O'Reilly logo

Signals and Systems by Smarajit Ghosh

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

3.3 FOURIER TRANSFORM OF SOME FUNCTIONS

3.3.1 Fourier Transform of Gate Function

The gate function is shown in Fig. 3.1.

 

Gate function

 

Fig. 3.1 Gate function

 

Mathematically, it can be written as

 

image

 

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

 

image

 

image

 

where and are called sampling functions.

Now x 0, Sa(x) 1

and Sa(x) = 0 when x = ± mπ where ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required