System Properties | Short Notes for Electrical Engineering - Electrical Engineering (EE) PDF Download

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Linear time-invariant system and convolution integral: 
LTI Systems: They are the systems that are linear and time invariant in nature.
Convolution: if h[n] is the impulse response of the system then if x[n] is the input
and y[n] is the output then,
y[n] = x[n] * h[n] // convolution
//convolution sum or superposition sum
Properties of LTI system:
1. Commutative: x1[n] * x2[n] = x2[n] * x1[n]
2. Distributive: x[n] * (h1[n] + h2[n]) = x[n] * h1[n] + x[n] * h2[n]
3. Associative: x[n] * (h1[n] * h2[n]) = (x[n] * h1[n]) * h2[n]
4. LTI system with and without memory
5. Invertibility and inverse system
6. Causality of LTI system
7. Stability of LTI system
8. Unit step response of LTI system: By convolution d[n] = u[n] * h[n] there
for h[n] in discrete time LTI system is h[n] = d[n]. d[n-1]
Causal LTI system described by:
1. Linear constant coefficient differential equation: dy(t)/dt + 2y(t) = x(t)
2. Linear constant coefficient difference equation
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Linear time-invariant system and convolution integral: 
LTI Systems: They are the systems that are linear and time invariant in nature.
Convolution: if h[n] is the impulse response of the system then if x[n] is the input
and y[n] is the output then,
y[n] = x[n] * h[n] // convolution
//convolution sum or superposition sum
Properties of LTI system:
1. Commutative: x1[n] * x2[n] = x2[n] * x1[n]
2. Distributive: x[n] * (h1[n] + h2[n]) = x[n] * h1[n] + x[n] * h2[n]
3. Associative: x[n] * (h1[n] * h2[n]) = (x[n] * h1[n]) * h2[n]
4. LTI system with and without memory
5. Invertibility and inverse system
6. Causality of LTI system
7. Stability of LTI system
8. Unit step response of LTI system: By convolution d[n] = u[n] * h[n] there
for h[n] in discrete time LTI system is h[n] = d[n]. d[n-1]
Causal LTI system described by:
1. Linear constant coefficient differential equation: dy(t)/dt + 2y(t) = x(t)
2. Linear constant coefficient difference equation