**1.1
SIGNALS**

** **

The signals we consider are discrete-space signals. A
2-D discrete-space signal (sequence) will be denoted by a function whose two
arguments are integers. For example; x(n_{1},n_{2}) represents
a sequence (digital signal) which is defined for all integer values of n_{1}
and n_{2 }. Note that x(n_{1},n_{2}) for non-integer
n_{1 }and n_{2} are not zero, but is undefined. The notation
x(n_{1},n_{2}) may refer either to the discrete-space function
x or to the value of the x at a specific (n_{1},n_{2}).

An example of 2-D sequence x(n_{1},n_{2})
is sketched in Figure 1.1 . In the figure, the height at (n_{1},n_{2})
represents the amplitude at (n_{1},n_{2}) . An alternative way
to sketch the 2-D sequence in Figure 1.1 is shown in Figure 1.2 . In this
figure open cicles representsamplitudes of 0 and filled-in circles represent
non-zero amplitudes, with the values in parentheses representing the amplitudes
. For example ;
x(3,0) is 0 and x(1,1) is 2 , x(-1,0) is 2, x(-1,-2)is
1.

** **

**Figure 1.1 :**
2-D sequence (digital signal) x(n_{1},n_{2})

**Figure 1.2 :**
Alternative way to sketch the 2-D sequence in Figure 1.1. Open circles
represent amplitudes of zero, and filled-in circles represent non-zero
amplitudes, with values in parentheses representing the amplitude.

**Figure 1.3 :**
Sequence in Figure 1.2 sketched with some simplification. Open circles have
been eliminated and filled-in circles with amplitude of 1 have no amplitude
specifications.