Spectral Analysis
\[\newcommand{\eq}[1]{\begin{align*}#1\end{align*}}\]
AP, ML Time Series
Distance
Estimated Frequency Densities (eye balled)
1. |10sec - 13sec| = 1/3 = 0.333 Hz
2. |10sec - 24.5sec| = 1/14.5 = 14.5 Hz
3. |24sec - 58sec| = 1/34 = 0.029 Hz
4. |13sec - 18sec| = 1/6 = 0.167 Hz
Velocity
Spectrum Analysis
The decomposition of a time series into underlying sine and cosine functions of different frequencies, allows to identify frequencies that appear strong or important. Or the power spectrum of a time series x(t) describes the distribution of power into frequency components composing that signal.
Frequency Spectrum Distance
Example: Power Seectrum of AP
The values at t=0, 0.01, 0.02 are deleted since the time equivalent is 100 respectively 50 seconds, which is to slow for motor control.
Area under the curve
\[\eq{ u_k = \sum{(m\Delta f)^k G[m] )} }\]
## [1] 4.553352Frequency Spectrum Velocity
Analysis
Ingestion
## 'data.frame': 480570 obs. of 17 variables:
## $ Trial : chr "BDS00001" "BDS00001" "BDS00001" "BDS00001" ...
## $ Subject : num 1 1 1 1 1 1 1 1 1 1 ...
## $ Vision : chr "Open" "Open" "Open" "Open" ...
## $ Surface : chr "Firm" "Firm" "Firm" "Firm" ...
## $ AgeGroup : chr "Young" "Young" "Young" "Young" ...
## $ Age : num 33 33 33 33 33 33 33 33 33 33 ...
## $ Illness : chr "Yes" "Yes" "Yes" "Yes" ...
## $ Illness2 : chr "Hypothyroidism" "Hypothyroidism" "Hypothyroidism" "Hypothyroidism" ...
## $ Disability : chr "No" "No" "No" "No" ...
## $ Disability2: chr "No" "No" "No" "No" ...
## $ Footwear : chr "Flip-Flops" "Flip-Flops" "Flip-Flops" "Flip-Flops" ...
## $ BMI : num 21.8 21.8 21.8 21.8 21.8 ...
## $ spx : num 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 ...
## $ RD.y : num 14.64 7 7.95 2.4 6.21 ...
## $ AP.y : num 14.76 82.38 9.39 71.72 9.85 ...
## $ ML.y : num 12.28 1.65 2.24 0.25 0.13 ...
## $ BMI.Class : Factor w/ 3 levels "normal","overweight",..: 1 1 1 1 1 1 1 1 1 1 ...Power Spectrum of Resulting Distance (RD.y) Subject | Surface
100 randomly selected subjects. 
Power Spectrum of Resulting Distance (RD.y) Subject | Eyes Open/Closed
100 randomly selected subjects. Comparing each subject 
Remarks
Showing for each subject the difference between eyes open and closed are visualized. The power density is higher for eyes closed.
Illnesses
| counts | illness |
|---|---|
| 56 | No |
| 29 | Hypertension |
| 20 | Hypercholesterolemia |
| 14 | Hypercholesterolemia |
| 13 | Hypothyroidism |
| 13 | Osteopenia |
| 12 | Diabetes mellitus |
| 12 | Arthrosis |
| 12 | Labyrinthitis |
| 11 | Rhinitis |
| 11 | Osteoporosis |
| 10 | Hypertension |
| 9 | Asthma |
| 8 | Arthrosis |
| 7 | Labyrinthitis |
| 6 | Osteoporosis |
| 5 | Sinusitis |
| 4 | Rhinitis |
| 4 | Hypothyroidism |
| 3 | Tendinitis |
| 3 | Hypoglycemia |
| 3 | Hyperthyroidism |
| 2 | Gastritis |
| 2 | Bronchitis |
| 2 | Gastroesophageal reflux |
| 2 | Migraine |
| 2 | Depression |
| 2 | Diabetes mellitus |
| 2 | Heel spurs |
| 2 | Heart problem |
| 2 | Arrhythmia |
| 2 | Allergy |
| 2 | Anxiety |
| 2 | Endometriosis |
| 2 | Arthritis |
| 2 | Chodromalacia of the knees |
| 2 | Asthma |
| 2 | Spine problem |
| 1 | Dermatitis |
| 1 | Keratoconus |
| 1 | Vasovagal syncope |
| 1 | Vitiligo |
| 1 | Kidney stones |
| 1 | Intestine disorder |
| 1 | Sickle cell anemia |
| 1 | Melanoma |
| 1 | Ascending colon cancer |
| 1 | Progressive breast cancer |
| 1 | Herniated lumbar of the L4-L5 discs |
| 1 | Rheumatism |
| 1 | Anxiety |
| 1 | Heart disease |
| 1 | Lymphedema of the lower members |
| 1 | Stroke |
| 1 | Hepatitis B |
| 1 | Arthrosis of the left knee |
| 1 | Essential tremor |
| 1 | Esophagitis |
| 1 | Poliomyelitis |
| 1 | Breathlessness |
| 1 | Parkinson’s disease |
| 1 | Arthrosis of the hands |
| 1 | Hypoglycemia |
| 1 | Herniated lumbar disc |
| 1 | Hashimoto disease |
| 1 | Arthrosis of the feet/hands |
| 1 | Vascular leakage of the eyes |
| 1 | Glaucoma |
| 1 | Prostate disease |
| 1 | Skin disease |
| 1 | Inflammation of the tibial nerve |
| 1 | Prostatitis |
| 1 | Skin cancer |
| 1 | Familial Hypercholesterolemia |
| 1 | Chodromalacia of the knees |
| 1 | Lumbar tumor |
| 1 | Hyperthyroidism |
| 1 | Conjunctivitis |
| 1 | Arthrosis of the knees |
| 1 | Fibromyalgia |
| 1 | Urinary tract infection |
| 1 | Deep vein thrombosis |
| 1 | Osteeopenia |
| 1 | Arthrosis of the spine/knees/toes |
| 1 | Scoliosis |
| 1 | Bursitis |
| 1 | Sjogren’s syndrome |
| 1 | Hypertriglyceridemia |
| 1 | Fatty liver |
| 1 | Tendinitis of the knees |
| 1 | Varicose veins of the legs |
| 1 | Anemia |
| 1 | Tendinitis of the knees/feet |
| 1 | Ligament problems |
Age Group | BMI
Hyptertension
Condition: Firm, Open
Hypertension could have an influence in old age group. Sample size = 163
Spine|spine|lumbar|Lumbar
Heel
100 randomly selected subjects. 
Arthrosis
100 randomly selected subjects. 
Diabetes
100 randomly selected subjects. 
Illness (Yes, NO)
100 randomly selected subjects. 
Footwear
## Flip-Flops Walking shoes Casual shoes Boots
## 53784 297555 137448 14940
## Orthopedic shoes Sandal Dress shoes Tennis
## 2988 66483 14940 2988100 randomly selected subjects. 
Flip Flops vs Walking
