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Difference Equation Zero-Input Response Theory

http://adampanagos.org This video introduces the concept of the zero-input response of a difference equation. The zero-input response, denoted as y0[k], is the solution of a difference equation assuming zero input. As such, this solution is only due to the initial conditions of the system. The basic form of the zero-input response is derived and we find that the zero-input response must be a linear combination of the characteristic modes of the system, where the characteristic modes are exponential functions. We discuss the case where the roots of the system characteristic equation are distinct, repeated, and complex. While this video just develops the general theory, terminology, and form of the zero-input response, the videos that follow work specific examples. The next video in this playlist is: Difference Equation Zero-Input Response Example #1 (Distinct Roots) -    • Difference Equation Zero-Input Response Ex...   The previous video in this playlist is: Difference Equation Zero-Input Response Theory -    • Difference Equation Zero-Input Response Th...   Course website: https://www.adampanagos.org/dt-signal... If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!