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Реализация метода непрерывного Вейвлет преобразования для одномерных массивов

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2

IINEIANEEE AINOAeA?NOAAIIUE

EIAEAIA?II-OECE*ANEEE EINOEOOO

(OAOIE*ANEEE OIEAA?NEOAO)

IEOE

Eaoaae?a 17

IIssNIEOAEUeIAss CAIENEA

E O*AAII-ENNEAAeIAAOAEUeNEIE ?AAIOA

OAIA: “?AAEECAOeEss IAOIAeA IAI?A?UAIIAI

AAEAEAO I?AIA?ACIAAIEss AeEss IAeIIIA?IUO IANNEAIA ”

Auiieiee nooaeaio a?oiiu E7-171 Eoeao A.A.

Iao/iue ?oeiaiaeeoaeue Aaoaoei I.A.

Iineaa, 1999

IAEAAEAIEA

1. AAAAeAIEA

2. IINOAIIAEA CAAeA*E

3. IIAeOIAeU E AIAEECO NEAIAEIA NI NEIAEIUIE *ANOIOII- A?AIAIIUIE
OA?AEOA?ENOEEAIE

3.1 Iaoiaeu ia?aaioee ianoaoeeiia?iuo neaiaeia

3.2 E?aoeee iaci? i?aia?aciaaiey Oo?uea

3.3 Iniiaiua iieiaeaiey aaeaeao-aiaeeca

4. ?AAEECAOeEss AEAI?EOIA

4.1 Iaoiaeu au/eneaiey iai?a?uaiiai aaeaeao i?aia?aciaaiey e eo
n?aaiaiea n oi/ee c?aiey ?aaeecaoeee

4.1.1 Ai a?aiaiiie iaeanoe

4.1.2 A /anoioiie iaeanoe

4.2 Auai? iaoa?eineiai aaeaeaoa

4.3 Nenoaia “eeeaio-na?aa?” eae niinia iiauoaiey nei?inoe aeai?eoia

4.3.1 Ooieoeee “eeeaioa”

4.3.2 Ooieoeee “na?aa?a”

5. CAEETH*AIEA

6. NIENIE EEOA?AOO?U

7. I?EEIAEAIEss

1. AAAAeAIEA

Ethaua enneaaeiaaiey iau/ii oeeaaeuaathony a neaaeothuoth noaio:

1. Nai? eioi?iaoeee (oeenaoeey n?aaeianoaoenoe/aneeo aeaiiuo, i?eai
aeaiiuo io oao eee eiuo aeao/eeia e o. i.)

2. Aiaeec iieo/aiiuo aeaiiuo (auaeaeaiea oa?aeoa?iuo iniaaiiinoae,
aecoaeecaoeey, ionaeaaiea aiiiaeueiuo cia/aiee, ii?aaeaeaiea
ia?eiaee/iinoae, /anoioiiai niaeo?a e o. ae.)

A ?acoeueoaoa ia?aiai oaaa iieo/aaony iaeee iannea aeaiiuo, eioi?ue
aoaeai iacuaaoue neaiaeii. A neeo iiiaiia?acey ano?a/athueony a i?e?iaea
neaiaeia /anoi i?eoiaeeony noaeeeaaoueny n neaiaeaie, eiathueie neiaeiua
/anoioii-a?aiaiiua oa?aeoa?enoeee (i?inoui i?eia?ii neoaeeo
yeaeo?iea?aeeia?aiia /aeiaaea).

Aeaiiay ?aaioa iinayuaia eco/aieth e ?aaeecaoeee iai?a?uaiiai aaeaeao
i?aia?aciaaiey aeey neo/ay aeene?aoiiai neaiaea.

O?aaeeoeeiiiui iiaeoiaeii e enneaaeiaaieth /eneiauo ?yaeia yaeyaony
i?aia?aciaaiea Oo?uea, a ?acoeueoaoa eioi?iai iieo/aaony /anoioiue
niaeo? neaiaea. Iaaeinoaoeii i?aia?aciaaiey Oo?uea yaeyaony oi, /oi
/anoioiua eiiiiiaiou ia iiaoo auoue eieaeeciaaiu ai a?aiaie, a nayce n
/ai eiiaaea iaaiciiaeii iieo/eoue en/a?iuaathuae eioi?iaoeee i neaiaea.
A oaeeo neo/ayo aeey aiaeeca neaiaea oeaeaniia?acii i?eiaiyoue aaeaeao
i?aia?aciaaiea (AI), eioi?ia iicaieyao iieo/eoue /anoioii-a?aiaiioth
?acaa?oeo neaiaea, aeathuoth nouanoaaiii aieueoa eioi?iaoeee, /ai a
neo/aa Oo?uea-aiaeeca.

Aica?auaynue e aeaoi nooiaiyi enneaaeiaaiee, caiaoei, /oi nai?
eioi?iaoeee e aiaeec aeaiiuo /anoi iaoaeiaii i?iaiaeeoue niaianoii,
eiiaaea yoi i?ienoiaeeo a ?aciuo eaai?aoi?eyo, a, neaaeiaaoaeueii,
aicieeaao iaiaoiaeeiinoue nicaeaiey ?ani?aaeaeaiiie nenoaiu
“eeeaio-na?aa?”.

2. IINOAIIAEA CAAeA*E

Aeey ?ac?aaioee iiaeoey aiaeeca iniiaiuo oa?aeoa?enoee
yeaeo?iea?aeeia?aiiu (YEA) /aeiaaea a eiiiuethoa?iii ea?aeeieiae/aneii
eiiieaena iaiaoiaeeii ?aaeeciaaoue aeai?eoi iai?a?uaiiai aaeaeao
i?aia?aciaaiey.

Aeey yoiai neaaeoao:

· eco/eoue oai?aoe/aneea iniiau iai?a?uaiiai aaeaeao i?aia?aciaaiey;

· enneaaeiaaoue niiniau ?aaeecaoeee iai?a?uaiiai aaeaeao i?aia?aciaaiey;

· n?aaieoue iaoiaeu ?aaeecaoeee aeai?eoiia e aua?aoue niiniau eo
onei?aiey.

I?e i?iaaaeaiee enneaaeiaaiee eniieueciaaoue n?aaeo Matlab 5.0,
?ac?aaioaiiue aeai?eoi ?aaeeciaaoue a n?aaea i?ia?aiie?iaaiey Delphi
5.0.

3. IIAeOIAeU E AIAEECO NEAIAEIA NI NEIAEIUIE *ANOIOII-A?AIAIIUIE
OA?AEOA?ENOEEAIE

3.1 Iaoiaeu ia?aaioee ianoaoeeiia?iuo neaiaeia

Aaeaeao i?aia?aciaaiea no?aieoaeueii caaiaauaaao iiioey?iinoue a noieue
?aciuo iaeanoyo, eae oaeaeiiioieeaoeee, eiiiuethoa?iay a?aoeea,
aeieiaey, ano?ioeceea e iaaeeoeeia. Aeaaiaea?y oi?ioae
i?eniiniaeaiiinoe e aiaeeco ianoaoeeiia?iuo neaiaeia 1 iii noaei iiuiie
aeueoa?iaoeaie i?aia?aciaaieth Oo?uea a ?yaea iaaeeoeeineeo i?eeiaeaiee.
Oae eae iiiaea iaaeeoeeineea neaiaeu ianoaoeeiia?iu, iaoiaeu aaeaeao
aiaeeca eniieuecothony aeey ?aniiciaaaiey e iaia?oaeaiey eeth/aauo
aeeaaiinoe/aneeo i?eciaeia.

Iaeiaei, i?aaeaea /ai noaaeoue ia?aae niaie caaea/o ioai?a iiaeoiaeyueo
iaoiaeia aiaeeca neaiaea, iaiaoiaeeii ioaaoeoue ia neaaeothuea aii?inu:

· ssaeyaony ee neaiae noaoeeiia?iui ?

· Eaeea oa?aeoa?enoeee neaiaea enneaaeothony ?

A aeaiiie ?aaioa eco/athony /anoioii-a?aiaiiua oa?aeoa?enoeee
ianoaoeeiia?iuo neaiaeia, /oi e ii?aaeaeyao iniaue iiaeoiae e auai?o
iaoiaea.

I?aia?aciaaiea Oo?uea i?aaenoaaeyao neaiae, caaeaiiue ai a?aiaiiie
iaeanoe, a aeaea ?aceiaeaiey ii i?oiaiiaeueiui aaceniui ooieoeeyi
(neionai e eineionai), auaeaeyy oaeei ia?acii /anoioiua eiiiiiaiou.
Iaaeinoaoie i?aia?aciaaiey Oo?uea caeeth/aaony a oii, /oi /anoioiua
eiiiiiaiou ia iiaoo auoue eieaeeciaaiu ai a?aiaie, /oi iaeeaaeuaaao
ia?aie/aiey ia i?eiaieiinoue aeaiiiai iaoiaea e ?yaeo caaea/ (iai?eia?,
a neo/aa eco/aiey aeeiaieee eciaiaiey /anoioiuo ia?aiao?ia neaiaea ia
a?aiaiiii eioa?aaea).

Aieueoeinoai iaaeeoeeineeo neaiaeia eiaao neiaeiua /anoioii-a?aiaiiua
oa?aeoa?enoeee. Eae i?aaeei, oaeea neaiaeu ninoiyo ec aeeceeo ii
a?aiaie, ei?ioeiaeeaoueo auniei/anoioiuo eiiiiiaio e aeieaia?aiaiiuo,
aeeceeo ii /anoioa iecei/anoioiuo eiiiiiaio.

Aeey aiaeeca oaeeo neaiaeia ioaeai iaoiae, niiniaiue iaania/eoue
oi?ioaa ?ac?aoaiea e ii /anoioa, e ii a?aiaie. Ia?aia o?aaoaony aeey
eieaeecaoeee iecei/anoioiuo ninoaaeythueo, aoi?ia – aeey ?ac?aoaiey
eiiiiiaio aunieie /anoiou.

Nouanoaoao aeaa iiaeoiaea e aiaeeco ianoaoeeiia?iuo neaiaeia oaeiai
oeia. Ia?aue – eieaeueiia i?aia?aciaaiea Oo?uea (short-time Fourier
transform). Neaaeoy ii yoiio iooe, iu ?aaioaai n ianoaoeeiia?iui
neaiaeii, eae ni noaoeeiia?iui, i?aaeaa?eoaeueii ?acaea aai ia naaiaiou
(ieia), noaoenoeea eioi?uo ia iaiyaony ni a?aiaiai. Aoi?ie iiaeoiae –
aaeaeao i?aia?aciaaiea. A yoii neo/aa ianoaoeeiia?iue neaiae
aiaeece?oaony iooai ?aceiaeaiey ii aaceniui ooieoeeyi, iieo/aiiui ec
iaeioi?iai i?ioioeia iooai naeaoee, ?anoyaeaiee e naeaeaia. Ooieoeey
i?ioioei iacuaaaony iaoa?eineei, eee aiaeece?othuei aaeaeaoii.

___________________________

1 – oi anoue oaeeo, o eioi?uo oa?aeoa?enoeee iaiythony ai a?aiaie [5b]

3.2 E?aoeee iaci? i?aia?aciaaiey Oo?uea

Eeanne/aneei iaoiaeii /anoioiiai aiaeeca neaiaeia yaeyaony
i?aia?aciaaiea Oo?uea, nooue eioi?iai iiaeii au?aceoue oi?ioeie (1)

?acoeueoao i?aia?aciaaiey Oo?uea – aiieeooaeii-/anoioiue niaeo?, ii
eioi?iio iiaeii ii?aaeaeeoue i?enoonoaea iaeioi?ie /anoiou a
enneaaeoaiii neaiaea.

A neo/aa, eiaaea ia anoaao aii?in i eieaeecaoeee a?aiaiiiai iieiaeaiey
/anoio, iaoiae Oo?uea aeaao oi?ioea ?acoeueoaou. Ii i?e iaiaoiaeeiinoe
ii?aaeaeeoue a?aiaiiie eioa?aae i?enoonoaey /anoiou i?eoiaeeony
i?eiaiyoue ae?oaea iaoiaeu.

Iaeiei ec oaeeo iaoiaeia yaeyaony yaeyaony iaiauaiiue iaoiae Oo?uea
(eieaeueiia i?aia?aciaaiea Oo?uea). Yoio iaoiae ninoieo ec neaaeothueo
yoaiia:

1. a enneaaeoaiie ooieoeee nicaeaaony “ieii” – a?aiaiiie eioa?aae, aeey
eioi?iai ooieoeey f(x)0, e f(x)=0 aeey inoaeueiuo cia/aiee;

2. aeey yoiai “ieia” au/eneyaony i?aia?aciaaiea Oo?uea

3. “ ieii” naeaeaaaony, e aeey iaai oaeaea au/eneyaony i?aia?aciaaiea
Oo?uea

“I?ieaey” oaeei “ieiii” aaeieue anaai neaiaea, iieo/aaony iaeioi?ay
o?aoia?iay ooieoeey, caaenyuay io iieiaeaiey “ieia” e /anoiou.

Aeaiiue iiaeoiae iicaieyao ii?aaeaeeoue oaeo i?enoonoaey a neaiaea
ethaie /anoiou, e eioa?aae aa i?enoonoaey. Yoi cia/eoaeueii ?anoe?yao
aiciiaeiinoe iaoiaea ii n?aaiaieth n eeanne/aneei i?aia?aciaaieai
Oo?uea, ii nouanoaotho e ii?aaeaeaiiua iaaeinoaoee. Niaeanii neaaenoaeyi
i?eioeeia iaii?aaeaeaiiinoe Aaecaiaa?aa a aeaiiii neo/aa iaeuecy
ooaa?aeaeaoue oaeo iaee/ey /anoiou 0 a neaiaea a iiiaio a?aiaie t0 –
iiaeii eeoue ii?aaeaeeoue, /oi niaeo? /anoio (1,2) i?enoonoaoao a
eioa?aaea (t1,t2). I?e/ai ?ac?aoaiea ii /anoioa (ii a?aiaie) inoaaony
iinoiyiiui aia caaeneiinoe io iaeanoe /anoio (a?aiai), a eioi?uo
i?iecaiaeeony enneaaeiaaiea. Iiyoiio, anee, iai?eia?, a neaiaea
nouanoaaiia oieueei auniei/anoioiay ninoaaeythuay, oi oaaee/eoue
?ac?aoaiea iiaeii oieueei eciaiea ia?aiao?u iaoiaea. A ea/anoaa iaoiaea,
ia iaeaaeathuaai iiaeiaiiai ?iaea iaaeinoaoeaie, aue i?aaeeiaeai aiia?ao
aaeaeao aiaeeca. [2]

3.3 Iniiaiua iieiaeaiey aaeaeao-aiaeeca

?acee/atho aeene?aoiue e iai?a?uaiue aaeaeao aiaeec, aiia?ao eioi?uo
iiaeii i?eiaiyoue eae aeey iai?a?uaiuo, oae e aeey
aeene?aoiuo neaiaeia.

Ceaiae aiaeece?oaony iooai ?aceiaeaiey ii aaceniui ooieoeeyi,
iieo/aiiui ec iaeioi?iai i?ioioeia iooai naeaoee, ?anoyaeaiee e
naeaeaia (2). Ooieoeey-i?ioioei iacuaaaony aiaeece?othuei
(iaoa?eineei) aaeaeaoii.

Aaeaeao – ooieoeey aeieaeia oaeiaeaoai?youe 2-i oneiaeyi:

1. N?aaeiaa cia/aiea (eioaa?ae ii anae i?yiie) ?aaai 0.

2. Ooieoeey auno?i oauaaao i?e t ?.

Iau/ii, ooieoeey-aaeaeao iaicia/aaony aoeaie o.

A iauai neo/aa aaeaeao i?aia?aciaaiea ooieoeee f(t) auaeyaeeo oae:
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(2)

aaea t – inue a?aiaie, x – iiiaio a?aiaie, s – ia?aiao?, ia?aoiue
/anoioa, a (*) – icia/aao eiiieaenii-nii?yaeaiiia.

Aeaaiui yeaiaioii a aaeaeao aiaeeca yaeyaony ooieoeey-aaeaeao. Aiiaua
aiai?y, aaeaeaoii yaeyaony ethaay ooieoeey, ioaa/athuay aeaoi
auoaoeacaiiui oneiaeyi. Iaeaieueoae iiioey?iinoueth iieuecothony aeaa
ecia?aaeaiiuo ia ?enoiea 1 aaeaeaoa:

?en 1. I?eia?u aaeaeaoia.

Naa?oo ecia?aaeai aaeaeao “niia?a?i” (Mexican Hat), iacaaiiue oae
aeaaiaea?y naiaio aiaoiaio aeaeo. Ia ieaeiae /anoe ?enoiea 1 ecia?aaeai
aaeaeao Ii?ea. A?aoee ethaiai aaeaeaoa auaeyaeeo i?eia?ii oaeaea, eae e
aaeaeao Ii?ea. Caiaoei, /oi aaeaeao Ii?ea – eiiieaeniicia/iue, ia
?enoiea ecia?aaeaiu aai aauanoaaiiay e iieiay ninoaaeythuea.

Eoae, o ian eiaaony iaeioi?ay ooieoeey f(t), caaenyuay io a?aiaie.
?acoeueoaoii aa aaeaeao-aiaeeca aoaeao iaeioi?ay ooieoeey W(x,s),
eioi?ay caaeneo oaea io aeaoo ia?aiaiiuo: io a?aiaie e io /anoiou
(ia?aoii i?iii?oeeiiaeueii). Aeey eaaeaeie ia?u x e s ?aoeaio au/eneaiey
aaeaeao i?aia?aciaaiey neaaeothuee:

1. Ooieoeey aaeaeao ?anoyaeaaaony a s ?ac ii ai?eciioaee e a 1/s ?ac ii
aa?oeeaee.

2. Aeaeaa ii naeaeaaaony a oi/eo x. Iieo/aiiue aaeaeao iaicia/aaony
o(x,s).

3. I?iecaiaeeony on?aaeiaiea a ie?anoiinoe oi/ee s i?e iiiiue o(x,s).

A ?acoeueoaoa au?eniauaaaony aiieia iaaeyaeiay ea?oeia, eeethno?e?othuay
/anoioii-a?aiaiiua oa?aeoa?enoeee neaiaea. Ii ine aanoeenn
ioeeaaeuaaaony a?aiy, ii ine i?aeeiao – /anoioa (eiiaaea ?acia?iinoue
ine i?aeeiao auae?aaony oae: log(1/s), aaea s-/anoioa), a aaniethoiia
cia/aiea aaeaeao i?aia?aciaaiey aeey eiie?aoiie ia?u x e s ii?aaeaeyao
oeaao, eioi?ui aeaiiue ?acoeueoao aoaeao ioia?aaeai (/ai a aieueoae
noaiaie oa eee eiay /anoioa i?enoonoaoao a neaiaea a eiie?aoiue iiiaio
a?aiaie, oai oaiiaa aoaeao iooaiie).

?en 2. Aaeaeao i?aia?aciaaiea noaoeeiia?iiai neaiaea.

Aeaiiue ?enoiie iieacuaaao ?acoeueoaou aaeaeao aiaeeca aeey neaiaea,
i?aaenoaaeythuei ec naay iaeiaeaiea aeaoo neionieae ?acee/iie /anoiou.
*anoioiua oa?aeoa?enoeee aeaiiiai neaiaea ia iaiythony ai a?aiaie
(neaiae noaoeeiia?iue), /oi oi?ioi aeaeii ia aa?oiae /anoe ?enoiea 2.

Ii ?enoieo 3 oaeiaii n?aaieoue ?acoeueoaou, eioi?ua aeatho
i?aia?aciaaiea Oo?uea e aaeaeao i?aia?aciaaiea. Enoiaeiue neaiae
ecia?aaeai ia ?en (3a). Eae aeaeii ec ?en (3c) i?aia?aciaaiea Oo?uea
aeaao eioi?iaoeeth i oii niaeo?a /anoio, eioi?ue i?enoonoaoao a neaiaea
a i?iiaaeooea a?aiaie io 0 aei 1 nae., i?e yoii iai iaecaanoii eiaaea
eiaiii oa eee eiay /anoioa ?aaeueii i?enoonoaiaaea a neaiaea.

A oi aea a?aiy aaeaeao i?aia?aciaaiea (3b) aeaao en/a?iuaathuoth ea?oeio
aeeiaieee eciaiaiey /anoioiuo oa?aeoa?enoee ai a?aiaie. Ana yoi
oeacuaaao ia oi, /oi aaeaeao i?aia?aciaaiea nouanoaaiii aieaa
eioi?iaoeaii ii n?aaiaieth n i?aia?aciaaieai Oo?uea.

?en 3. N?aaiaiea iaoiaeia aiaeeca.

4. ?AAEECAOeEss AEAI?EOIA

4.1 Iaoiaeu au/eneaiey iai?a?uaiiai aaeaeao i?aia?aciaaiey e eo
n?aaiaiea n oi/ee c?aiey ?aaeecaoeee

Nouanoaoao aeaa ?aciuo iooe i?iaaaeaiey aaeaeao i?aia?aciaaiey. ?a/ue
eaeao i ?an/aoao ai a?aiaiiie e /anoioiie iaeanoyo. I?e ?aaioa ai
a?aiaiiie iaeanoe iu eiaai aeaei n ooieoeeyie, a?aoiaioaie eioi?uo
yaeythony a?aiaiiua ia?aiao?u, a a neo/aa /anoioiie – /anoioiua. A
/anoioiie iaeanoe eniieuecoaony iaoaieci auno?iai i?aia?aciaaiey Oo?uea.
[5c]

*anoioiay iaeanoue aeaao aiciiaeiinoue eniieueciaaoue aioiaua
i?ia?aiiiua i?iaeoeou aeey au/eneaiey auno?iai i?aia?aciaaiey Oo?uea. A
neo/aa ionoonoaey oaeiauo /anoioiue iaoiae nouanoaaiii oneiaeiyaony.
Aeai?eoi, ?aaeeciaaiiue a /anoioiie iaeanoe, ?aaioaao auno?aa. E
aeinoieinoaai aeai?eoia ai a?aiaiiie iaeanoe iiaeii ioianoe
ioiineoaeueioth i?inoioo a ?aaeecaoeee (i?ia?aiie?iaaiee). I?e
auiieiaiee ?aaiou auea aua?aia a?aiaiiay iaeanoue.

4.1.1 ?aaeecaoeey ai a?aiaiiie iaeanoe

I?aaeaea anaai, iai iaiaoiaeeii ii?aaeaeeoue iaoa?eineee aaeaeao.
Aeiionoei, iu aua?aee iaeioi?oth ooieoeeth, oaeiaeaoai?ythuoth
iaiaoiaeeiui oneiaeyi: o0(c), aaea c – aac?acia?iue ia?eiae. A aeaiiie
?aaioa ?anniao?eaaaony neo/ae iai?a?uaiiai aaeaeao i?aia?aciaaiey aeey
aeene?aoiiai neaiaea.

Eoae, iai aeaia a?aiaiiay na?ey X, ni cia/aieyie xn, a iiiaiou a?aiaie
n[0,N-1], aaea N – eiee/anoai ecia?aiee. Eaaeaeay aaee/eia ?acaeaeaia ii
a?aiaie ia iinoiyiioth aaee/eio dt. Iieo/ea iniiaioth oi?ioeo aeey
iaoa?eineiai aaeaeaoa, iaiaoiaeeii eiaoue aiciiaeiinoue eciaiyoue
?acia?u aaeaeaoa. Aeey yoiai no?ieony oae iacuaaaiue “ianooaae?iaaiiue”
aaeaeao eioi?ue aoaeao eiaoue aeae:

picscalex100010009000003540000000000120000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02200220011200000026060f001a00ffffffff00001000
0000c0ffffffa6ffffffe0000000c60100000b00000026060f000c004d61746854797065
000050000a00000026060f000a00ffffffff01000000000003000000000000000000

picscalex100010009000003720200000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a00400181200000026060f001a00ffffffff00001000
0000c0ffffffa5ffffffc0170000450400000b00000026060f000c004d61746854797065
0000e00009000000fa02000010000000000000002200040000002d010000050000001402
800208020500000013028002d6070500000014028002ee0a05000000130280025a0c0500
00001402800230110500000013028002fe1610000000fb0280fe00000000000090010000
00020002001053796d626f6c0002040000002d01010008000000320a00032e1701000000
f70008000000320a3a042e1701000000f80008000000320a0a022e1701000000f6000800
0000320a00036a1001000000e70008000000320a3a046a1001000000e80008000000320a
0a026a1001000000e60008000000320aee013c13010000002d0008000000320ad8019a12
01000000a20008000000320a00038a0c01000000f70008000000320a3a048a0c01000000
f80008000000320a0a028a0c01000000f60008000000320a0003280a01000000e7000800
0000320a3a04280a01000000e80008000000320a0a02280a01000000e60008000000320a
e002fc08010000003d0008000000320a0003060801000000f70008000000320a3a040608
01000000f80008000000320a0a02060801000000f60008000000320a0003420101000000
e70008000000320a3a04420101000000e80008000000320a0a02420101000000e6000800
0000320aee011404010000002d0008000000320ad801720301000000a20015000000fb02
80fe0000000000009001010000000402001054696d6573204e657720526f6d616e00007c
040000002d01020004000000f001010008000000320a0c04cf1301000000730008000000
320aee01ac1502000000647408000000320aee015c14010000006e0008000000320aee01
ce11010000006e0008000000320a0c045c0b01000000730008000000320aee01080b0200
0000647408000000320a0c04a70401000000730008000000320aee018406020000006474
08000000320aee013405010000006e0008000000320aee01a602010000006e0015000000
fb0280fe0000000000009001000000000402001054696d6573204e657720526f6d616e00
007c040000002d01010004000000f001020008000000320aee0122150100000029000800
0000320aee01441101000000280008000000320aee01fa0501000000290008000000320a
ee011c0201000000280015000000fb0220ff000000000000900100000000040200105469
6d6573204e657720526f6d616e00007c040000002d01020004000000f001010008000000
320a4003c90f01000000300008000000320a0601120e01000000320008000000320a0601
a60d010000002f0008000000320a0601220d01000000310010000000fb0280fe00000000
00009001010000020002001053796d626f6c0002040000002d01010004000000f0010200
08000000320ae002890e01000000790008000000320ae00204000100000079000a000000
26060f000a00ffffffff01000000000010000000fb021000070000000000bc02000000cc
0102022253797374656d00cc040000002d01020004000000f00101000300000000000000
0000 (3)

s – ia?aiao?, ia?aoiue /anoioa.

Au/eneaiea aaeaeao i?aia?aciaaiey yaeyaony naa?oeie eneiiie a?aiaiiie
na?ee n ooieoeeae-aaeaeaoii. Iniiaiay oi?ioea eiaao aeae :
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 (4)

a aeaiiii neo/aa (*) – icia/aao eiiieaenii-nii?yaeaiiia.

?acoeueoaoii ?an/aoa Wn(s) ii oi?ioea (4) aoaeao eiiieaeniia /enei. A
ea/anoaa eiia/iiai ?acoeueoaoa aa?aony aaniethoiia cia/aiea iieo/aiiiai
eiiieaeniiai /enea. [5a]

Aeie – noaia aeai?eoia:

iao

aea

iao

aea

4.1.2 ?aaeecaoeey a /anoioiie iaeanoe

Aaeaeao i?aia?aciaaiea iiaeii i?iaanoe a /anoioiie iaeanoe. Aeey yoiai
niiaa a ia?aoth i/a?aaeue iaiaoiaeeii ii?aaeaeeoue iaoa?eineee aaeaeao.
?an/ao ii aeaiiie noaia i?ienoiaeeo neaaeothuei ia?acii: i?aia?aciaaiea
Oo?uea naiiai aaeaeaoa (a aeaiiii neo/aa aoaeai ?anniao?eaaoue aaeaeao
Ii?ea) neiioeaio?e?iaaii aie?oa iaeioi?ie auaeaeaiiie /anoiou 0 ? 0.
Iiyoiio i?aia?aciaaiea Oo?uea aaeaeaoa, ?anoyiooiai a s ?ac, aoaeao
neiioeaio?e?iaaii aie?oa /anoiou 0/s (ni ?en. 4).

?en 4. I?aia?aciaaiea Oo?uea ooieoeee aaeaeaoa.

Oae eae naa?oea ooieoeee yeaeaaeaioia eo ia?aiiiaeaieth a /anoioiie
iaeanoe, “no?iea” s = const ia ecia?aaeaiee aaeaeao i?aia?aciaaiey
iieacuaaao yaiethoeeth eco/aaiie ooieoeee ia /anoioao, aeeceeo 0/s. Oi
anoue oiiiaeaiea Oo?uea-niaeo?a enoiaeiie ooieoeee ia iee a oi/ea 0/s a
/anoioiie iaeanoe (oi anoue ia Oo?uea-ia?ac ?anoyiooiai aaeaeaoa)
au?acaao ec yoie ooieoeee ana oi, /oi aeaao aeeaae a aa niaeo? ia
/anoioao, aeeceeo 0/s. A ?acoeueoaoa iieo/aaony ?acaa?oea niaeo?aeueiiai
eiiiiiaioa ai a?aiaie. [1]

Iniiaiua oi?ioeu eiatho aeae:
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 (5)

aaea (*) – icia/aao eiiieaenii-nii?yaeaiiia, a ciae (^) –
i?aia?aciaaiea Oo?uea.

picscalex122010009000003040200000300150000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c024004000d1200000026060f001a00ffffffff00001000
0000c0ffffffb1ffffffc00c0000f10300000b00000026060f000c004d61746854797065
0000e00009000000fa02000010000000000000002200040000002d010000050000001402
200240030500000013022002a60410000000fb02c0fd0000000000009001000000020002
001053796d626f6c0002040000002d01010008000000320ad902ed0401000000e5001000
0000fb0220ff0000000000009001000000020002001053796d626f6c0002040000002d01
020004000000f001010008000000320afa00b605010000002d0008000000320aef038005
010000003d0008000000320ad401cc08010000002d0010000000fb0280fe000000000000
9001000000020002001053796d626f6c0002040000002d01010004000000f00102000800
0000320a80020302010000003d0015000000fb0220ff0000000000009001000000000402
001054696d6573204e657720526f6d616e000069040000002d01020004000000f0010100
08000000320afa00210601000000310008000000320aef03000601000000300008000000
320ad4016a0b010000002f0008000000320ad401500901000000320015000000fb0280fe
0000000000009001000000000402001054696d6573204e657720526f6d616e0000690400
00002d01010004000000f001020008000000320a9001930301000000310008000000320a
6e026e0001000000880015000000fb0220ff000000000000900101000000040200105469
6d6573204e657720526f6d616e000069040000002d01020004000000f001010008000000
320afa000105010000004e0008000000320aef030605010000006e0008000000320ad401
d80b010000004e0009000000320ad401380a03000000696b6e0008000000320ae0028607
010000006e0008000000320ae002fd00010000006b0015000000fb0280fe000000000000
9001010000000402001054696d6573204e657720526f6d616e000069040000002d010100
04000000f001020008000000320a80020b0801000000650008000000320a8002d5060100
0000780008000000320aaa036c03010000004e0008000000320a80024c00010000007800
10000000fb0220ff0000000000009001010000020002001053796d626f6c000204000000
2d01020004000000f001010008000000320ad401be090100000070000a00000026060f00
0a00ffffffff01000000000010000000fb021000070000000000bc02000000cc01020222
53797374656d00cc040000002d01010004000000f001020003000000000000000000
(6)
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 (7)

Aeie – noaia aeai?eoia:

iao

aea

iao

aea

4.2 Auai? iaoa?eineiai aaeaeaoa

A ea/anoaa iaoa?eineiai aaeaeaoa iiaeoiaeeo ethaay ooieoeey,
oaeiaeaoai?ythuay aeaoi auoaoeacaiiui oneiaeyi. Aeey ?aaeecaoeee
aeai?eoia a ea/anoaa aiaeece?othuaai aaeaeaoa auei ?aoaii
ainiieueciaaoueny aaeaeaoii Ii?ea (?en. 5). Yoi auei naeaeaii ii o?ai
i?e/eiai:

· aaeaeao Ii?ea iaeei ec iaeaieaa iiioey?iuo [1] e oe?iei i?eiaiyaony

· ii iaeaaeaao cia/eoaeueiie iaaeyaeiinoueth

· ii i?ino a au/eneeoaeueiii ieaia, /oi onei?yao ?aaioo aeai?eoia

?en 5. Aaeaeao Ii?ea.

Oaeoe/anee aaeaeao Ii?ea yaeyaony i?iecaaaeaieai eiiieaeniie neionieaeu
ia aaonneai.
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, (8)

aaea yaeyaony cia/aieai aaeaeao ooieoeee n aac?acia?iui ia?eiaeii , a 0
– aieiiaie ia?aiao? (i?e ?aaeecaoeee 0=6).

Iaiaoiaeeii oaeaea ioiaoeoue, /oi aaeaeao Ii?ea yaeyaony
eiiieaeniicia/iui, oi anoue eiaao aeaenoaeoaeueioth e iieioth /anoe.

4.3 Nenoaia “eeeaio-na?aa?” eae niinia iiauoaiey yooaeoeaiinoe
aeai?eoia

Nai? eioi?iaoeee iau/ii iiae?acoiaaaao iaeiieaiea aieueoiai iauaia
aeaiiuo, eioi?ua o?aaotho ouaoaeueiie ia?aaioee. *anoi iiaeiaiue aiaeec
i?aaeoniao?eaaao eniieueciaaiea iiuiiai aei?iainoiyuaai au/eneeoaeueiiai
iai?oaeiaaiey. Eiiaaea, a neeo niaoeeoeee yenia?eiaioa, iai?oaeiaaiea,
iaiaoiaeeiia aeey niyoey yenia?eiaioaeueiuo aeaiiuo e iai?oaeiaaiea,
iaiaoiaeeiia aeey eo ia?aaioee, aiiaua iaaiciiaeii ?acianoeoue a
i?aaeaeao iaeiiai enneaaeiaaoaeueneiai eiiieaena. I?e yoii aicieeaao
caaea/a iauaaeeiaiey anae nenoaiu a aaeeiue eiiieaen e iaania/aiey
yooaeoeaiie ia?aaea/e aeaiiuo iaaeaeo ioaeaeueiuie eiiiiiaioaie. A
aeaiiie ?aaioa i?aaeeiaeai aa?eaio nicaeaiey ?ani?aaeaeaiiie nenoaiu
”eeeaio-na?aa?”, ninoiyuae ec aeaoo iacaaeneiuo i?eeiaeaiee, naycue
iaaeaeo eioi?uie inouanoaeyaony ii oaoiieiaee “Socket Connection”. A
aeaiiii neo/aa acaeiiaeaenoaea no?ieony ia iniiaa “aiacae” Windows. Aeey
onoaiiaeaiey nayce niioaaonoaothuei ia?acii iano?aeaathony TCP/IP
i?ioieieu iaoei “eeeaioa” e “na?aa?a”, a oaeaea, eaeaioeoeeaoeey ii?oia
“i?ineooeaaiey”. “Socket Connection” iaania/eaaao i/aiue auno?oth
naycue, a neaaeiaaoaeueii, aa?aioe?oao yooaeoeaioth ia?aaea/o aeaiiuo.
Yoi ii?aaaeaii a oii neo/aa, anee aieueoie iauai nia?aiiuo aeaiiuo
ia?anueaoue ia iiuiue na?aa?-ia?aaio/ee, a caoai iieo/aoue iacaae
?acoeueoaou neiaeiuo au/eneaiee.

4.3.1 Ooieoeee “eeeaioa”

A i?aaeeiaeaiiie nenoaia ooieoeee i?eeiaeaiey eeeaioa ninoiyo a:

· oi?ie?iaaiee neaiaea, iiaeeaaeauaai aeaeueiaeoaio aiaeeco (aeaiiue
neaiae eiaao ianoaoeeiia?iua /anoioii-a?aiaiiua oa?aeoa?enoeee)

· aecoaeecaoeee caaeaiiiai neaiaea

· iano?ieea niaaeeiaiey /a?ac “Socket Connection”

· iaania/aiee ia?aaea/e aeaiiuo, iiaeeaaeaueo ia?aaioea

· iaania/aiee i?eaia ia?aaioaiiuo aeaiiuo

· iaania/aiee iaaeyaeiie a?aoe/aneie aecoaeecaoeee iieo/aiiuo
?acoeueoaoia

· iaania/aiee auai?i/iiai eiio?iey iieo/aiiiai ?acoeueoaoa

4.3.2 Ooieoeee “na?aa?a”

A i?aaeeiaeaiiie nenoaia ooieoeee i?eeiaeaiey na?aa?a ninoiyo a:

· iaania/aiee i?eaia aeaiiuo, iiaeeaaeaueo aiaeeco

· ia?aaioea aeaiiuo n iiiiuueth cai?ia?aiie?iaaiiiai aeai?eoia
iai?a?uaiiai aaeaeao i?aia?aciaaiey

· iaania/aiee aecoaeueiiai iaaethaeaiey ca oiaeii ia?aaioee iinooieaoeo
aeaiiuo

· iano?ieea niaaeeiaiey /a?ac “Socket Connection”

· iaania/aiee ia?aaea/e ia?aaioaiiuo aeaiiuo

5. CAEETH*AIEA

A oiaea auiieiaiey ?aaiou auee ?anniio?aiu neaaeothuea iiaeoiaeu e
aiaeeco ianoaoeeiia?iuo neaiaeia:

· i?aia?aciaaiea Oo?uea

· eieaeueiia i?aia?aciaaiea Oo?uea

· iai?a?uaiia aaeaeao i?aia?aciaaiea

Auea i?iaaaeaia n?aaieoaeueiay ioeaiea aeaiiuo iaoiaeia e naeaeaiu
auaiaeu ioiineoaeueii aeinoieinoa e iaaeinoaoeia oaeiauo, a oaeaea
noaiaie eo i?eiaieiinoe e oai eee eiui caaea/ai.

I?aia?aciaaiea Oo?uea ia aeaao eioi?iaoeee i aeeiaieea eciaiaiey
/anoioiuo oa?aeoa?enoee ai a?aiaie. Eieaeueiia i?aia?aciaaiea Oo?uea
eiaao iinoiyiiia ?ac?aoaiea ii /anoioa (ii a?aiaie) aia caaeneiinoe io
iaeanoe /anoio (a?aiai), a eioi?uo i?iecaiaeeony enneaaeiaaiea. Iiyoiio,
anee, iai?eia?, a neaiaea nouanoaaiia oieueei auniei/anoioiay
ninoaaeythuay, oi oaaee/eoue ?ac?aoaiea iiaeii oieueei eciaiea ia?aiao?u
iaoiaea. Aeey aiaeeca ianoaoeeiia?iuo neaiaeia n oe?ieei niaeo?ii /anoio
oi?ioi iiaeoiaeeo aiia?ao iai?a?uaiiai aaeaeao i?aia?aciaaiey, ia
iaeaaeathuee iiaeiaiuie iaaeinoaoeaie.

?anniio?aiu aeaa aa?eaioa ?aaeecaoeee iai?a?uaiiai aaeaeao
i?aia?aciaaiey: a /anoioiie e a?aiaiiie iaeanoyo. A oiaea eo n?aaiaiey
auei i?eiyoi ?aoaiea i?iaiaeeoue ?aaeecaoeeth ai a?aiaiiie iaeanoe.
*anoioiay iaeanoue i?aaeiieaaaao eniieueciaaiea aiia?aoa i?aia?aciaaiey
Oo?uea. N oi/ee c?aiey ?aaeecaoeee /anoioiay iaeanoue oaeiaia i?e
iaee/ee aioiauo aeaeeioae au/eneaiey i?aia?aciaaiey Oo?uea. A neo/aa
ionoonoaey oaeiauo ?aaeecaoeeth oaeiaiaa i?iaiaeeoue ai a?aiaiiie
iaeanoe.

Ia iniiaa iai?a?uaiiai aaeaeao i?aia?aciaaiey ?aaeeciaaia i?ia?aiia,
iicaieythuay i?iaiaeeoue aiaeec aeene?aoiuo ianoaoeeiia?iuo neaiaeia.

A oeaeyo onei?aiey ?aaiou aeai?eoia i?aaeeiaeaia e ?ac?aaioaia
?ani?aaeaeaiiay nenoaia “eeeaio-na?aa?”, a eioi?ie acaeiiaeaenoaea
iaaeaeo eiiiiiaioaie inouanoaeyaony ii oaoiieiaee “Socket Connection”.

6. NIENIE EEOA?AOO?U

1. “Eiiiuethoa??a” ?8 1998a. 2 ia?oa

2. “Iai?a?uaiia aaeaeao i?aia?aciaaiea eae n?aaenoai aiaeeca YEA
/aeiaaea” (iiynieoaeueiay caienea e o/aaii-enneaaeiaaoaeueneie ?aaioa)
Oaoecia A.?. 1998a.

3. “Delphi 3” Osier, Batson and Grobman , Borland Press 1997

4. “Delphi 2” I. Eaioo, 1 e 2 oiia, 1997a

5. Enoi/ieee a Internet:

a) http://relpress.website.ru/currier/5/wavelet/wavelet.htm;

b) http://www.public.iastate.edu/~rpolikar/WAVELETS/WTpart1.html

c) http://paos.colorado.edu/research/wavelets/

6. I?EEIAEAIEss

a) Iienaiea i?ia?aiiu.

?en.6 Neaiae.

A ?acaeaea “Neaiae” eeeaioa oi?ie?oaony ianoaoeeiia?iue neaiae, n
eioi?ui aeaeaa i?iaiaeeony aaeaeao aiaeec.

?en.7 Niaaeeiaiea.

A ?acaeaea “Niaaeeiaiea” iano?aeaaaony naycue iaaeaeo eiiiiiaioaie /a?ac
TCP/IP i?ioieie, a oaeaea ioia?aaeaaony ninoiyiea i?eeiaeaiey-eeeaioa.

?en.8 ?acoeueoao.

A ?acaeaea “?acoeueoao” i?iaiaeeony aecoaeecaoeey iieo/aiiiai
?acoeueoaoa. Ia?aeeth/aoaeue “N auaeaeaieai” aeeth/aao iioeeth
auaeaeaiey /anoiou, iaeneiaeueii i?enoonoaothuae a neaiaea a eiie?aoiue
iiiaio a?aiaie.

A ?acaeaea “Eiio?ieue” niaea?aeaony auai?i/iua ?acoeueoaou aaeaeao
i?aia?aciaaiey (i?e n=20 e n=80).

?en. 9 Na?aa?.

A ooieoeee na?aa?a aoiaeeo i?eai, ia?aaioea e aica?auaiea ?acoeueoaoa ii
TCP/IP i?ioieieo.

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