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- What is the relationship between input and output of an LTI system?
- What would happen to the LTI system output when the input or the impulse response is a shifted impulse?
- What are the characteristic of LTI system?
- What is the impulse response of two LTI systems connected in series?
What is the relationship between input and output of an LTI system?
A linear time-invariant (LTI) system can be represented by its impulse response (Figure 10.6). More specifically, if X(t) is the input signal to the system, the output, Y(t), can be written as Y(t)=∫∞−∞h(α)X(t−α)dα=∫∞−∞X(α)h(t−α)dα.
What would happen to the LTI system output when the input or the impulse response is a shifted impulse?
In general, however, any relationship which is linear and time-invariant, with unit impulse as input qualifies as a valid impulse response for an LTI system. Because such systems are time-invariant, if the impulse is shifted to a new location, the output is simply a shifted version of the impulse response.
What are the characteristic of LTI system?
In addition to linear and time-invariant, LTI systems are also memory systems, invertible, casual, real, and stable. That means they have memory, they can be inverted, they depend only on current and past events, they have fully real inputs and outputs, and they produce bounded output for bounded input.
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).
