| Reflection: |
| Let {x[n]} be the original sequence, and {y[n]} be reflected sequence, then y[n] is defined by
|
y[n] = x[-n] |
| {x[n]} |
 |
| We will denote this by {x[-n]} |
| When we have complex valued signals, sometimes we reflect and do the complex conjugation, ie, y[n] is defined by
y[n] = x*[-n], where * denotes complex conjugation. This sequence will be denoted by
{x*[-n]}. |
| We will learn about more complex operations later on. Some of these operations commute, ie. if we apply two operations we can interchange their order and some do not commute. For example scalar multiplication and reflection commute. |
| Then v[n] = z[n] for all n. Shifting and scaling do not commute. |
|
| {x[n]} {y[n]} = {x[n-1} {z[n]} = {y[-n]} |
|
| {x[n]} {w[n]} = {x[-n]} {u[n]} = {w[n-1]} |
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| |
| We can combine many of these operations in one step, for example {y[n]} may be defined as
y[n] = 2x [3-n]. |
