Moving average for a single data and accumulative average for several data

(1) Moving average

Apply moving average algorithm with various window sizes to the following signal with noise.

• signal with noise
• true signal
  * The data format is two-columns data with (x_i,f_i). The lines beginning with '#' are comment lines.

Evaluate the performance by using a residual between the averaged signal and the true signal.
The residual is defined as a square root of the mean of square of difference of each point. In the mathematical notation, it can be written as
((<(g_i-f'_i)**2>_i)**(1./2.))
where g_i and f'_i are the averaged signal of point x_i and the true signal of the same point, respectively; and <...>_i represents the average over all points.

Discuss about the effect of the window size.

(2) Accumulative average for several data

Consider several measurements for a certain measurement system.

The following zip-file has 16 data in which the true signal is same but the noise is different, which file names are f_n1.dat to f_n16.dat.

• Several signals with different noise: 　 (zip format,line end=LF) or (zip format,line end=CR+LF)
  (In this zip-file, two file shown in (1) are also included.)

Compute accumulative average and evaluate the residual.

Discuss through a comparison between the result of (1) and that of (2).

Note

Append source codes to the report.

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