Are real exponential signals still eigen functions of LTI systems?

1. What is Eigen function of LTI system?
2. Which of the following discrete time signals could be eigenfunctions of any stable LTI system?
3. Is exponential time-invariant?
4. What is eigenfunction in signals?

What is Eigen function of LTI system?

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.

Is exponential time-invariant?

First, let's define an exponential impulse as the input signal. Clearly, the system is not time-invariant: When the inputs of the system are time-shifted exponential impulses, the outputs of the system are not just time-shifted versions of each other. Hence, the system is not time-invariant, but it is time-variant.

What is eigenfunction in signals?

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.