A Physical Study of River RamGanga by using Complex Morlet Wavelets

Yogendra Singh, Sachin Kumar, Rakesh Kumar

Abstract


Wavelets provide local information about data in time and scale (frequency), wavelet-based coherence allows to measure time-varying correlation as a function of frequency. In other words, a coherence measure suitable for nonstationary processes. Time Frequency analysis is an important tool in modern signal analysis. In this paper, we analyze the relationship between different time series after distributing their energies in both time and frequency domain. Wavelets have the special ability to localize the signal in both time and frequency domain simultaneously. By using this ability, we perform an analytical framework for modeling the statistical behavior of physical parameters of river water such as Width, Velocity and depth. For this purpose, we used ‘cmor1-1’ wavelet of complex Morlet family. Physical parameters of river water are taken from river Ramganga of the time period 2005-2008. CWT of two time series and the cross examination of the two decompositions can reveal localized similarities in time and scale. The magnitude of the wavelet cross spectrum (Wcs) can be interpreted as the absolute value of the local covariance between the two time series in the time-scale plane. 

Keywords


cmor1-1, CWT, River Ramganga, Time frequency domain, Wcs.

References


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S. G. Mallat, Multiresolution approximations and wavelet orthonormal bases

of〖 L〗^2 (R),Trans. Amer. Math. Soc.315: 69-87, 1989.

P. K. Singh, B. Rashmi, Analysis of Water Parameters Using Daubechies Wavelet,

American Journal of Mathematics and Statistics, 2(3): 57-63, 2012.

J. K. Pathak, Evaluation of limnological characteristics and its trophic status of river

Ramganga of western Uttar Pradesh”. FTR submitted to DST, Government of India,

S. Kumar, A. Kumar, R. Kumar, J. K. Pathak, Mohd. Alam, Spectral Analysis of

Biochemical Oxygen Demand in River water: An Analytical Approach to Discrete

Wavelet Transform, American Journal of Mathematics and Statistics, 4(2): 107-112,

M. Alam, J. K. Pathak, Running water environment: A case of Ramganga basin, Lambert

Academic Publications, Scholars Press, Germany, 2013.

I. Daubechies, Ten lectures on wavelets, CBS-NSF, Regional Conference in Applied

Mathematics, SIAM Philadelphia 61: 278 – 285, 1994.

Quin. S. and D. Chen, joint Time–frequency Analysis-Methods and Applications,

LongmanCheshire, Melbourne, Australia, 1992.

J. P. Antoine, Wavelet analysis: A new tool in Physics, Wavelets in Physics, Van Der

Berg, J. C.(Eds.), 9-21, 2004.

Jean DuclosAlegue, Albrecht Gnauck, Signal Analysis of Water Quality

Indicators.Enviro. Info 2006 (Graz). Managing Environmental Knowledge (2006),

-376.




DOI: http://dx.doi.org/10.29218/srmsmaths.v2i01.28

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