The frequency response of an LTI filter is given by the formula H(e^{jw})=(1+e^{-j2w})(1- \frac{1}{2}e^{-jw}+\frac{1}{4}e^{-j2w}) a) Write the difference equation that gives the relation between the input x[n] and the output y[n]. b) Determine the impulse response of this LTI filter. c) If the input is of the form x[n]=Ae^{j\phi}e^{jwn} , for what values of –\pi<\omega \leq \pi is y[n]=0 for all n?