# Frequency Response of Cascade Composition

Consider the cascade of two LTI systems:

where the frequency response of *S*_{1}
is *H*_{1}
and the frequency response of *S*_{2}
is *H*_{2}.
The frequency response of the composition is *H*: *Reals* →
*Complex* such that for all ω
∈
*Reals*,

*H*(ω)
= *H*_{1}(ω)*H*_{2}(ω).

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