Problem 2 The periodic triangular wave shown below has Fourier series coefficients ak sin(kx/2)-kP,k≠0 k=0. Consider the LTI system with frequency response H(w) depicted below c (t) HOw) Ay 923-92-9191929 Determine values of A1, A2, A3, 1, Q2, and Q of the LTI filter H(u) such that y(t)=1-cos Problem 3 Consider a causal discrete-time LTI system whose input an] and output yInI are related by the following difference equation y]-yn-1]=rn]+2an-4 Find the Fourier series representation of the output y[n] when the input n=2+sin(Tn/4)-2 cos(Tn/2)Problem 2 The periodic triangular wave shown below has Fourier series coefficients ak. x(t) � �2 sin(k�/2)e−jk�/2 ⎧ , k =� 0 1 ak = j(k�)2 ⎧� 1 , k = 0. 2 · · · · · · −4 −2 0 2 4 t Consider the LTI system with frequency response H(j�) depicted below: H(j�) x(t) H( ) j� y(t) −�3 −�2 −�1 �1 �2 �3 � A1 A2 A3 Determine values of A1, A2, A3, �1, �2, and �3 of the LTI filter H(j�) such that ⎨ ⎩ 3� y(t) = 1 − cos t . 2 Problem 3 Consider a causal discrete-time LTI system whose input x[n] and output y[n] are related by the following difference equation: 1 y[n] − y[n − 1] = x[n] + 2x[n − 4] 4 Find the Fourier series representation of the output y[n] when the input is x[n] = 2 + sin(�n/4) − 2 cos(�n/2). 2