This document discusses different types of systems including linear time-invariant systems, discrete time systems, and causal systems. Linear time-invariant systems have outputs that are scaled and shifted versions of the input. Discrete time systems operate on discrete time signals represented by sequences of numbers. Causal systems have outputs that depend only on current and prior input values, not on future input values. The document provides examples of each type of system to illustrate their properties.

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3. LTI tizimlari
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5. Chiziqli tizim
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• 𝑦1(𝑛) 𝑥1(𝑛)
• 𝑦2(𝑛) 𝑥2(𝑛)

6. Diskret vaqt tizim
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7. Chiziqli tizim
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Example: A digital amplifier is represented by
𝑦(𝑛) = 10𝑥(𝑛), the input is multiplied by 10 to
generate the output.

8. Chiziqli tizim
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9. Chiziqli tizim
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10. Vaqt o’zgarmas tizim
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11. Vaqt o’zgarmas tizim
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12. Vaqt o’zgarmas tizim
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Example: Determine whether the linear system y(𝑛) =
2𝑥(𝑛) − 5 is time invariant.

13. Time-Invariant System
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14. Sababli tizim (Causal System)
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Example: Determine whether the following systems are causal or
not.
Solution
1) Causal
2) Non-causal
Sababli tizim (Causal System)

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