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##Library dependencies The script run_analysis.R uses two external R-libraries, namely readr and dplyr.

##Process steps

  1. The original data is divided into two datasets, namely trainning and testing datasets. This scripts merges the datasets together using rbind function for the data.frames.
  2. The original data contains 561 variables derived from accelerometer and gyroscope measurements. In this script the standard deviation and mean variables are extracted from the original data by using case sensitive grep-function filtering variables having words "mean()" or "std()" from the variable names and subsetting the corresponding columns from the dataset.
  3. The activity id has been replaced from the original dataset by the corresponding activity name. Then the activity and subject names have been added to the dataset by function cbind.
  4. The resulting tidy dataset has been sorted by activity and subject and saved as a text file "tidy_data_step4.txt".
  5. Mean of each variable has been calculated over the measurements of the same activities and presented separately for each subject.

##Variables The varbles are mean and standard deviation estimates from the accelerometer and gyroscope 3-axial raw signals tAcc-XYZ and tGyro-XYZ. These time domain signals (prefix 't' to denote time) were captured at a constant rate of 50 Hz. Then they were filtered using a median filter and a 3rd order low pass Butterworth filter with a corner frequency of 20 Hz to remove noise. Similarly, the acceleration signal was then separated into body and gravity acceleration signals (tBodyAcc-XYZ and tGravityAcc-XYZ) using another low pass Butterworth filter with a corner frequency of 0.3 Hz.

Subsequently, the body linear acceleration and angular velocity were derived in time to obtain Jerk signals (tBodyAccJerk-XYZ and tBodyGyroJerk-XYZ). Also the magnitude of these three-dimensional signals were calculated using the Euclidean norm (tBodyAccMag, tGravityAccMag, tBodyAccJerkMag, tBodyGyroMag, tBodyGyroJerkMag).

Finally a Fast Fourier Transform (FFT) was applied to some of these signals producing fBodyAcc-XYZ, fBodyAccJerk-XYZ, fBodyGyro-XYZ, fBodyAccJerkMag, fBodyGyroMag, fBodyGyroJerkMag. (Note the 'f' to indicate frequency domain signals).

These signals were used to estimate variables of the feature vector for each pattern:
'-XYZ' is used to denote 3-axial signals in the X, Y and Z directions. The additional mean() and std() in the variable names indicate, mean and standard deviation values, respectively.

The variable names are:

  • tBodyAcc-XYZ
  • tGravityAcc-XYZ
  • tBodyAccJerk-XYZ
  • tBodyGyro-XYZ
  • tBodyGyroJerk-XYZ
  • tBodyAccMag
  • tGravityAccMag
  • tBodyAccJerkMag
  • tBodyGyroMag
  • tBodyGyroJerkMag
  • fBodyAcc-XYZ
  • fBodyAccJerk-XYZ
  • fBodyGyro-XYZ
  • fBodyAccMag
  • fBodyAccJerkMag
  • fBodyGyroMag
  • fBodyGyroJerkMag

The units for accelerations "acc" are in standard gravity units 'g'. The units for the angular velocity measurements "gyro" are in radians/seconds.

Moreover the variables are normalized and bounded within [-1,1].