(Solved): Exercise 8: A linear time-invariant system is described by the difference equation y[n]=2x[n]+4x[n ...

Exercise 8: A linear time-invariant system is described by the difference equation $$y[n]=2x[n]+4x[n?1]?3x[n?2]+3x[n?3]?4x[n?4]?2x[n?5]$$ a) Write a simple formula for the magnitude of the frequency response $$\left|H\left(e^{j\widehat{?}}\right)\right|$$. Take advantage of the odd symmetry of the filter coefficients (i.e., $$b_0=?b_5,b_1=$$ $$?b_4$$, etc.) to express your answer in terms of real-valued functions only. b) Derive a simple formula for the phase of the frequency response $$?H\left(e^{j\widehat{?}}\right)$$. c) Determine the impulse response $$h[n]$$, and plot $$h[n]$$ as a function of $$n$$.