EECS20N: Signals and Systems

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.