Signals and Systems

3.3 FOURIER TRANSFORM OF SOME FUNCTIONS

3.3.1 Fourier Transform of Gate Function

The gate function is shown in Fig. 3.1.

 

 

Fig. 3.1 Gate function

 

Mathematically, it can be written as

 

 

Therefore, Fourier transform of f(t) is given by

 

 

 

where and are called sampling functions.

Now x 0, Sa(x) 1

and Sa(x) = 0 when x = ± mπ where ...