Howtosignalprocessing
- What is the eigenfunction property of LTI systems?
- Which of the following discrete time signals could be eigenfunctions of any stable LTI system?
- Which of the following can be the eigen signal of an LTI system?
- What is an eigenfunction of a system?
What is the eigenfunction property of LTI systems?
According to the eigenfunction property of discrete-time LTI systems, the steady-state response of a discrete-time LTI system to a sinusoidal input is also a sinusoid of the same frequency as that of the input, but with magnitude and phase affected by the response of the system at the frequency of the input.
Which of the following discrete time signals could be eigenfunctions of any stable LTI system?
The sequences ej2ωn, 5n, and 5nej2ωn are of that form, hence they are eigenfunctions of any stable LTI system.
Which of the following can be the eigen signal of an LTI system?
Which of the following can be the eigen signal of an LTI system? Hence, the second derivative operator being linear and time-invariant, t→cos2t is an eigen signal with eigenvalue −4. Even-order derivatives would work as well.
What is an eigenfunction of a system?
In the study of signals and systems, an eigenfunction of a system is a signal f(t) that, when input into the system, produces a response y(t) = λf(t), where λ is a complex scalar eigenvalue.
