|
First a Square wave F(t)
and its spectrum an
is shown. Since this wave is even the spectrum includes only even terms with bn = 0 for all n. The expression for the spectrum is shown below. Since the terms decrease as 1/n, then the series converge slowly. Slow convergence is characteristic of functions with discontinuities. The square wave has disconuities in F(t) at -T/4 (-1 to +1) and at +T/4 (+1 to -1). 
|
 |
|
A Triangular wave F(t)
and its spectrum bn
is shown opposite.
Unlike the square wave it does not have disconuities in F(t).
However there are discontinuities in its derivatives at -T/4 and +T/4.
Convergence of the series is faster than that for the square wave as shown
by the spectrum plotted opposite. In this case the wave is odd
and its Spectrum is also odd with an = 0 for all n. The expression for the Fourier series is given below.  |
 |