EECS20N: Signals and Systems

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Week 14

• Home
• Themes
• Modem
• Answer tone
• Identification
• Freq response
• Filtering
• Better filtering
• Cost
• IIR design
• Response
• Analytically
• Using Matlab
• Filter quality
• Filter design
• State machine

State Machine Model

Our Chebyshev filter design is given by the linear difference equation of the form

y(n) = −a₂ y(n-1) − a₃ y(n-2) + b₁ x(n) + b₂ x(n-1) + b₃ x(n-2).

We can interpret this difference equation as a state machine.

To get a state machine model, we need to define a state vector s, a matrix A, column vectors b and c and a real number d such that for all n,

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

y(n) = c^Ts(n) + dx(n)

A straightforward possibility for the state is

s(n) = [y(n-1), y(n-2), x(n-1), x(n-2)]^T.

In this case, we get

A = [-a₂, -a₃, b₂, b₃; 1,0,0,0; 0,0,0,0; 0,0,1,0]

b =[b₁, 0,1,0]^T

c^T = [-a₂, -a₃, b₂, b₃]

d = b₁

(using Matlab notation for the matrix). A more compact state machine description for this system is possible, but that is the subject of a followup course.