Figure 3.29 shows a system having impulse response. The system function H(ω) of the system is the Fourier transform of h(t).
Fig. 3.29 Impulse response
In Fig. 3.29, the input is x(t) and its output y(t) can be obtained by convolving x(t) with h(t).
We can write Y(ω) = X(ω) * H(ω)
i.e., y(t) = F−1[X(ω) * H(ω)]
where X(ω) is the Fourier transform of x(t), Y(ω) is the Fourier transform of y(t) and H(ω) is the system function.