EECS20N: Signals and Systems

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: RealsComplex 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).