4

Linear Systems and Transfer Functions

4.1    Continuous and Discrete Linear Systems

Digital signal processing (DSP) technology has its roots in the analysis of continuous linear systems. We saw in the previous chapter how continuous signals may be regarded as limiting forms of corresponding discrete sample vectors, and the same idea holds for continuous and discrete processing systems. Continuous linear systems7,8 are described with linear differential equations, and discrete linear systems are described with linear difference equations.

There are many reasons to keep these “continuous roots” in our thoughts as we proceed to develop the subject of DSP. In this chapter particularly, the time and frequency domains are similar for digital ...

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