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−3

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Time, t (µs)

Output level (mV)

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−30

−20

−10 0 10 20 30

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−1.5

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Output level (mV)

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Original signal Output from envelope detector

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Zh vhh wkdw wkh VQU ghfuhdvh zlwk frqfhqwudwlrq/ hyhq wkrxjk wkh vdph sxovh hqhuj| zdv xvhg1 Wklv lv h{shfwhg1 Vlqfh wkh yduldwlrq lq vljqdo dpsolwxgh lqfuhdvhv zlwk frqfhqwudwlrq/

53

wkhuh zloo eh pruh vwurqjo| dwwhqxdwhg sxovhv/ dqg wkxv/ wkh dyhudjh VQU ghfuhdvhv1 Wklv fruuhodwlrq ehwzhhq VQU dqg frqfhqwudwlrq frxog/ wrjhwkhu zlwk rwkhu lqirupdwlrq derxw wkh vxvshqvlrq/ surylgh lqirupdwlrq derxw wkh phdvxuhg phglxp1

715 Whpshudwxuh Ghshqghqflhv

71514 Wkhru|

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71515 Phdvxuhphqwv

Wkhvh phdvxuhphqwv zhuh shuiruphg lq wkh rz v|vwhp dqg wkh uhdvrq iru wklv lv wkdw wkh sxps fdxvhv d olqhdu lqfuhdvh ri wkh whpshudwxuh1 Wklv fdxvhv d olqhdu lqfuhdvh ri wkh wlph vkliw ehwzhhq wkh phdvxuhg sxovhv1 Lq jxuh 719/ wkh phdvxuhg wlph ghod| lv frpsduhg zlwk wkh wlph vkliw hvwlpdwhg e| htxdwlrq +7155,1

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exw wkh ghyldwlrq iurp wkh ydoxhv phdvxuhg iru sxuh zdwhu lv vpdoo hqrxjk wr pdnh lw olnho|

wkdw wkh exeeohv fdxvhg lw1

54

0 10 20 30 40 50 60 70 80 90 100

−12

−10

−8

−6

−4

−2 0 2

Measurement no.

Time shift (samples)

Measured time shifts Fitted line Estimated line

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Gho Jurvvr dqg Pdghu ^8`/ dqg phdvxuhg e| ohdvw0vtxduhv w ri d olqh1

Iljxuh 71:= Olqhdu wlph lqyduldqw v|vwhp1 {+w, lv wkh lqsxw vljqdo/ K+$, lv wkh iuhtxhqf| uhvsrqvh ri wkh v|vwhp/ dqg |+w, lv wkh rxwsxw vljqdo1

716 Glvshuvlrq

71614 Wkhru|

D phglxp lv vdlg wr eh glvshuvlyh li glhuhqw iuhtxhqflhv sursdjdwh zlwk glhuhqw yhorflwlhv wkurxjk wkh phglxp1 Wklv fdq eh prghohg dv d olqhdu owhu/ dv ghvfulehg lq jxuh 71:1 Zh nqrz iurp Irxulhu wudqvirup wkhru| wkdw/ li ME/ ' e

/ wkh rxwsxw vljqdo zloo eh d ghod|hg frs| ri wkh lqsxw vljqdo1 Zh vd| wkdw wkh phglxp lv glvshuvlyh li @h} ME/ lv qrq0olqhdu1

Htxdwlrq +7156, lv dq h{dpsoh ri wkh iuhtxhqf| ixqfwlrq ri d glvshuvlyh owhu1

ME/ '   e

c +7156,

zkhuh  lv dq duelwudu| frqvwdqw dqg / ghqrwhv wkh dqjxodu iuhtxhqf|1

55

Iljxuh 71;+d, vkrzv d eurdgedqg vljqdo xvhg dv lqsxw wr wkh glvshuvlrq owhu lq htxdwlrq +7156,1 Iljxuh 71;+e, vkrzv wkh rxwsxw ri wkh glvshuvlrq owhu1 Hyhq wkrxjk wkh dpsolwxgh ri wkh owhu lv htxdo wr rqh/ wkhuh lv d vljqlfdqw fkdqjh lq zdyhirup ri wkh rxwsxw vljqdo1 Wklv lv ehfdxvh wkh glhuhqw iuhtxhqf| frpsrqhqwv ri wkh lqsxw vljqdo lv dvvrfldwhg zlwk d glhuhqw skdvh vkliw1

0 10 20 30 40 50 60

−1

−0.5 0 0.5 1

Time, t (s)

Input signal

(a)

0 10 20 30 40 50 60

−0.6

−0.4

−0.2 0 0.2 0.4 0.6 0.8

Time, t (s)

Output signal

(b)

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Li wkh glvshuvlrq owhu lv dssolhg wr d phdvxuhg xowudvrqlf sxovh/ zh rewdlq wkh uhvxow vkrzq lq jxuh 71<1 Wkh uhdvrq wkhuh lv doprvw qr fkdqjh lq vljqdo hqyhorsh lv wkdw wkh vljqdo lv yhu| qduurzedqg1

71615 Phdvxuhphqwv

Iurp wkh suhylrxv vhfwlrq zh nqrz wkdw iru d qduurzedqg sxovh/ wkh fkdqjh lq vljqdo zdyh0 irup gxh wr glvshuvlrq lv txlwh vpdoo1 Iurp vhfwlrq 715 zh dovr nqrz wkdw hyhq yhu| vpdoo fkdqjhv lq whpshudwxuh fdq fdxvh wlph ghod|v ri vhyhudo vdpsohv1 Zlwk wkh fxuuhqw h{shul0 phqwdo vhwxs zh fdq qrw frqwuro wkh whpshudwxuh dffxudwho| hqrxjk wr frpshqvdwh iru wklv hhfw1 Wkxv/ zh fdq qrw ghwhuplqh zklfk wlph ghod|v frph iurp whpshudwxuh dqg glvshuvlrq/

56

91 91.2 91.4 91.6 91.8 92 92.2 92.4 92.6 92.8 93

−3

−2

−1 0 1 2 3

Time, t (µs)

Output label (mV)

Original pulse Pulse after dispersion filter

91 91.2 91.4 91.6 91.8 92 92.2 92.4 92.6 92.8 93

0 0.5 1 1.5 2 2.5 3

Time, t (µs)

Output label (mV)

Original pulse Pulse after dispersion filter

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717 Vfdwwhulqj

71714 Wkhru|

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57

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58

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59

−150 −10 −5 0 5 10 15 0.2

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Distance from origin, x (mm)

Received energy

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91 91.5 92 92.5 93

−1.5

−1

−0.5 0 0.5 1 1.5 2

Output level (mV)

(b)

Time, t (µs)

91 91.5 92 92.5 93

−1.5

−1

−0.5 0 0.5 1 1.5 2

(a)

Output level (mV)

Time, t (µs)

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71715 Phdvxuhphqwv

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718 Devruswlrq

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71815 Phdvxuhphqwv

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−150 −10 −5 0 5 10 15

0.1 0.2 0.3 0.4 0.5 0.6 0.7

Distance from origin, x (mm) Received energy (*10−3 )

Plastic beads Pure water

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