GATE 2024 Signals & Systems Foundation Quiz 94

Consider the following system

The system is

Let x(t) and y(t) are the input and output of an LTI system described as

The system is

The frequency response H(jω) of a continuous-time filter is shown below:

If the input to this system is x(t) = 1, The output will be at ω = 0

The inverse Fourier transform of is

Consider the signal x(t)= r(t)-2r(t+1)+3r(t-2)-4r(t-3)

Find the value of