Question

Consider a continuous-time, linear time-invariant system with unit impulse response function given by

h(t)=δ(t+2)+δ(t−2)

(a) Find the frequency response of the system. Simplify as much as you can

Answer 1

The frequency response of the system is 2cos(2ω).

Step-by-step explanation:

The frequency response of a linear time-invariant system can be found by taking the Fourier transform of its impulse response function. In this case, the impulse response function of the system is given by h(t) = δ(t+2) + δ(t-2), where δ is the Dirac delta function.

Taking the Fourier transform of h(t) gives us:

H(ω) = e-j2ω + ej2ω

This can be simplified as:

H(ω) = 2cos(2ω)