Question

Consider an LTI system with an impulse response, h(t) = −2(). Find the Fourier series representation of the output y(t), which is a resultant of the system input x(t).

a) y(t)=−2X(jω)
b) y(t)=−2jX(jω)
c) y(t)=2X(jω)
d) y(t)=2jX(jω)

Answer 1

The Fourier series representation of the output y(t) of an LTI system with an impulse response h(t) = -2δ(t) is given by y(t) = -2X(jω), where X(jω) is the Fourier transform of the system input x(t).

Step-by-step explanation:

The Fourier series representation of the output y(t) of an LTI system with an impulse response h(t) = -2δ(t) is given by y(t) = -2X(jω), where X(jω) is the Fourier transform of the system input x(t).

The Fourier transform of x(t) represents the frequency content of the input signal, and multiplying it by -2 gives us the frequency content of the output signal.

Therefore, the correct answer is option a) y(t) = -2X(jω).