Digital Signal Processing, 10th Edition

15Neural Networks

Adaptive systems are at the heart of digital communication networks. They are particularly critical for data transmission efficiency, which is achieved through channel equalization. This operation involves an initial learning phase, an operational phase, and subsequent decisions and improvements throughout the duration of the communication. Thanks to artificial intelligence, these concepts can be extended to all technical fields, with operational devices that are ever more complex and sophisticated. Signal processing and adaptive techniques, as presented above, are profoundly involved in one such device – namely, the neural network.

The present chapter describes how neural networks operate, and how signal-processing techniques, and specifically adaptive techniques, are exploited. As a starting point, we look at a simple classification operation.

15.1 Classification

Classification is a basic operation in shape recognition. Its complexity depends on the space in which it is carried out. In a two-dimensional space, objects defined by their coordinates can be grouped together, and the different groups can be separated by curves. Whenever a new object appears, it is assigned to an existing group, depending on its position with respect to the separation curves. An illustration is provided in Figure 15.1.

N objects are separated into two groups (a and b) by a line with equation:

(15.1)

The structure of the corresponding classifier is shown in Figure 15.2.

Assuming ...