Howtosignalprocessing
- How can LTI systems be uniquely identified by their impulse response?
- What is a unit impulse response of an LTI system?
- What is the impulse response of two LTI systems connected in series?
- What would happen to the LTI system output when the input or the impulse response is a shifted impulse?
How can LTI systems be uniquely identified by their impulse response?
The impulse response h[n] uniquely describes the system… so we can identify the system by specifying its impulse response h[n]. Because impulse response h[n] is only defined for LTI systems, if you see a box with the symbol h[n] inside it you can assume that the system is an LTI system.
What is a unit impulse response of an LTI system?
The impulse response for an LTI system is the output, y ( t ) y(t) y(t), when the input is the unit impulse signal, σ ( t ) \sigma(t) σ(t). In other words, when x ( t ) = σ ( t ) , h ( t ) = y ( t ) .
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).
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.
