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[(b)-1000(orho)-1000(o)-1000(d)-14000(of)-13000(the)-15000(sp)-1000(ectrum,)-14000(and)-14000(the)-15000(e\013ect)-15000(of)-14000(smo)-1000(othing)-12000(v)]TJ 1009 0 TD [(anishes)-14000(as)-14000(the)]TJ -1788 48.9999 TD [(smo)-1000(othing)-12000(k)]TJ 223 0 TD [(ernel)-14000(is)-14000(narro)]TJ 239 0 TD (w)Tj 29 0 TD [(ed)-14000(to)-14000(an)-14000(impulse.)]TJ -429 100 TD [(More)-15000(precisely)]TJ 260 0 TD [(,)-14000(giv)]TJ 80 0 TD [(en)-14000(a)-14000(windo)]TJ 198 0 TD (w)Tj /T5 1 Tf 43 0 TD (W)Tj /T12 1 Tf 58.9999 0 TD [(of)-13000(in)]TJ 81.0001 0 TD (tensities)Tj /T5 1 Tf 162 0 TD (I)Tj /T12 1 Tf 21 0 TD (\()Tj /T10 1 Tf 16 0 TD (x)Tj /T12 1 Tf 25 0 TD [(\),)-15000(w)]TJ 72 0 TD [(e)-14000(describ)-1000(e)-16000(i)0(t)-14000(b)]TJ 256.9999 0 TD [(y)-14000(the)-14000(most)-13000(signi\014can)]TJ 377.0001 0 TD [(t)-14000(comp)-1000(onen)]TJ 213 0 TD [(ts)-14000(of)-13000(a)]TJ -1926 50 TD 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(\014)Tj T* (\014)Tj /T12 1 Tf 669.0001 -2.0001 TD (\(1\))Tj -1987 88 TD (where)Tj /T5 1 Tf 120 0 TD (g)Tj /T12 1 Tf 21 0 TD (\()Tj /T10 1 Tf 16 0 TD (x)Tj /T12 1 Tf 25 0 TD [(\))-15000(i)0(s)-14000(a)-14000(wide)-14000(Gaussian)-14000(windo)]TJ 491.9999 0 TD [(w.)-17000(This)-14000(windo)]TJ 262.0001 0 TD [(wing,)-13000(as)-14000(will)-12000(b)-1000(e)-15000(illustrated)-14000(b)-1000(elo)]TJ 570 0 TD [(w,)-13000(is)-14000(equiv)]TJ 191.9999 0 TD (alen)Tj 73 0 TD [(t)-14000(t)0(o)-14000(smo)-1000(othing)]TJ -1770.9999 50 TD [(the)-16000(F)]TJ 97 0 TD [(ourier)-15000(transform)-14000(of)]TJ /T5 1 Tf 361 0 TD (I)Tj /T12 1 Tf 21 0 TD (\()Tj /T10 1 Tf 16 0 TD (x)Tj /T12 1 Tf 25 0 TD [(\),)-16000(but)-16000(is)-15000(computed)-14000(more)-14000(e\016cien)]TJ 584.9999 0 TD (tly)Tj 47 0 TD 22 Tc (.W)Tj 74.0001 0 TD 0 Tc [(e)-14000(then)-16000(normalize)]TJ /T5 1 Tf 318.9999 0 TD (S)Tj /T4 1 Tf 25 6 TD (W)Tj /T12 1 Tf 38 -6 TD (\()Tj /T10 1 Tf 16 0 TD (f)Tj /T12 1 Tf 20.0001 0 TD [(\))-14000(and)-15000(restrict)-17000(it)-15000(to)-15000(its)]TJ /T5 1 Tf -1644 49.0001 TD (p)Tj /T12 1 Tf 21 0 TD [(-th)-18000(p)-1000(ercen)]TJ 187 0 TD [(tile)-20000(most)-16000(signi\014can)]TJ 351 0 TD [(t)-18000(comp)-1000(onen)]TJ 217 0 TD [(ts,)-19000(that)-18000(is,)-18000(to)-18000(those)-19000(frequency)-20000(samples)-17000(that)-18000(that)-18000(are)-19000(greater)-19000(than)]TJ /T5 1 Tf 1243 0 TD (p)Tj /T12 1 Tf -2019 49.9999 TD [(p)-1000(ercen)]TJ 116 0 TD [(t)-19000(o)0(f)-17000(all)-15000(the)-18000(samples)-16000(in)-17000(the)-18000(sp)-1000(ectrum,)-18000(and)-17000(w)]TJ 816 0 TD [(e)-17000(normalize)-16000(the)-18000(result.)-28000(Let)]TJ /T5 1 Tf 522 0 TD (\013)Tj /T4 1 Tf 27 6.0001 TD (W)Tj /T12 1 Tf 36.9999 -6.0001 TD (\()Tj /T5 1 Tf 16 0 TD (p)Tj /T12 1 Tf 21 0 TD [(\))-17000(b)-1000(e)-18000(the)]TJ /T5 1 Tf 168 0 TD (p)Tj /T12 1 Tf 21.0001 0 TD [(-th)-17000(p)-1000(ercen)]TJ 186 0 TD [(tile)-19000(of)]TJ -1930 50 TD [(the)-16000(v)]TJ 93 0 TD [(alues)-15000(in)]TJ /T5 1 Tf 155 0 TD (S)Tj /T4 1 Tf 25 6.0001 TD (W)Tj /T12 1 Tf 39 -6.0001 TD (\()Tj /T10 1 Tf 16 0 TD (f)Tj /T12 1 Tf 20 0 TD [(\),)-14000(that)-16000(is,)-15000(let)]TJ /T5 1 Tf 250.9999 0 TD (p)Tj /T12 1 Tf 36.0001 0 TD [(p)-1000(ercen)]TJ 116 0 TD [(t)-17000(o)0(f)-15000(the)-16000(sp)-1000(ectral)-17000(comp)-1000(onen)]TJ 496 0 TD [(ts)-15000(b)-1000(e)-16000(b)-1000(elo)]TJ 179 0 TD (w)Tj /T5 1 Tf 44.9999 0 TD (\013)Tj /T4 1 Tf 27 6.0001 TD (W)Tj /T12 1 Tf 38 -6.0001 TD (\()Tj /T5 1 Tf 16 0 TD (p)Tj /T12 1 Tf 21 0 TD [(\).)-23000(Then,)-16000(w)]TJ 202.0001 0 TD [(e)-15000(de\014ne)-17000(a)]TJ /T5 1 Tf 190.9998 0 TD (p)Tj /T12 1 Tf 21.0002 0 TD (-th)Tj -1987 50 TD [(p)-1000(ercen)]TJ 116 0 TD (tile)Tj /T11 1 Tf 72.9999 0 TD (signi\014c)Tj 125 0 TD (anc)Tj 61 0 TD [(e)-16000(mask)]TJ /T12 1 Tf 140.0001 0 TD [(as)-14000(follo)]TJ 129 0 TD (ws:)Tj /T5 1 Tf -57 98.0001 TD (m)Tj /T4 1 Tf 36 5.9999 TD (W)Tj /T12 1 Tf 37.9999 -5.9999 TD (\()Tj /T10 1 Tf 16 0 TD 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0 TD (f)Tj /T12 1 Tf 20.0001 0 TD 11 Tc (\)=)Tj /T5 1 Tf 126 -28.0001 TD 0 Tc (m)Tj /T4 1 Tf 36 6 TD (W)Tj /T12 1 Tf 39 -6 TD (\()Tj /T10 1 Tf 15.9999 0 TD (f)Tj /T12 1 Tf 20.0001 0 TD (\))Tj /T5 1 Tf 16 0 TD (S)Tj /T4 1 Tf 25 6 TD (W)Tj /T12 1 Tf 36.9999 -6 TD (\()Tj /T10 1 Tf 16.0001 0 TD (f)Tj /T12 1 Tf 20 0 TD (\))Tj ET q 82.08 0 0 -0.48 281.976 285.036 cm BI /W 1 /H 1 /BPC 1 /IM true ID EI Q BT /T3 1 Tf 0.24 0 0 -0.24 282 282.9 Tm 6 Tc (PP)Tj /T5 1 Tf 100.9999 31 TD 0 Tc (m)Tj /T4 1 Tf 36.0001 6 TD (W)Tj /T12 1 Tf 38 -6 TD (\()Tj /T10 1 Tf 15.9999 0 TD (f)Tj /T12 1 Tf 20.0001 0 TD (\))Tj /T5 1 Tf 16 0 TD (S)Tj /T4 1 Tf 25 6 TD (W)Tj /T12 1 Tf 38 -6 TD (\()Tj /T10 1 Tf 16 0 TD (f)Tj /T12 1 Tf 19.9999 0 TD (\))Tj /T5 1 Tf 32 -29 TD (:)Tj /T12 1 Tf 709.0001 0 TD (\(3\))Tj -1987 100 TD [(Equations)-13000(\(1\))-13000(through)-13000(\(2\))-13000(together)-13000(comprise)-13000(our)-13000(de\014nition)-12000(of)-13000(sp)-1000(ectral)-14000(descriptor.)-19000(W)]TJ 1526 0 TD 12 Tc [(en)12000(o)]TJ 72.9999 0 TD 0 Tc [(w)-13000(analyze)-12000(this)-13000(de\014nition)]TJ -1598.9999 49.9999 TD [(in)-13000(some)-13000(detail.)]TJ 62 99 TD (Remo)Tj 105 0 TD [(ving)-14000(phase)-16000(information)-13000(discards)-17000(p)-1000(oten)]TJ 699 0 TD [(tially)-15000(useful)-16000(information.)-22000(F)]TJ 503 0 TD [(or)-15000(instance,)-17000(\014gure)-17000(1)-16000(sho)]TJ 442 0 TD [(ws)-16000(a)-16000(texture)]TJ -1811 50 TD [(from)-16000(Bro)-1000(datz's)-18000(album)]TJ /T9 1 Tf 407.9999 -14.9999 TD (Bro66)Tj /T12 1 Tf 102.9999 14.9999 TD [(on)-17000(the)-18000(left)-17000(and)-17000(the)-18000(corresp)-1000(onding)-19000(texture)-18000(without)-17000(phase)-18000(information)-15000(on)-17000(the)-18000(righ)]TJ 1502 0 TD (t.)Tj -2013 50 TD [(The)-15000(texture)-16000(without)-15000(phase)-15000(lo)-1000(oks)-14000(more)-14000(random)-13000(than)-15000(the)-16000(original,)-12000(and)-15000(consequen)]TJ 1463.9999 0 TD [(tly)-16000(p)-1000(erceptually)-15000(di\013eren)]TJ 437.0001 0 TD [(t:)-21000(some)]TJ -1901 50 TD [(p)-1000(oten)]TJ 101 0 TD [(tially)-19000(imp)-1000(ortan)]TJ 282 0 TD [(t)-19000(information)-18000(has)-20000(b)-1000(een)-22000(discarded.)]TJ 673 0 TD [(This)-20000(problem)-19000(can)-21000(b)-1000(e)-21000(addressed)-22000(b)]TJ 632.9999 0 TD [(y)-21000(preserving)-21000(phase)]TJ -1688.9999 49 TD [(information)-15000(after)-18000(remo)]TJ 420.9999 0 TD [(ving)-16000(the)-19000(b)-1000(est-\014t)-19000(plane)-18000(to)-17000(the)-19000(phase,)-19000(for)-17000(p)-1000(osition)-18000(in)]TJ 956.9999 0 TD (v)Tj 20.0001 0 TD [(ariance,)-17000(and)-18000(smo)-1000(othing,)-17000(as)-18000(for)-17000(the)]TJ -1398 50 TD [(magnitude)-12000(information.)-15000(Ho)]TJ 496.9999 0 TD (w)Tj 29 0 TD (ev)Tj 39 0 TD [(er,)-14000(w)]TJ 89 0 TD [(e)-14000(d)0(o)-14000(not)-14000(pursue)-15000(this)-14000(direction)-14000(in)-13000(this)-14000(pap)-1000(er.)]TJ -592 100.0001 TD (P)Tj 27 0 TD [(erio)-1000(dograms)-19000(are)-20000(usually)-19000(de\014ned)]TJ /T9 1 Tf 592 -15.0001 TD (OS75)Tj /T12 1 Tf 100.0001 15.0001 TD [(in)-19000(terms)-20000(of)-19000(the)]TJ /T11 1 Tf 307 0 TD (squar)Tj 94.9999 0 TD (e)Tj 17.0001 0 TD (d)Tj /T12 1 Tf 41 0 TD [(magnitude)-18000(of)-19000(the)-21000(F)]TJ 366 0 TD [(ourier)-19000(transform)-19000(of)-19000(the)]TJ -1607 50 TD [(signal,)-16000(whic)]TJ 215 0 TD [(h)-17000(i)0(s)-17000(the)-18000(F)]TJ 184 0 TD [(ourier)-16000(transform)-16000(of)-17000(the)-17000(signal's)-16000(auto)-1000(correlation)-17000(function.)-27000(This)-17000(square)-17000(is)-17000(imp)-1000(ortan)]TJ 1515 0 TD [(t)-15000(when)]TJ -1914 50 TD 1 Tc (po)Tj 44 0 TD 0 Tc (w)Tj 29 0 TD [(er)-14000(considerations)-15000(m)]TJ 354 0 TD [(ust)-12000(b)-1000(e)-15000(made,)-12000(but)-14000(is)-14000(irrelev)]TJ 476 0 TD (an)Tj 42.9999 0 TD [(t)-14000(for)-13000(our)-14000(purp)-1000(oses.)]TJ -883.9999 98.9999 TD (T)Tj 27 0 TD 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