Digital Signal Processing with Kernel Methods

2 Introduction to Digital Signal Processing

Signal processing deals with the representation, transformation, and manipulation of signals and the information they contain. Typical examples include extracting the pure signals from a mixture observation (a field commonly known as deconvolution) or particular signal (frequency) components from noisy observations (generally known as filtering). Before the 1960s, the technology only permitted processing signals analogically and in continuous time. The rapid development of computers and digital processors, plus important theoretical advances such as the FFT, caused an important growth of DSP techniques. This chapter first outlines the basics of signal processing and then introduces the more advanced concepts of time–frequency and time–scale representations, as well as emerging fields of compressed sensing and multidimensional signal processing.

2.1 Outline of the Signal Processing Field

A crucial point of DSP is that signals are processed in samples, either in batch or online modes. In DSP, signals are represented as sequences of finite precision numbers and the processing is carried out using digital computing techniques. Classic problems in DSP involve processing an input signal to obtain another signal. Another important part consists on interpreting or extracting information from an input signal, where one is interested in characterizing it. Systems of this class typically involve several steps, starting from a digital ...