Howtosignalprocessing
- Is exponential function causal?
- What is the condition for causal LTI system?
- Can a continuous time LTI system change the frequency of a complex exponential signal?
- Is exponential time-invariant?
Is exponential function causal?
back to bt. We will prove the amazing fact that bt must be causal too. Each term in the infinite series corresponds to a causal response, so the sum, bt, is causal.
What is the condition for causal LTI system?
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.
Can a continuous time LTI system change the frequency of a complex exponential signal?
The response of LTI systems to complex exponentials
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.
