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.

Start Free Trial

No credit card required