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Week 6

• Infinite state
• Factoring
• Update
• Time
• Differential eqns
• Linear Functions
• LTI systems
• State response
• Output response
• Convolution

LTI Systems

Consider the 1-dimensional system given by: ∀ n ∈ Naturals₀ ,

s(n + 1) = as(n) + bx(n)

y(n) = cs(n) + dx(n)

where a, b, c, d are fixed real-valued constants. This is a particularly simple form of the nextState and output functions. A system of this form is called a linear, constant-coefficient difference equation (LCCDE) system.

If the initial state is zero, s(0) = 0, and if we interpret the index n to represent (discrete) time, then it is also called a linear time-invariant (LTI) system.