The name of CNNs comes from their signature operation: convolution. This operation is a mathematical operation that is very common in the signal processing area. Let's go ahead and discuss the convolution operation.
1-dimension
Let's start with the discrete-time convolution function in one dimension. Suppose that we have input data, 
, and some weights, 
, we can define the discrete-time convolution operation between the two as follows:
.
In this equation, the convolution operation is denoted by a * symbol. Without complicating things too much, we can say that 
is inverted, 
, and then shifted, 
. The resulting vector is 
, which can be interpreted as the filtered version of the input when the filter 
is applied.
If we define the two vectors as follows, 
and 
, then the convolution operation yields 
.
Figure 12.1 shows every single step involved in obtaining this result by inverting and shifting the filter and multiplying across the input data:
