5. Digital Filters

This chapter covers a central aspect of digital signal processing: digital filters. The digital signal processing systems use samples of input signals, which constitute series of numbers. The result may be also series of numbers, to be used as output signals. The signal processing computations usually take into account a record of recent values of the input and output samples. In the case of linear digital filters, the output y(n) in the instant n, is computed as a linear combination of the input u(n) and previous samples of input and output signals. There are two main classes of digital filters: FIR and IIR. Many types of FIR filters are based on using a window; while others are based on optimization of certain criteria. With respect to IIR filters, there are types corresponding to the filters introduced in chapter 4, and other more related to impulse responses. The chapter introduces also some special filters, like the non-causal filter, and details of pertinent functions and tools of the MATLAB Signal Processing Toolbox.