# Frequency Response - Continuous-Time

The continuous-time version starts with the convolution integral

*y*(

*t*) = ∫

_{ (− ∞ to ∞ )}

*x*(

*t*

*τ*

*)*

*h*(

*τ*)

*dτ*

Following the same steps as above, we find that the frequency response and impulse response of a continuous-time LTI system are related by

*H*(

*ω*) = ∫

_{ (− ∞ to ∞ )}

*h*(

*t*)

*e*

^{−iω t}*dt*

*H*(ω ) is called the **continuous-time
Fourier transform (CTFT)** of *h*(*t*), or more commonly, simply
the **Fourier transform (FT)**. We will study the FT in more detail
shortly, and will examine its relationship to the Fourier series. For now,
however, just notice that once again the impulse response fully defines
the frequency response, and in principle, if you know the impulse response,
you can calculate the frequency response.