TABLE OF CONTENTS 
Parseval's theorems:
| Property | x( t) | X( ?) |
|---|---|---|
| Linearity | a 1 x 1( t) + a 2 x 2( t) | a 1 X 1( ?) + a 2 X 2( ?) |
| Time shifting | x( t ? t 0) | X( ?) e ?j ?to |
| Scaling | x( at) | |
| Time reversal | x( ? t) | X( ??) |
| Duality | X( t) | 2 ? x( ??) |
| Frequency shifting | x( t) e ?0t | X( ? ? ?) |
| Modulation | x( t)cos ?0t | |
| Time differentiation | x i( t) | j ? X( ?) |
| Frequency differention | ? jtx( t) | X'( ?) |
| Integration | t ??x( ?) d ? | |
| Convolution | x 1( t) * x 2( t) | X'1( ?) X 2( ?) |
| Multiplication | x 1( t) x 2( t) | |
| |
