Pattern Recognition Applet: Linear Prediction

The Linear Prediction algorithm uses the following procedure to determine the set of linear coefficients for the data points entered by the user:
  • Checks for validity of the data points entered by the user, which is checking if the user has entered the data points in time progression from left to right.

  • Most of the times, the data points entered by the user are not evenly spaced from each other so next step is to evenly space these points using cubic interpolation. This is similar to converting the non-uniformly sampled data into uniformly sampled data points.

  • The autocorrelation coefficients are then calculated using the following formula:

    Linear Prediction

  • The linear prediction coefficients are determined by the following formula:

    Linear Prediction

    The formula also includes calculation of reflection coefficients, estimated error energy calculation.

  • Here is an example of how the Linear Prediction Algorithm works:

    First enter the data points by either clicking into the input window or clicking and dragging the mouse in the input window. The horizontal axis represents time axis and the vertical axis represents the amplitude of the signal. The click of individual points represents the sampled points. The users need not click exactly at regular intervals in time progression from left to right. The data points will be interpolated by the algorithm. The user can select the interpolation factor right now alongwith the linear prediction order. By default the values are set to 10 and 8 respectively.

    Next, select Linear Prediction under the Algorithms menu. Initialize this algorithm by selecting Initialize from the Go menu. The algorithm proceeds to check for validity of the data points. If the user has not entered data points in time progression from left to right, then the algorithm will catch it as invalid entry and permit the user to enter the data points again.

    Linear Prediction

  • The second step of the process interpolates the data points. The step includes calculation of valid uniformly sampled data points (calculated by cubic interpolation). To move on to the next step, select the Next option under the Go menu. This will display the first step of the process, i.e., it will display the data sets in both the input plot (top left) and the output plot (bottom left). The process description box further indicates the step that we are currently on and the algorithm that is being used to compute the linear prediction coefficients. The data sets are displayed on the output plot as bigger red dots.

    Linear Prediction

  • The third step of the process calculates almost all the necessary items for the algorithm. It includes the calculation of autocorrelation coefficients, reflection coefficients, estimated errors and actual error energy for the data points entered. The total number of points (including the interpolated points), the autocorrelation coefficients, reflection coefficients, and prediction coefficients alongwith estimated error energy and actual error energy for each data set are then displayed on the process description box. Please refer lecture notes for more information on linear prediction theory. and Correlation Documentation and Prediction Documentation for more information on algorithm used for autocorrelation calculation and prediction calculation.

    Linear Prediction

  • The final step of the process is to display the linear predicted signal. Thus completing the algorithm.

    Linear Prediction



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