Write a subroutine that calculates a moving average. Your subroutine should average data within a (variable length) window that moves along the array of  N data points.
 

• The data which you will be using for this hw is the output of HW#3. Read the data.
• Filter the data using 5 point moving average filter. Plot the original and filtered data set.
• The data which was provided to you had 2 sin waves. The period of one of them is 24. Find the period of the other wave. ( Hint: Filter the data, output of Hw #3, using different window lengths till you get a sin wave with minimum distortion and period 24).
• Write a subroutine to do convolution. Filter the output of HW#3 using this subroutine and square window of 5 points. Compare and comment on the results of this step and result of moving average filter.

Turn in:

A copy of the moving average subroutine and a copy of convolution subroutine.

The original and filtered data from step 2, 3 and 4.Turn in only the plots not the data values.

Supplement:

Some of you have problems understanding convolution. Here is a small example to try to show how easy it is to do, and direct you on how to write a subroutine to do convolution.

Suppose you have 2 arrays that you want to convolve. We shall call these arrays A and B. Let,

A=(a₁,a₂,a₃,a₄,a₅)
B=(b₁,b₂,b₃)

To convolve these 2 arrays you must reverse the order of one of them. Let us reverse the order of B. You then slide the 2 arrays along, multiplying and adding as you do. We will put the output into the array C. Note that the length of C is one less than the sum of lengths of A and B (i.e array C will have a length 7).

After much tedious work by hand, we get the following values for the variables of C.

c₁ = a₁b₁
c₂ = a₁b₂ + a₂b₁
c₃ = a₁b₃ + a₂b₂ + a₃b₁
c₄ =            a₂b₃ + a₃b₂ + a₄b₁
c₅ =                        a₃b₃ + a₄b₂ + a₅b₁
c₆ =                                    a₄b₃ + a₅b₂
c₇ =                                                a₅b₃

Note that as your proceed across the columns from left to right, the subscript on the a's increase. As you go down the rows, the subscript on the b's increase. As you go down the rows, note also that the c's increase. This should give you some hint on how to write a FORTRAN subroutine that will take care of the subscripts and only use 2 do loops. Another hint that you may want to note: you don't always have to calculate all of the variables for each value of C before going to the next value. You can fill several values within the same loop.