ◽  
Wavelet Power Spectrum ◽  
Charge Coupled Device

scholarly journals Time series analysis of observed maximum and minimum air temperature at four urban cities of India during 1951-2015

MAUSAM ◽  
2021 ◽  
Vol 71 (1) ◽  
pp. 57-68
Author(s):  
PRAMANIK SAIKAT ◽  
SIL SOURAV ◽  
MANDAL SAMIRAN
Keyword(s):  
Time Series ◽  
Power Spectrum ◽  
Air Temperature ◽  
India Meteorological Department ◽  
Wavelet Power Spectrum ◽  
Maximum Temperature ◽  
Coastal Cities ◽  
Increasing Trend ◽  
Two Peaks ◽  
Minimum Air Temperature

A sixty - five year (1951-2015) long data for monthly minimum temperature (TMIN) and maximum temperature (TMAX), observed by the India Meteorological Department (IMD), is statistically analyzed at four urban stations namely Bhubaneswar, Delhi, Mumbai and Chennai of India. A bimodal nature in seasonality is noticed for TMAX and TMIN at all locations. Two peaks for TMAX and TMIN are observed in May and September. Exceptionally, Mumbai shows TMAX peaks during May and November and Delhi shows TMIN peaks during June and September. Higher standard deviations (SD) for TMAX is noted at Delhi with a maximum in March (1.78 °C), while for Chennai, the SD for TMIN is lesser compared to other cities. Two different periods 1951-1980 (P1, the first half of the study period) and 1981-2015 (P2, the second half of the study period) were identified from the time series of both TMAX and TMIN. A higher increasing trend is observed during P2 than P1 in all the cities except in TMIN at Mumbai. The highest increasing trend (0.040 °C/year) is observed for TMIN in Mumbai during P1 time, but the trend is almost constant (0.001 °C/year) during P2 time. The highest increasing trend for TMIN at Mumbai is mainly contributed by the increasing trend in post-monsoon and winter months in P1. Surprisingly, in both P1 and P2, the trends are less during monsoon months for all the cities. A consistent 5-year (3-year) band is observed throughout the wavelet power spectrum at the coastal cities Bhubaneswar, Mumbai (Chennai). However, the 5-year signal is not consistent at Delhi and it is observed only during the year 1975-1980. The global wavelet power spectrum showed that TMIN at Chennai has less power (0.6 °C2) corresponding to 3-year signal and Mumbai has highest power (12 °C2) corresponding to the 5-year signal in comparison to other cities.

scholarly journals Feature selection using Haar wavelet power spectrum

2006 ◽  
Vol 7 (1) ◽  
Author(s):  
Prabakaran Subramani ◽  
Rajendra Sahu ◽  
Shekhar Verma
Keyword(s):  
Feature Selection ◽  
Power Spectrum ◽  
Haar Wavelet ◽  
Wavelet Power Spectrum

scholarly journals Quasi ~500-year Cycle Signals in Solar Activity

2018 ◽  
Vol 7 (1) ◽  
pp. 131
Author(s):  
Lihua Ma ◽  
Zhiqiang Yin ◽  
Yanben Han
Keyword(s):  
Solar Activity ◽  
Power Spectrum ◽  
Wavelet Power Spectrum ◽  
Geomagnetic Variations ◽  
The Past ◽  
Direct Observations ◽  
Periodic Signals ◽  
Activity Series

Direct observations of solar activity are available for the past four century, so some proxies reflecting solar activity such as 14C, 10Be and geomagnetic variations are used to reconstruct solar activity in the past. In this present paper, the authors use rectified wavelet power transform and time-averaged wavelet power spectrum to investigate long-term fluctuations of the reconstructed solar activity series. Results show obvious a quasi ~500-year cycle exists in the past solar activity. Three reconstructed solar activity series from 14C variations confirm the periodic signals.

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