October 2006
Intermediate to advanced
369 pages
8h 11m
English
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1.4. Properties of discrete-time systems
1.4.1. Invariant linear systems
The important features of a system are linearity, temporal shift invariance (or invariance in time) and stability.
A system represented by the operator T is termed linear if 
x1, x2 a1, a2 so we get:
A system is called time-invariant if the response to a delayed input of l samples is the delayed output of l samples; that is:
and this holds, whatever the input signal x(k) and the temporal shift l.
As well, a continuous linear system time-invariant system is always called a stationary (or homogenous) linear filter.
1.4.2. Impulse responses and convolution products
If the input of a system is the impulse unity δ(k), the output is called the impulse response of the system h(k), or:
Figure 1.9. Impulse response
A usual property of the impulse δ(k) helps us describe any discrete-time signal as the weighted sum of delayed ...
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