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rent amplitude and gets characteristic band signal

through filtering. References[9,10] use wavelet packet to

extract the transient signal, determined band which the

transient capacitive cu rrent most concentrate by the prin-

ciple of maximum energy and elected fault feeder. How-

ever, the feature band that can be used for line selection

is influenced by the system parameters, failure modes

and so on. Various feeders transient capacitive current

concentration of energy bands are not the same, if the

band is selected improperly, it is easy to make the fail

selection of the fault line.

The paper [12] uses S-transform to process zero se-

quence current of each feeder, and determines the domi-

nant frequency of the capacitive current by comparing

transient energy of different frequency points, and selects

the fault line according to the size of the energy.

S-transform is the development of continuous wavelet

transform and the short time Fourier transform, and has

good time-frequency characteristic, but amount of infor-

mation is so much after decomposition. As well as there

is some line selection methods which combine steady

state with transient state, but neural network algorithm

exists local optimum problem, poor convergence, longer

training time and limited reliability.

To compensate for these shortcomings, this paper pro-

vides an algorithm that can decomposes signal into a

linear expansion of waveforms that belong to a redundant

dictionary of functions, these waveforms are selected in

order to best match the signal structures. For a particular

signal, according to the characteristics of the signal, the

algorithm can choose the best spread functions adap-

tively. By using less function more accurate represent the

signal, it can decompose a signal into coherent compo-

nents. The new feature extraction of the fault signal me-

thod in the neutral indirectly grounded system which is

based on the atomic sparse decomposition.

2. Time-Frequency Atom Dictionaries

Time-frequency signal decomposition such as Fourier

transforms and wavelet transforms has been used for

many years. It is often essential to adapt the time-fre-

quency decomposition to the particular signal structures

to extract information from complex signals. The algo-

rithm provided in this paper can decomposes signal into a

linear expansion of waveforms that belong to a redundant

dictionary of functions, the selected waveforms are the

best match of the signal structures. For a particular signal,

the algorithm can choose the best spread functions adap-

tively on the basis of the characteristics of the signal. The

functions more accurate to represent the signal are called

atom, the possibly redundant dictionary of functions

called atoms.

The matching pursuit algorithm is often used in the

atomic decomposition process, it is a greedy adaptive

decomposition to decompose signal into a linear expan-

sion of waveforms that belong to atoms. The selected

atoms have good time-frequency characteristic and can

represent the inherent characteristics and critical infor-

mation of the signal.

2.1. The Gabor Dictonary

Decomposing a signal over a redundant dictionary im-

proves the compression efficiency, especially at low bit

rate where most of the signal energy is captured by only

few elements. We often use Gabor dictionary in atomic

sparse decomposition. Define

1

()( )

t

t

tge

s

s

(1)

The real Gabor atoms:

()( )cos()

Kt

gt gt

s

s

(2)

2

1

4

() 2t

te

is Gaussian window function, (,, , )s

,

is the index of ()

t

, s is Scaling parameters,

is

Displacement parameters,

is Frequency parameters,

is Phase parameters. Such atomic space is boundless,

and in practice, we can’t search a boundless space, so the

atomic database should be dispersed. (,

jj

apa ,

),

j

ka

while 2,a

12,

,

2

0l ogjN ,

1j

02pN ,

1

2

j

0k.

Then we can get a Gabor

dictionary

1

()(2)cos( 2)

jj

rd j

gn gnpnk

(3)

() 0

()(2)[1, )

1

0,1,..., 1

j

jd

jj

nKgn jL

jL

N

nN

(4)

2.2. Matching Pursuits Algorithm

In contrast to orthogonal transforms, over complete ex-

pansions of signals are not unique. The number of feasi-

ble decompositions is infinite, and finding the best solu-

tion under a given criteria is a NP-complete problem. In

compression, one is interested in representing the signal

to be coded with the smallest number of elements, which

is in finding the solution with most of the energy on only

a few coefficients. Matching Pursuit is one of the sub-

optimal approaches that greedily approximate the solu-

tion to this NP-complete problem [13].

Matching Pursuits algorithm, which is a greedy adap-

tive decomposition that has the potential of decomposing

a signal into coherent components.

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