Frequency Domain HRV Parameters Deviation from the GT Estimated from the Noisy and Reconstructed Series (The values are in percentage deviation)
P D Noisy/Reconstructed Frequency domain
ULF VLF LF HF LF/HF VLF Peak LF Peak HF Peak Fraction LF Fraction HF
10% 1 Noisy (σ = 1) 1.87 × 1014 2.63 × 1014 4.03 × 1014 3.46 × 1015 81.22 47.18 68.30 40.65 52.86 277.34
CSI 29.95 28.30 37.45 102.13 32.06 8.13 13.30 9.71 9.02 39.90
GP (Linear) 111.76 103.21 172.25 2.38 × 103 78.63 22.43 37.44 71.42 47.60 252.11
GP (Periodic) 14.87 14.90 13.95 25.63 27.00 4.85 8.73 7.83 6.59 33.65
GP (Brownian) 5.46 3.63 7.42 11.08 7.13 2.88 4.70 3.85 1.72 5.13
GP (Exponential) 4.82 3.23 3.32 9.52 8.96 2.61 3.97 3.57 2.26 5.98
GP (Matern 3/2 / 5/2) 5.14 / 5.10 3.74 / 3.75 3.57 / 3.46 9.24 / 12.93 9.29 / 14.77 3.08 / 2.91 5.47 / 4.98 3.28 / 3.50 1.91 / 2.85 6.87 / 10.15
GP (RBF / RQ) 5.66 / 4.56 4.19 / 2.98 4.06 / 3.04 14.35 / 8.05 16.39 / 7.05 3.10 / 2.55 5.47 / 4.19 5.45 / 2.85 3.00 / 1.65 11.17 / 4.90
3 Noisy (σ =1) 2.75 × 1014 3.97 × 1014 6.23 × 1014 5.84 × 1015 82.15 48.37 79.55 40.24 54.61 284.81
CSI 733.12 865.98 980.55 3.84 × 103 58.16 20.62 22.91 13.15 13.60 46.70
GP (Linear) 162.10 171.52 273.14 2.31 × 103 70.21 28.28 36.84 39.41 35.75 195.46
GP (Periodic) 15.18 13.24 11.50 12.91 16.63 6.09 10.12 5.13 3.53 18.35
GP (Brownian) 9.27 6.28 9.86 10.15 7.18 4.27 7.22 4.60 1.58 5.76
GP (Exponential) 8.40 5.89 5.88 10.92 8.73 4.03 6.01 3.87 2.15 5.92
GP (Matern 3/2 / 5/2) 9.88 / 10.14 7.27 / 7.81 6.26 / 6.60 10.26 / 13.26 11.78 / 18.16 4.82 / 4.74 7.58 / 7.41 4.33 / 5.72 3.05 / 4.49 10.61 / 11.46
GP (RBF / RQ) 10.94 / 7.68 8.23 / 5.15 6.45 / 6.02 13.91 / 9.96 19.12 / 7.18 5.01 / 3.79 8.10 / 6.09 7.71 / 3.74 3.37 /1.45 12.46 / 5.16
5 Noisy (σ = 1) 2.94 × 1014 4.28 × 1014 6.68 × 1014 6.36 × 1015 81.67 47.95 79.10 41.68 54.20 284.23
CSI 3.24 × 104 2.59 × 104 1.07 × 104 6.30 × 104 106.23 26.54 31.46 15.52 17.99 55.90
GP (Linear) 222.76 247.05 334.64 2.04 × 103 62.43 29.87 33.73 27.80 27.07 148.37
GP (Periodic) 15.75 12.87 10.67 8.93 12.53 7.05 10.84 4.99 2.59 12.68
GP (Brownian) 11.77 8.04 10.54 9.75 6.76 4.96 8.88 4.34 1.49 5.52
GP (Exponential) 11.57 8.24 7.09 10.63 7.78 4.87 7.92 3.85 1.91 5.44
GP (Matern 3/2 / 5/2) 16.09 / 17.26 12.99 / 14.99 8.42 / 9.33 10.68 / 13.17 14.55 / 21.31 6.44 / 6.67 9.07 / 8.69 4.32 / 6.30 3.05 / 5.49 9.59 / 12.87
GP (RBF / RQ) 20.66 / 10.09 17.84 / 6.70 11.75 / 7.60 13.56 / 9.96 24.87 / 6.60 7.29 / 4.60 9.86 / 7.38 7.33 / 3.95 4.17 / 1.45 15.10 / 4.89
7 Noisy (σ =1) 3.39 × 1014 5.29 × 1014 7.35 × 1014 7.08 × 1015 81.62 47.37 77.93 41.68 53.90 281.09
CSI 1.94 × 104 2.14 × 104 3.35 × 104 2.75 × 105 136.41 25.12 36.26 21.51 21.77 73.00
GP (Linear) 276.44 321.95 373.58 1.78 × 103 58.48 30.13 32.66 24.36 22.46 118.11
GP (Periodic) 16.32 12.82 10.61 7.76 10.40 7.71 10.66 4.28 2.16 9.93
GP (Brownian) 14.04 9.53 11.10 10.24 6.46 6.17 9.68 4.19 1.42 5.26
GP (Exponential) 14.69 10.32 8.20 10.77 7.13 6.20 9.22 4.36 1.68 5.18
GP (Matern 3/2 / 5/2) 23.18 / 27.39 19.12 / 23.70 10.12 / 13.08 11.18 / 13.09 16.89 / 25.45 8.77 / 8.85 11.92 / 11.70 4.66 / 6.10 3.49 / 5.27 10.66 / 14.41
GP (RBF / RQ) 39.09 / 12.07 34.35 /7.88 21.07 / 8.93 14.57 / 10.27 34.21 / 6.31 10.16 / 5.65 13.81 / 8.77 7.54 / 4.07 5.24 / 1.37 19.09 / 4.80
Variable Duration Noisy (σ = 1) 3.08 × 1014 4.30 × 1014 6.44 × 1014 6.47 × 1015 81.86 47.63 79.55 42.85 54.47 284.37
CSI 2.21 × 105 3.33 × 105 7.23 × 105 5.63 × 106 108.66 25.00 32.66 16.99 18.56 57.83
GP (Linear) 266.11 295.24 327.33 1.59 × 103 61.22 28.79 32.73 30.35 26.35 142.65
GP (Periodic) 15.88 13.14 10.80 9.54 13.20 7.03 10.42 4.94 2.76 13.59
GP (Brownian) 12.22 8.34 10.30 9.83 6.52 5.41 8.53 4.86 1.43 5.30
GP (Exponential) 12.04 8.58 6.94 10.37 7.39 5.34 7.80 4.10 1.81 5.23
GP (Matern 3/2 / 5/2) 17.13 / 18.31 14.02 / 15.70 8.29 / 9.21 10.13 / 12.79 13.96 / 20.53 7.17 / 7.18 9.14 / 9.22 4.08 / 5.59 2.87 / 4.27 9.23 / 12.53
GP (RBF / RQ) 26.18 / 10.30 22.95 / 6.91 14.58 / 7.43 13.70 / 9.68 26.43 / 6.23 8.62 / 5.00 10.26 / 7.26 7.02 / 3.95 4.35 / 1.37 15.63 / 4.64
20% 1 Noisy (σ = 1) 3.77 × 1014 5.29 × 1014 7.81 × 1014 7.26 × 1015 79.88 46.89 68.68 33.34 50.32 266.50
CSI 2.21 × 103 3.63 × 103 4.89 × 103 2.06 × 105 54.01 16.84 23.35 16.29 18.48 85.59
GP (Linear) 171.89 204.04 308.59 4.29 × 103 82.29 26.39 50.70 80.44 53.96 282.05
GP (Periodic) 26.97 28.62 27.33 42.61 41.67 7.47 13.32 11.76 12.50 64.93
GP (Brownian) 8.33 5.64 15.35 21.50 13.74 3.82 7.92 6.54 3.31 9.43
GP (Exponential) 7.44 5.25 6.28 19.26 19.88 3.55 5.94 5.12 4.72 12.12
GP (Matern 3/2 / 5/2) 8.47 / 8.43 6.68 / 6.63 7.04 / 6.84 17.07 / 26.24 18.14 / 34.68 4.42 / 4.22 7.68 / 7.09 4.46 / 5.21 3.52 / 5.66 12.61 / 20.79
GP (RBF / RQ) 9.45 / 6.83 7.44 / 4.59 7.86 / 5.84 27.63 / 16.67 38.39 / 14.87 4.57 / 3.50 7.01 / 5.59 8.08 / 3.96 5.94 / 3.29 22.41 / 9.63
3 Noisy (σ =1) 4.41 × 1014 6.28 × 1014 1.05 × 1015 1.07 × 1016 81.43 47.13 78.58 34.84 52.91 277.13
CSI 5.97 × 104 9.19 × 104 2.60 × 104 1.95 × 105 83.24 28.44 32.68 19.68 19.44 72.24
GP (Linear) 262.47 302.82 509.26 4.49 × 103 74.41 32.76 45.46 49.58 41.05 222.07
GP (Periodic) 25.98 25.33 22.16 21.83 27.79 9.12 15.21 7.81 6.81 36.46
GP (Brownian) 14.04 9.63 19.49 19.85 11.75 5.74 11.69 6.44 2.62 9.50
GP (Exponential) 13.03 9.54 10.96 21.74 17.73 5.42 9.13 5.63 4.18 10.98
GP (Matern 3/2/5/2) 17.86/16.48 14.69/13.87 12.38/10.89 18.18/26.67 24.89/41.24 7.60/6.99 11.06/10.15 7.19/9.05 4.77/6.65 15.43/22.98
GP (RBF/RQ) 20.01/11.55 16.86/7.85 12.77/11.88 27.13/19.82 46.74/13.51 7.21/5.43 11.39/8.60 12.35/5.27 6.65/2.81 24.83/9.05
5 Noisy (σ =1) 6.08 × 1014 8.79 × 1014 1.34 × 1015 1.29 × 1016 81.07 47.08 75.72 36.60 52.60 277.27
CSI 2.55 × 105 7.20 × 105 1.50 × 106 2.00 × 107 131.91 27.63 41.29 33.28 27.39 108.58
GP (Linear) 467.77 569.50 701.92 3.58 × 103 64.38 35.92 38.72 28.99 26.04 138.81
GP (Periodic) 26.19 23.07 20.60 13.47 18.12 11.48 15.34 5.92 3.94 19.67
GP (Brownian) 21.91 15.20 22.18 20.05 10.26 8.33 17.84 4.95 2.27 8.67
GP (Exponential) 23.18 17.53 16.17 21.25 12.43 8.53 16.94 5.22 3.03 8.43
GP (Matern 3/2/5/2) 45.82/49.04 43.03/47.95 21.44/23.57 20.15/25.74 39.17/55.75 13.73/12.66 19.92/18.89 5.28/8.57 6.70/8.95 20.92/26.38
GP (RBF/RQ) 71.90/18.16 72.50/12.31 43.65/18.04 30.73/20.15 78.45/10.08 15.42/7.95 18.98/13.92 10.46/4.79 8.94/2.16 33.64/7.49
7 Noisy (σ =1) 5.49 × 1014 7.62 × 1014 1.06 × 1015 1.02 × 1016 79.99 47.21 75.38 32.96 50.89 269.56
CSI 7.40 × 106 5.14 × 106 1.16 × 107 7.68 × 107 118.12 29.91 33.09 36.71 29.37 125.96
GP (Linear) 466.74 556.93 841.90 6.04 × 103 71.38 37.81 46.95 40.80 35.78 194.83
GP (Periodic) 35.84 34.53 31.97 20.92 21.50 13.91 19.29 8.04 7.49 39.97
GP (Brownian) 23.73 16.22 32.39 21.67 15.05 9.10 23.47 7.51 3.34 13.26
GP (Exponential) 24.45 18.80 21.20 14.25 14.34 9.16 20.06 6.76 5.44 13.84
GP (Matern 3/2 / 5/2) 42.70 / 39.49 41.86 / 38.16 27.30 / 19.88 18.05 / 16.63 26.07 / 60.67 13.61 / 9.67 19.29 / 18.94 7.76 / 6.67 4.32 / 6.30 10.61 / 12.46
GP (RBF / RQ) 61.04 / 19.09 60.89 / 12.66 36.60 / 24.16 27.75 / 18.65 107.68 / 16.41 15.30 / 8.67 15.58 / 11.21 11.81 / 8.77 10.34 / 3.28 40.48 / 11.09
Variable Duration Noisy (σ = 1) 5.21 × 1014 7.20 × 1014 1.12 × 1015 1.16 × 1016 81.10 46.85 77.74 35.00 52.48 275.11
CSI 4.37 × 107 4.21 × 107 1.84 × 108 5.71 × 108 111.19 27.44 38.08 25.11 22.52 83.67
GP (Linear) 439.99 522.22 623.68 3174.74 66.48 34.25 38.34 36.75 30.73 165.93
GP (Periodic) 26.19 23.98 21.37 17.19 23.48 11.04 15.05 6.73 5.44 28.32
GP (Brownian) 17.98 12.34 20.49 19.36 10.52 7.60 15.61 5.66 2.38 8.64
GP (Exponential) 18.47 13.68 13.46 20.72 14.01 7.70 13.09 5.36 3.48 8.99
GP (Matern 3/2 / 5/2) 32.68 / 31.35 29.86 / 29.15 17.26 / 15.23 17.88 / 25.74 30.98 / 45.18 10.75 / 10.14 14.75 / 14.85 5.65 / 7.95 5.60 / 7.27 17.91 / 24.03
GP (RBF / RQ) 47.20 / 15.11 44.59 / 10.14 27.20 / 14.76 26.39 / 19.29 60.28 / 10.77 12.42 / 7.10 16.04 / 11.02 11.04 / 4.85 7.77 / 2.34 28.80 / 7.61
30% 1 Noisy (σ =1) 5.49 × 1014 7.62 × 1014 1.20 × 1015 1.11 × 1016 79.15 45.61 67.72 31.98 49.37 263.22
CSI 3.94 × 1010 1.72 × 1010 1.04 × 108 6.59 × 107 75.29 27.68 37.10 27.52 28.24 136.98
GP (Linear) 268.03 312.04 405.65 5.82 × 103 84.17 28.30 57.70 85.09 57.55 298.33
GP (Periodic) 38.25 41.21 40.58 52.42 52.28 10.13 16.54 16.97 18.57 95.55
GP (Brownian) 11.63 7.97 24.48 31.58 20.73 5.09 12.83 6.54 4.94 13.73
GP (Exponential) 10.77 7.83 10.15 29.60 33.85 4.72 8.01 6.65 7.36 18.63
GP (Matern 3/2/5/2) 12.68/12.34 10.47/10.18 11.30/11.28 21.89/39.06 26.07/60.67 5.93/5.57 9.68/9.39 5.91/6.27 4.83/8.20 16.43/31.08
GP (RBF/RQ) 13.84/9.54 11.72/6.47 13.19/10.03 39.50/25.97 67.21/24.34 6.07/4.98 9.90/7.42 9.86/5.45 8.63/5.00 32.98/14.54
3 Noisy (σ = 1) 7.20 × 1014 1.01 × 1015 1.65 × 1015 1.63 × 1016 80.10 46.10 74.03 31.50 50.74 268.43
CSI 4.85 × 107 3.54 × 107 4.27 × 107 1.61 × 108 103.75 30.84 40.10 31.13 26.32 111.44
GP (Linear) 353.10 410.31 674.33 6.34 × 103 77.23 35.89 52.41 54.56 45.28 243.30
GP (Periodic) 36.58 37.23 33.85 29.29 37.96 12.48 19.77 9.75 10.78 57.53
GP (Brownian) 18.15 12.61 29.62 29.86 16.63 7.51 19.26 8.17 3.78 13.41
GP (Exponential) 17.68 13.44 16.65< 32.78 29.57 7.20 13.28 6.86 6.61 16.53
GP (Matern 3/2/5/2) 25.78/22.95 22.96/20.52 18.56/14.78 27.70/39.78 43.49/69.47 10.36/9.26 13.74/13.30 9.05/11.25 7.20/8.88 23.25/33.04
GP (RBF/RQ) 30.51/15.01 27.68/10.37 19.56/18.65 39.42/29.88 83.22/20.71 10.45/6.94 14.44/11.10 17.52/6.42 9.28/4.13 35.90/12.83
5 Noisy (σ =1) 8.03 × 1014 1.06 × 1015 1.72 × 1015 1.70 × 1016 79.99 47.21 75.38 32.96 50.89 269.56
CSI 7.40 × 106 5.14 × 106 1.16 × 107 7.68 × 107 109.60 29.91 43.09 36.71 29.37 125.96
GP (Linear) 466.74 556.93 841.90 6.04 × 103 71.38 37.81 46.95 40.80 35.78 194.83
GP (Periodic) 35.84 34.53 31.97 20.92 29.70 13.91 19.29 8.04 7.49 39.97
GP (Brownian) 23.73 16.22 32.39 29.47 15.05 9.10 23.47 7.51 3.34 13.26
GP (Exponential) 24.45 18.80 21.20 32.45 23.31 9.16 20.06 6.71 5.44 13.84
GP (Matern 3/2/5/2) 42.70/39.49 41.86/38.16 27.30/19.88 27.97/39.34 56.85/79.18 13.61/12.60 19.62/18.94 7.75/11.39 8.64/9.68 27.71/35.04
GP (RBF/RQ) 61.04/19.03 60.89/12.66 36.60/24.16 38.88/30.20 107.68/16.41 15.30/8.67 19.29/16.45 15.93/6.34 10.34/3.28 40.48/11.09
7 Noisy (σ = 1) 7.51 × 1014 1.02 × 1015 1.76 × 1015 1.80 × 1016 80.50 47.63 74.70 34.94 51.66 271.95
CSI 9.21 × 108 6.83 × 108 2.48 × 108 5.46 × 109 124.42 28.24 45.81 44.48 33.30 145.70
GP (Linear) 600.95 724.28 984.16 5.37 × 103 66.93 38.37 42.82 33.12 28.60 153.63
GP (Periodic) 35.80 33.69 31.11 19.06 25.35 14.52 19.38 7.81 6.06 31.24
GP (Brownian) 28.52 19.30 33.84 30.27 13.97 10.02 25.70 7.19 3.12 12.45
GP (Exponential) 30.76 23.62 24.69 32.02 18.52 10.29 23.96 6.51 4.44 11.88
GP (Matern 3/2/5/2) 76.94/68.14 74.60/69.96 36.05/30.65 28.71/38.31 72.79/93.07 16.99/16.10 27.02/25.13 7.31/11.04 10.00/11.21 31.96/36.98
GP (RBF/RQ) 112.23/22.91 116.33/15.60 66.81/27.80 42.17/30.24 138.03/13.87 20.22/9.62 25.32/19.25 14.13/6.36 11.64/2.86 45.06/10.12
Variable Duration Noisy (σ = 1) 7.76 × 1014 1.07 × 1015 1.68 × 1015 1.68 × 1016 80.17 47.00 75.29 32.99 51.11 269.70
CSI 6.38 × 106 5.25 × 106 8.56 × 106 6.52 × 107 117.16 29.08 42.96 34.63 27.93 111.29
GP (Linear) 530.88 641.90 880.50 4.76 × 103 69.79 37.63 42.40 41.78 34.07 183.03
GP (Periodic) 35.74 34.67 32.31 23.83 33.08 13.71 19.11 8.80 8.71 46.50
GP (Brownian) 23.50 16.02 30.68 28.86 14.38 8.82 22.22 6.69 3.30 12.22
GP (Exponential) 24.58 18.50 19.83 30.89 21.81 8.75 18.55 6.48 5.24 12.98
GP (Matern 3/2 / 5/2) 45.15 / 39.62 44.20 / 38.63 24.73 / 18.40 26.60 / 38.06 50.02 / 71.38 13.43 / 12.53 20.45 / 19.66 7.36 / 9.07 7.89 / 9.02 25.43 / 33.16
GP (RBF / RQ) 69.71 / 19.39 68.12 / 13.06 42.29 / 22.29 61.64 / 28.67 100.00 / 15.21 15.60 / 8.16 20.35 / 15.50 13.82 / 5.72 10.13 / 3.21 39.06 / 10.27