Please help with answering this question and please write clearly and explain clearly, thanks. (d) Now let's think about how we could cancel out the echo from a received signal y(t) andrecover the original signal f(t). We can actually construct a second LTI system to dothis:cancellation systemf(t)original echo systemαdelayT secondsIn the frequency domain, we will havey(t)h₂(t)g(t)G(w) = H₂(w)Y(w).If we want G(w) = F(w) (so that g(t) = f(t)), how should we choose H₂(w)?(e) Taking the inverse Fourier transform of H₂(w), we can find the impulse response of the"inverse" (or cancellation) system:h₂(t) = ???? 8(t) + ???? - 8(t – T).Fill in the blanks in the equation above.(f) We can write the input-output relationship of this inverse system as follows:g(t) = ???? - y(t) + ???? - y(t – T).Fill in the blanks in the equation above.(g) Draw a block diagram for the inverse system.(h) Finally, returning to the specific example from part (a) with a = 0.5 and T = 2, showthat if you feed the output y(t) from part (a) into the inverse system from part (g), youcorrectly recover the original signal f(t). Recall the echo system from the lecture notes in the section "Frequency responseof LTI systems: Example D." In this problem, we will consider a different model for howan echo might be generated in a received signal. Specifically, we consider the model below,where T> 0 is a delay and a € (0, 1) is an attenuation factor:f(t).0α1delayT seconds(a) As an example, suppose a = 0.5 and T = 2. Consider the input signal f(t) as shownbelow:f(t)y(t)Plot the resulting output signal y(t).(b) Let's return to thinking about a and T as generic parameters, not associating them withspecific values. In the time domain, we can write the input-output relationship of theecho system as follows:ty(t) = f(t) + ay(t-T).Taking the Fourier transform of both sides of this equation, and using the time delayproperty of the Fourier transform, we can writeY(w) = F(w) + ???? .Y (w).H(w) =Using your answer from part (b), find H(w).Fill in the blanks in the equation above.(c) Rearranging terms in the equation above, we can writeY(w) (1 - ????) = F(w).Dividing Y(w) by F(w), we obtain H(w), the frequency response of the system:Y(w)F(w)

“Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”.Given, The block diagram of the system is shown below,Part (a) - Consider,α=0.5T=2 The input signal is shown below, The resulting output signal is shown below,Part (b) - For the echo system,The input-output relationship is given as,yt=ft+αyt-TApplying fourier transform and time delay property,The equation becomes,Y(ω)=F(ω)+αe-jωTY(ω) Part (c) - From part b,The equation is,Y(ω)=F(ω)+αe-jωTY(ω)Now,Rearranging the above equation,Y(ω)=F(ω)+αe-jωTY(ω)Y(ω)-αe-jωTY(ω)=F(ω)Y(ω)1-αe-jωT=F(ω)Y(ω)F(ω)=11-αe-jωTWe know,Hω=Y(ω)F(ω)So,H(ω)=1[1-αe-jωT]