Signals and Systems

2.4 WAVE SYMMETRY

Since periodic waveform exhibits certain types of symmetry, therefore, knowledge of such symmetry becomes useful to reduce the labour involved in calculation of the Fourier co-efficients. In order to examine the reduction of labour for calculation of Fourier co-efficients, let us consider Eq. (2.3) taking the interval, –T/2 to T/2 instead of 0 to T.

 

 

In general, it can be written as

 

 

Similarly, it can be written as

 

2.4.1 Even or Mirror Symmetry

A function f(t) is said to be even if

 

f(t) = f(−t)     (2.20)