Abstract:

Linear Time Invariant (LTI) Systems have a particularly convenient and elegant representation, and this representation leads us to several fundamental tools in signal and image processing. Also a discrete linear system can be expressed in a matrix notation and not always necessarily time invariant. However, if the corresponding matrix is circulant, then it is time invariant and hence it is a Linear Time Invariant System, which refers to shift in the input signal and gives the corresponding shift in the output signal. That is, a system does not behave differently at different times. By revisiting these properties through linear algebraic, methods employing circulant matrices certain classes of stable LTI systems are obtained.