Parallel LTI system

1. What is the impulse response of two LTI system connected in parallel?
2. What is meant by LTI system?
3. What is the impulse response of two LTI systems connected in series?
4. Is convolution a LTI system?

What is the impulse response of two LTI system connected in parallel?

The impulse response of the overall system represented by the two LTI systems that are interconnected in parallel is the sum of their individual impulse responses. Mathematically, the preceding result implies that convolution possesses the distributive property.

What is meant by LTI system?

In system analysis, among other fields of study, a linear time-invariant (LTI) system is a system that produces an output signal from any input signal subject to the constraints of linearity and time-invariance; these terms are briefly defined below.

What is the impulse response of two LTI systems connected in series?

Hence the impulse response of two LTI systems connected in cascade is the convolution of the individual impulse responses. The cascade connection is input-output equivalent to the single system represented by the impulse response h(t) as shown in Fig. 2.14(b).

Is convolution a LTI system?

Therefore, in signals and systems, the convolution is very important because it relates the input signal and the impulse response of the system to produce the output signal from the system. In other words, the convolution is used to express the input and output relationship of an LTI system.