Smart Grid

PLOTTING IN EXCEL
OF FOURIER SERIES IN FUNCTION SQUARE WAVE

The function square wave of period 2π , is defined in a piecewise
way:

− 1 , si - π < x < 0
f (t ) = 
1 , si 0 < x < πIts representation in series of Fourier is

4senx

π

4sen3x 4sen5x
4 ∞ sen(2n − 1) x
+
+
+ ........... = ∑
3π
5π
π n=1 (2n − 1)

Suppose that you want to graph the first five terms.For graphing its
first five terms by using Excel:
i) Put X in the cell A1, T1 in the cell B1, T2 in the cell C1, T3 in
the cell D1, T4 in the cell E1, T5 in the cell F1, and It adds
up of thefirst five terms, in the cell G1. In the cell H2, we
can write the series that we wish to graph.
ii) Put 0.00 in the cell A2, and define for next 316 cells of the
column A, the values Ak +1 =Ak + 0.02

iii) In B2, define the formula for the first term of the series, and
then, drag it for next 316 cells of B. The formula in B2 could
be:

= 4 * seno( A2 ) / pi()

iv) In C2,built the formula for the second term of the series, and
drag it for next 316 cells of C. The formula in C2 could be:

= 4 * seno(3 * A2 ) /(3 * pi())
v) Analogously, In D2, E2 and F2 we can makeformulas for the
third, fourth and fifth term respectively, and drag them for all
the next 316 cells in columns D, E, F. The following set of
formulas are suggested:
Third term:
Fourth term:Fifth term:

= 4 * seno(5 * A2 ) /(5 * pi())
= 4 * seno(7 * A2 ) /(7 * pi())
= 4 * seno (9 * A2 ) /( 9 * pi ())

vi) In G2, make the formula for the sum of the first five terms of
theseries and drag it for next 316 cells of column G. A
formula could be:

= B 2 + C 2 + D 2 + E 2 + F2
vii) To graph the term 1,select the data obtained in column B. For
sketching, choose anappropriate sort of plot (in this case,
look at next picture).

viii)Analogously, to graph the sum S5, select the data obtained in
column G, an the same kind of plot as in the first trial.