TABLE OF CONTENTS |
 |
| | a ? 0 |
| | a > 0 |
| | a ? 0 |
| | a > 0 |
| m > 0 |
| Property | Mathematical Expression |
|---|---|
| Commutative | f ? g = g ? f |
| Associative | f ? ( g ? h) = ( f ? g) ? h |
| Distributive | f ? ( g + h) = f ? g + f ? h |
| Property | Space Domain | Fourier Domain |
|---|---|---|
| Linearity | af( x, y) + bg( x, y) | aF( u, v) + bG( u, v) |
| Sign change | f( ? x, ? y) | F( ? u, ? v) |
| Scale change | f( x/ a, y/ b) | ab F( au, bv) |
| Shift | f( x ? a, y ? b) | F( u, v) exp[ ? j2 ?( au + bv)] |
| Frequency shift | f( x, y) exp[ j2 ?( ax + by)] | F( u ? a, v ? b) |
| Conjugation | f*( x, y) | F*( ? u, ? v) |
| Space | ? f( x, y)* ? x | j2 ? uF( u, v) |
| Differentiation | ? f( x, y)/ ? y |
