Are all exponential functions eigensignals of LTI systems?

1. Which of the following can be the eigen signal of an LTI system?
2. What are eigenfunctions of LTI systems?
3. Is exponential time-invariant?
4. Are all LTI systems causal?

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 are eigenfunctions of LTI systems?

Complex exponential signals are known as eigenfunctions of the LTI systems, as the system output to these inputs equals the input multiplied by a constant factor. Both amplitude and phase may change, but the frequency does not change.

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.

Are all LTI systems causal?

LTI System Properties

An LTI system is called causal if the output signal value at any time t depends only on input signal values for times less than t. It is easy to see from the convolution integral that if h(t) = 0 for t < 0, then the system is causal.