Fourier Series of Pulse.

Cuthbert Nyack

The pulse considered is shown opposite. The function f(t) has a discontinuity at T/4 and a discontinuity in its derivates at t = 0 and is given by
f(t) = 4t/T for 0 £ t £ T/4
and zero elsewhere. Pulse is periodic with period equal to T.

Since this function is neither even or odd then both coefficients a_n and b_n in the Fourier Series must be calculated using the expressions below.

Substituting f(t) into the above expressions give the equations opposite.

Carrying out the integrations results in the expressions below for the coefficients.

And evaluating the limits results in the following final equations for the coefficients. This series has terms which converge as n^-1 and as n^-2. a_n and b_n .

Return to main page
Return to page index