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Week 10

• FS coefficients
• Negative freq.
• Transfer function
• Filtering
• Filtering sounds
• Filtering images
• Cascade
• Freq response
• Commutativity
• Feedback
• Freq response

Feedback Systems

Consider the feedback composition with two LTI systems:

The circle adds z to x. The signals are related by

y = S₁(u) = S₁(x + z ) = S₁(x) + S₁(z)

since S₁ is linear. Since z = S₂(y),

y = S₁(x) + S₁(S₂(y))

It is possible to use this to show that this system is LTI (see the text).