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1 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal 2 2 = (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
2 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal mm 14.5mm (1, 1), (1, 2),,(9, 9) (1, 1) (5, 6) Δt = (5, 6) (5, 5) (4, 5) (4, 4) s 1 (t) s 2 (t) s 3 (t) s 4 (t) (5, 6) (5, 5) (4, 5) (4, 4).81λ λ λ xz (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
3 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal z [mm] Ch3 Ch4 Ch1 Ch2 5 5 x [mm] T =1/T (t)dt s (DC) i s (raw) i s 1 (t) s 2 (t) s 3 (t) s 4 (t) s i (t) =s (raw) i (t) s (DC) i (i =1, 2, 3, 4) s (raw) i (t) s (DC) i P BF (θ, φ) P BF (θ, φ) = 1 T T a(θ, φ) H s(t) 2 dt, = a(θ, φ) H R ss a(θ, φ). s(t) = [s 1 (t),s 2 (t),s 3 (t),s 4 (t)] T R ss R ss = 1 T s(t)s H (t)dt, T a(θ, φ) a(θ, φ) =[k r 1, k r 2, k r 3, k r 4 ] T, k r 1 r 2 r 3 r 4 k θ φ k(θ, φ) =k[sin θ cos φ, sin θ sin φ, cos θ] T, k = 2π/λ λ = 3.6 y(t) =w1s 1 (t) +w2s 2 (t) +w3s 3 (t) +w4s 4 (t) =w H s(t) (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
4 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal w =[w 1,w 2,w 3,w 4 ] T y(t) 2 = w H s(t) 2 = w H s(t)(w H s(t)) H = w H s(t)s H (t)w, E[ y(t) 2 ] = w H R ss w E[] R ss =E[s(t)s H (t)] s(t) P C (θ, φ) P C (θ, φ) =minw w H R ss w, subject to w H a(θ, φ) =1. w E[ y(t) 2 ]=w H R ss w (θ, φ) (θ, φ) (θ, φ) E[ y(t) 2 ] w P C (θ, φ) P C (θ, φ) = 1 a H (θ, φ)(r ss + ɛi) 1 a(θ, φ), I ɛ ɛ = ɛ tr(r ss ) P C (θ, φ) θ φ (θ,φ ) w opt =argminw w H R ss w, subject to w H a =1, w a a = a(θ,φ ) θ φ arg max θ,φ P C (θ, φ) L L(w,λ ) = 1 2 wh R ss w +Re[λ (w H a 1)] = 1 2 wh R ss w λ (w H a 1) λ (w T a 1), λ L(w,λ ) w wl(w,λ )=R ss w + λ a =. w w = λ R 1 ss a, R ss 1 λ =. a H R 1 ss a w = R 1 ss a. a H R 1 ss a w R ss R ss Rss 1 w opt = (R ss + ɛ I) 1 a a H (R ss + ɛ I) 1 a. s DCMP (t) s DCMP (t) =w H opts(t). ɛ = ɛ tr(r ss ) ɛ w H s(t) s d (t) (θ,φ ) s i (t) (θ i,φ i ) G(θ,φ )=1 G(θ i,φ i )= α(w) 2 w α(w) (θ i,φ i ) w H s(t) =s d (t) +α(w)s i (t) E[ s d (t)+α(w)s i (t) 2 ]=E[ s d (t) 2 ]+ α(w) 2 E[ s i (t) 2 ] s d (t) (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
5 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal w α(w) s i (t) s DCMP (t) (θ,φ ) s DCMP (t) s DCMP (t) xz (x, y) =(.3m,.5m) (x, y) = (.3m,.5m) s A (t) s B (t) s A (t)+s B (t) s A (t) s B (t) λ = 35.7 λ λ xz y =.5 s A (t)+s B (t) ɛ =1 5 (x, z) =(28.9cm,.8cm) (θ,φ ) a s B (t) 1 j 1 j 1 +j 1+j s B (t) (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
6 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal [db] 5 5 z [cm] x [cm] [db] [db] 5 z [cm] z [cm] x [cm] x [cm] 25 3 R ss s B (t) R ss w opt a P DCMP (θ, φ) =w H opta(θ, φ) ɛ =.1 z [cm] x [cm] [db] s DCMP (t) =w H opts B (t) P r(t) 4 P (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
7 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal 2 1 Imaginary 1 1 Ch3 Ch1 Ch4 Ch Real Imaginary Real s B (t) [db] s DCMP (t) z [cm] x [cm] r s 1 (t) s DCMP (t) d DCMP (t) d DCMP (t) = λ 4π unwrap( s DCMP (t)), unwrap( ) θ(t) ( θ(t) θ(t Δt) π), unwrap(θ(t)) = θ(t)+2π (θ(t) θ(t Δt) < π), θ(t) 2π (θ(t) θ(t Δt) >π). Δt Displacement [mm] d DCMP (t) s DCMP (t) s B (t) d 1 (t) s 1 (t) d DCMP (t) s DCMP (t) s A (t)+s B (t) s 1 (t) s A (t)+s B (t) (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
8 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal [db] Imaginary 1 Ch3 Ch1 Ch4 Ch Real z [cm] x [cm] s A (t)+s B (t) Displacement [mm] Imaginary Real s 1 (t) s DCMP s A (t)+s B (t) R ss θ φ s DCMP (t) s A (t)+s B (t) t =1 Displacement [mm] d DCMP (t) s DCMP (t) s A (t)+s B (t) (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
9 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal Displacement [µm] 1 1 Displacement [µm] s DCMP (t) s B (t) s 1 (t) s A (t)+s B (t) 15 s t 45 s μ t Displacement [µm] s DCMP (t) s A (t)+s B (t) (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
10 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal s B (t) s 1 (t) s DCMP (t) Interbeat Interval [s] s B (t) Interbeat Interval [s] s A (t) +s B (t) (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
11 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal.7 12 Interbeat Interval [s] Heart Rate [bpm] s A (t)+ s B (t) Time [sec] s B (t).7 12 Interbeat Interval [s] Heart Rate [bpm] s A (t) + s B (t) Time [sec] s A (t) +s B (t) R s Δt τn ECG τn radar n =1, 2,,N Δt =.5 τn ECG τn radar < τ τ = 5 N R s = N /N R s R s (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
12 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal Heart Rate [bpm] Time [sec] s A (t)+s B (t) Normalized Frequency DCMP for One Participant DCMP for Two Participants Single Channel for Two Participants Heart Rate Error [bpm] (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
13 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
14 This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 1.119/JETCAS , IEEE Journal (c) 218 IEEE. Translations and content mining are permitted for academic research only. Personal use is also permitted, but republication/redistribution requires IEEE permission. See
Appendix to On the stability of a compressible axisymmetric rotating flow in a pipe. By Z. Rusak & J. H. Lee
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