Time‐Invariant Discrete Linear Systems
Maurice Bellanger · Digital Signal Processing · 2024
Time-invariant discrete linear systems represent a very important area for digital signal processing – digital filters with fixed characteristics. These systems are characterized by the fact that their behavior is governed by a convolution equation. Their properties are analyzed using the Z-transform, which plays the same role in discrete systems as the Laplace or Fourier transforms do in continuous systems. This chapter introduces the elements which are most useful for studying such systems. The most interesting linear time-invariant systems are those where the input and output sets are related by a linear difference equation with constant coefficients. On the one hand, they represent simple examples, and on the other, they offer an excellent representation of many natural systems. Analysis of a system using its frequency response corresponds to steady-state operation.