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Week 10

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

Frequency Response of Cascade Composition

Consider the cascade of two LTI systems:

where the frequency response of S₁ is H₁ and the frequency response of S₂ is H₂. The frequency response of the composition is H: Reals → Complex such that for all ω ∈ Reals,

H(ω) = H₁(ω)H₂(ω).

This is obvious if you consider what happens when x(t) = exp(iω t).