Wavelets from Math to Practice

Radunović, Desanka P.

doi:10.1007/978-3-642-00614-2

Cited by 37 publications

(14 citation statements)

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“…Discrete wavelets are usually part by part continuous functions which scaled and translated in discrete steps (Radunovic, 2009): Where and are integers, while is the fixed scaling step. It is taken to be , so that the division on the frequency axis is dyadic.…”

Section: Methodology 31 Wavelet Transformmentioning

confidence: 99%

Hydrological Time Series Forecasting Using Anfis Models With Aid of Wavelet Transform

Ibrahim

Mustafa

Rashid

2017

juod

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The precise and accurate models of hydrological time series that are embedded with high complexity, nonstationarity, and non-linearity in both spatial and temporal scales can provide important information for decision-making in water resources management and environmental related issues. Hybrid wavelet transform (WT) and adaptive neuro-fuzzy inference system (ANFIS) has been used in this study to improve the forecasting capability of ANFIS model by decomposing the time series into sub-time series (approximation and details) using wavelet transform then combining the effective and significant time lags of sub-time series to form a set of input variables. The present study attempts to add the effective and significant time lags of original time series as extra variables to the input variables set. In addition, different combinations of variables, 1-3, from the set of input variables as inputs to the ANFIS model were used to forecast the time series.To examine the potential of the approach for practical applications, the model is applied to forecast, one step-ahead, the monthly data of hydrological time series (rainfall, evaporation, minimum and maximum temperature, average wind speed and reservoir inflow) for Kirkuk, Sulaimani, Dokan and Darbandikhan meteorological stations in Iraq. The best fit models were selected using the coefficient of determination ( ) and root mean square error ( ). Based on the results, the proposed model has high performance in forecasting the monthly minimum and maximum temperature, evaporation and reservoir inflow with values ranged from 0.93 to 0.99 and relatively good performances in forecasting the monthly rainfall and average wind speed with values ranged from 0.77 to 0.93.

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Section: Methodology 31 Wavelet Transformmentioning

confidence: 99%

Hydrological Time Series Forecasting Using Anfis Models With Aid of Wavelet Transform

Ibrahim

Mustafa

Rashid

2017

juod

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“…Com relação às características das quatro Wavelets que usamos, a Biorthogonal 3.9 não apresenta a propriedade de ortogonalidade, embora seja a única simétrica dessas quatro. Por outro lado, a Daubechies 6 é assimétrica, enquanto a Symlet 9 e a Coiflet 3 apresentam a propriedade de quase simetria [13].…”

Section: Wavelets Discretasunclassified

Escolha da Base Wavelet na Recuperação de Dados Sísmicos via Compressive Sensing

Nascimento¹,

Marinho²,

Rocha³

et al. 2016

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…s J,k and s j,k are approximation and detailed coefficients. Scaling and wavelet functions can be expressed as follows [38]:…”

Section: Dwmt Receiver With Ofdementioning

confidence: 99%

“…DWT of the signal is composed of approximation and detailed coefficients, which are produced due to series expansion. These coefficients are calculated as follows [38]:…”

Section: Dwmt Receiver With Ofdementioning

confidence: 99%

DWMT transceiver equalization using overlap FDE for downlink ADSL

Khan¹,

Baig²,

Nawaz³

2015

Turk J Elec Eng & Comp Sci

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Discrete wavelet multitone (DWMT) modulation is a wavelet transform based technique implemented using perfect reconstruction filter banks. It has been recently proposed for various wireline channels such as digital subscriber loops (DSLs) as a solution to the problems posed by a discrete multitone (DMT) transceiver including interblock interference (IBI) and lower spectral efficiency due to the employment of a cyclic prefix (CP) in the guard interval (GI) for DMT symbols. The greater side lobe attenuation offered by wavelet filter banks results in improved spectral containment and lower IBI in DWMT transceivers. However, no standard equalization technique exists for a DWMT based transceiver so as to remove the effect of channel on the transmitted signal in DWMT systems. This paper proposes the application of overlap frequency domain equalization (OFDE) in DWMT modulated systems and compares the bit error rate (BER) performance with time domain equalization (TDE) technique. It is shown through simulation results that minimum mean square error (MMSE) based OFDE can be applied as an equalization technique for a downlink asymmetric DSL (ADSL) channel with lower computational complexity and BER performance comparable to that of TDE.

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Wavelets from Math to Practice

Cited by 37 publications

References 0 publications

Hydrological Time Series Forecasting Using Anfis Models With Aid of Wavelet Transform

Hydrological Time Series Forecasting Using Anfis Models With Aid of Wavelet Transform

Escolha da Base Wavelet na Recuperação de Dados Sísmicos via Compressive Sensing

DWMT transceiver equalization using overlap FDE for downlink ADSL

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